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4.6: Summary and further reading

4.6: Summary and further reading


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This chapter introduced three important ideas in category theory: profunctors, cate- gorification, and monoidal categories. Let’s talk about them in turn.

Profunctors generalize binary relations. In particular, we saw that the idea of pro- functor over a monoidal preorder gave us the additional power necessary to formalize the idea of a feasibility relation between resource preorders. The idea of a feasibility re- lation is due to Andrea Censi; he called them monotone codesign problems. The basic idea is explained in [Cen15], where he also gives a programming language to specify and solve codesign problems. In [Cen17], Censi further discusses how to use estimation to make solving codesign problems computationally efficient.

We also saw profunctors over the preorder Cost, and how to think of these as bridges between Lawvere metric space. We referred earlier to Lawvere’s paper [Law73]; plenty more on Cost-profunctors can be found there.

Profunctors, however are vastly more general than the two examples we have dis- cussed; V-profunctors can be defined not only when V is a preorder, but for any symmetric monoidal category. A delightful, detailed exposition of profunctors and related concepts such as equipments, companions and conjoints, symmetric monoidal bicategories can be found in [Shu08; Shu10].

We have not defined symmetric monoidal bicategories, but you would be correct if you guessed this is a sort of categorification of symmetric monoidal categories. Baez and Dolan tell the subtle story of categorifying categories to get ever higher categories in [BD98]. Crane and Yetter give a number of examples of categorification in [CY96].

Finally, we talked about monoidal categories and compact closed categories. Monoidal categories are a classic, central topic in category theory, and a quick introduction can be found in [Mac98]. Wiring diagrams play a huge role in this book and in applied category theory in general; while informally used for years, these were first formalized in the case of monoidal categories. You can find the details here [JS93; JSV96].

Compact closed categories are a special type of structured monoidal category; there are many others. For a broad introduction to the different flavors of monoidal category, detailed through their various styles of wiring diagram, see [Sel10].


4.6 Problem-Solving Strategies

Success in problem solving is obviously necessary to understand and apply physical principles, not to mention the more immediate need of passing exams. The basics of problem solving, presented earlier in this text, are followed here, but specific strategies useful in applying Newton’s laws of motion are emphasized. These techniques also reinforce concepts that are useful in many other areas of physics. Many problem-solving strategies are stated outright in the worked examples, and so the following techniques should reinforce skills you have already begun to develop.

Problem-Solving Strategy for Newton’s Laws of Motion

Step 1. As usual, it is first necessary to identify the physical principles involved. Once it is determined that Newton’s laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation. Such a sketch is shown in Figure 4.21(a). Then, as in Figure 4.21(b), use arrows to represent all forces, label them carefully, and make their lengths and directions correspond to the forces they represent (whenever sufficient information exists).

Step 2. Identify what needs to be determined and what is known or can be inferred from the problem as stated. That is, make a list of knowns and unknowns. Then carefully determine the system of interest. This decision is a crucial step, since Newton’s second law involves only external forces. Once the system of interest has been identified, it becomes possible to determine which forces are external and which are internal, a necessary step to employ Newton’s second law. (See Figure 4.21(c).) Newton’s third law may be used to identify whether forces are exerted between components of a system (internal) or between the system and something outside (external). As illustrated earlier in this chapter, the system of interest depends on what question we need to answer. This choice becomes easier with practice, eventually developing into an almost unconscious process. Skill in clearly defining systems will be beneficial in later chapters as well.

A diagram showing the system of interest and all of the external forces is called a free-body diagram . Only forces are shown on free-body diagrams, not acceleration or velocity. We have drawn several of these in worked examples. Figure 4.21(c) shows a free-body diagram for the system of interest. Note that no internal forces are shown in a free-body diagram.

Step 3. Once a free-body diagram is drawn, Newton’s second law can be applied to solve the problem. This is done in Figure 4.21(d) for a particular situation. In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples. If the problem is one-dimensional—that is, if all forces are parallel—then they add like scalars. If the problem is two-dimensional, then it must be broken down into a pair of one-dimensional problems. This is done by projecting the force vectors onto a set of axes chosen for convenience. As seen in previous examples, the choice of axes can simplify the problem. For example, when an incline is involved, a set of axes with one axis parallel to the incline and one perpendicular to it is most convenient. It is almost always convenient to make one axis parallel to the direction of motion, if this is known.

Applying Newton’s Second Law

Before you write net force equations, it is critical to determine whether the system is accelerating in a particular direction. If the acceleration is zero in a particular direction, then the net force is zero in that direction. Similarly, if the acceleration is nonzero in a particular direction, then the net force is described by the equation: F net = ma F net = ma size 12 > = ital "ma"> <> .

For example, if the system is accelerating in the horizontal direction, but it is not accelerating in the vertical direction, then you will have the following conclusions:

You will need this information in order to determine unknown forces acting in a system.

Step 4. As always, check the solution to see whether it is reasonable. In some cases, this is obvious. For example, it is reasonable to find that friction causes an object to slide down an incline more slowly than when no friction exists. In practice, intuition develops gradually through problem solving, and with experience it becomes progressively easier to judge whether an answer is reasonable. Another way to check your solution is to check the units. If you are solving for force and end up with units of m/s, then you have made a mistake.

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    Lesson 2: Never trust Mr. Market.

    Graham’s most famous analogy is the one of Mr. Market, where he pictures the entire stock market as a single person.

    If you imagine Mr. Market showing up on your doorstep every day, quoting you different prices for various stocks, what would you do?

    According to Benjamin Graham, you’d be best off ignoring him altogether, day in and day out. Sometimes the prices he’d tell you would seem suspiciously cheap, sometimes astronomically high.

    That’s because Mr. Market is not very clever, totally unpredictable and suffers from serious mood swings.

    For example about a month before a new iPhone is released, stocks rally while people cue in line in front of the Apple store. But when the new phone is not exactly as expected, stocks can plummet the very next day.

    As humans we’re so good at recognizing patterns, that we’re trying to find them even where none exist. That’s why we naturally a stock price that’s been going up for 10 days must go up further – which is of course not true.

    If you want to be an intelligent investor, rely on your own research and ignore the market altogether.


    1. What Is Biodiversity?.

    2. Biodiversity Through Time:.

    A Brief History Of Biodiversity.

    How Many Extant Species Are There?.

    3. Mapping Biodiversity:.

    Extremes Of High And Low Diversity.

    Gradients In Biodiversity.

    4. Does Biodiversity Matter?.

    Populations, Individuals And Genetic Diversity.

    The Scale Of The Human Enterprise.

    6. Maintaining Biodiversity:.

    Objectives Of The Convention.

    General Measures For Conservation And Sustainable Use.

    Identification And Monitoring.

    Sustainable Use Of Components Of Biological Diversity.

    Reponses To The Convention.


    Converting Grams to Moles of an Element and Vice Versa

    We can also convert back and forth between grams of an element and moles. The conversion factor for this is the molar mass of the substance. The molar mass is the ratio giving the number of grams for each one mole of the substance. This ratio is easily found by referring to the atomic mass of the element using the periodic table. This ratio has units of grams per mole or ( ext).

    Conversions like this are possible for any substance, as long as the proper atomic mass, formula mass, or molar mass is known (or can be determined) and expressed in grams per mole. Figure 6.4.1 illustrates what conversion factor is needed and two examples are given below.

    Figure (PageIndex<1>): A Simple Flowchart for Converting Between Mass and Moles of an Element.

    Example (PageIndex<2>): Chromium

    Chromium metal is used for decorative electroplating of car bumpers and other surfaces. Find the mass of 0.560 moles of chromium.

    Prepare a concept map and use the proper conversion factor.

    Since the desired amount was slightly more than one half of a mole, the mass should be slightly more than one half of the molar mass. The answer has three significant figures because of the (0.560 : ext)

    Example (PageIndex<3>): Silicon

    How many moles are in 107.6g of Si?

    Prepare a concept map and use the proper conversion factor.

    Since 1 mol of Si is 28.09g, 107.6 should be about 4 moles.


    Giving notice is the first step in the eviction process. The notice required in Georgia for violations of a lease agreement in situations NOT involving late payment of the rent is a 3 Day Notice.

    Who: Give this to the tenant who has clearly violated a major covenant of the lease. Note that this form is not for tenants late or behind on the rent. In that instance, you would need to file a 3 Day Notice to Pay or Quit, which is different.

      All covenants should be spelled out in the lease agreement and might include:
  • Abandoning the property (moving out before the lease is up)
  • Having too many people staying at the property who aren’t on the lease
  • Making unauthorized changes to the property (remodeling, etc.)
  • When: The notice must be served to the tenant before filing a dispossessory warrant with the magistrate court in the county where the rental property is located. Once the notice has been served, the tenant has three days to make the needed changes or to move out. If they do neither, your next step is to file for an eviction in court. At the hearing, you’ll present your case (and the tenant will present his or her case if they choose to appear). If you’re granted permission, you’ll then schedule an actual eviction date with the county sheriff.

      How to Serve the Notice: You have several options for serving the 3 Day Notice to Quit. These include the following:
    • Certified Mail (make sure you request a return receipt)
    • Regular mail
    • Hand deliver (make sure you get the tenant’s signature at the bottom of the Notice)
    • Leaving a copy at the premises
    • Posted copy at the premises (post it somewhere very visible, such as the front door)

    Note that if you choose to mail the notice, an additional three days are added to the period (to give the postal office time to deliver the notice to your tenant).

    Tips and Tricks for Landlords: Make sure that you are familiar with the language of the lease being used before you attempt to serve the tenant with a 3 Day Notice to Quit. Also, understand that DIY evictions are illegal – you can’t change the locks, intimidate the tenant, or remove their belongings from the property without following the law. If you attempt to do this, you may find yourself on the other end of a lawsuit in court.


    Contents

    Creation of the text Edit

    According to Ban Gu, writing in the Book of Han, the Analects originated as individual records kept by Confucius's disciples of conversations between the Master and them, which were then collected and jointly edited by the disciples after Confucius's death in 479 BC. The work is therefore titled Lunyu meaning "edited conversations" or "selected speeches" (i.e. analects). [2] [3] This broadly forms the traditional account of the genesis of the work accepted by later generations of scholars, for example the Song dynasty neo-Confucian scholar Zhu Xi stated that Analects is the records of Confucius's first- and second-generation pupils. [4]

    This traditional view has been challenged by Chinese, Japanese, and Western scholars. The Qing dynasty philologist Cui Shu argued on linguistic ground that the last five books were produced much later than the rest of the work. Itō Jinsai claimed that, because of differences he saw in patterns of language and content in the Analects, a distinction in authorship should be made between the "upper Analects" (Books 1–10) and "lower Analects" (Books 11–20). Arthur Waley speculated that Books 3–9 represent the earliest parts of the book. E. Bruce Brooks and A. Taeko Brooks reviewed previous theories of the chapters' creation and produced a "four stratum theory" of the text's creation. [1] [5] Many modern scholars now believe that the work was compiled over a period of around two hundred years, some time during the Warring States period (476–221 BC), with some questioning the authenticity of some of the sayings. [6] [7] Because no texts dated earlier than about 50 BC have been discovered, and because the Analects was not referred to by name in any existing source before the early Han dynasty, some scholars have proposed dates as late as 140 BC for the text's compilation. [8]

    Regardless of how early the text of the Analects existed, most Analects scholars believe that by the early Han dynasty (206 BC–220 AD) the book was widely known and transmitted throughout China in a mostly complete form, and that the book acquired its final, complete form during the Han dynasty. However, Han dynasty writer Wang Chong claimed that all copies of the Analects that existed during the Han dynasty were incomplete and formed only a part of a much larger work. [9] This is supported by the fact that a larger collection of Confucius's teachings did exist in the Warring States period than has been preserved directly in the Analects: 75% of Confucius's sayings cited by his second-generation student, Mencius, do not exist in the received text of the Analects. [10]

    Versions Edit

    According to the Han dynasty scholar Liu Xiang, there were two versions of the Analects that existed at the beginning of the Han dynasty: the "Lu version" and the "Qi version". The Lu version contained twenty chapters, and the Qi version contained twenty-two chapters, including two chapters not found in the Lu version. Of the twenty chapters that both versions had in common, the Lu version had more passages. Each version had its own masters, schools, and transmitters. [11]

    In the reign of Emperor Jing of Han (r. 157–141 BC), a third version (the "Old Text" version) was discovered hidden in a wall of the home then believed to be Confucius's when the home was in the process of being destroyed by King Gong of Lu (r. 153–128 BC) in order to expand the king's palace. The new version did not contain the two extra chapters found in the Qi version, but it split one chapter found in the Lu and Qi versions in two, so it had twenty-one chapters, and the order of the chapters was different. [11]

    The old text version got its name because it was written in characters not used since the earlier Warring States period (i.e. before 221 BC), when it was assumed to have been hidden. [12] According to the Han dynasty scholar Huan Tan, the old text version had four hundred characters different from the Lu version (from which the received text of the Analects is mostly based), and it seriously differed from the Lu version in twenty-seven places. Of these twenty-seven differences, the received text only agrees with the old text version in two places. [13]

    Over a century later, the tutor of the Analects to Emperor Cheng of Han, Zhang Yu (d. 5 BC), synthesized the Lu and Qi versions by taking the Lu version as authoritative and selectively adding sections from the Qi version, and produced a composite text of the Analects known as the "Zhang Hou Lun". This text was recognized by Zhang Yu's contemporaries and by subsequent Han scholars as superior to either individual version, and is the text that is recognized as the Analects today. [11] The Qi version was lost for about 1800 years but re-found during the excavation of the tomb of Marquis of Haihun in 2011. [14] No complete copies of either the Lu version or the old text version of the Analects exist today, [12] though fragments of the old text version were discovered at Dunhuang. [13]

    Before the late twentieth century the oldest existing copy of the Analects known to scholars was found in the "Stone Classics of the Xinping Era", a copy of the Confucian classics written in stone in the old Eastern Han dynasty capital of Luoyang around 175 AD. Archaeologists have since discovered two handwritten copies of the Analects that were written around 50 BC, during the Western Han dynasty. They are known as the "Dingzhou Analects", and the "Pyongyang Analects", after the location of the tombs in which they were found. The Dingzhou Analects was discovered in 1973, but no transcription of its contents was published until 1997. The Pyongyang Analects was discovered in 1992. Academic access to the Pyongyang Analects has been highly restricted, and no academic study on it was published until 2009. [15]

    The Dingzhou Analects was damaged in a fire shortly after it was entombed in the Han dynasty. It was further damaged in an earthquake shortly after it was recovered, and the surviving text is just under half the size of the received text of the Analects. Of the sections that survive, the Dingzhou Analects is shorter than the received Analects, implying that the text of the Analects was still in the process of expansion when the Dingzhou Analects was entombed. There was evidence that "additions" may have been made to the manuscript after it had been completed, indicating that the writer may have become aware of at least one other version of the Analects and included "extra" material for the sake of completeness. [16]

    The content of the Pyongyang Analects is similar to the Dingzhou Analects. Because of the secrecy and isolationism of the North Korean government, only a very cursory study of it has been made available to international scholars, and its contents are not completely known outside of North Korea. Scholars do not agree about whether either the Dingzhou Analects or the Pyongyang Analects represent the Lu version, the Qi version, the old text version, or a different version that was independent of these three traditions. [16]

    Importance within Confucianism Edit

    During most of the Han period the Analects was not considered one of the principal texts of Confucianism. During the reign of Han Wudi (141–87 BC), when the Chinese government began promoting Confucian studies, only the Five Classics were considered by the government to be canonical (jing). They were considered Confucian because Confucius was assumed to have partially written, edited, and/or transmitted them. The Analects was considered secondary as it was thought to be merely a collection of Confucius's oral "commentary" (zhuan) on the Five Classics. [17]

    The political importance and popularity of Confucius and Confucianism grew throughout the Han dynasty, and by the Eastern Han the Analects was widely read by schoolchildren and anyone aspiring to literacy, and often read before the Five Classics themselves. During the Eastern Han, the heir apparent was provided a tutor specifically to teach him the Analects. The growing importance of the Analects was recognized when the Five Classics was expanded to the "Seven Classics": the Five Classics plus the Analects and the Classic of Filial Piety, and its status as one of the central texts of Confucianism continued to grow until the late Song dynasty (960–1279), when it was identified and promoted as one of the Four Books by Zhu Xi and generally accepted as being more insightful than the older Five Classics. [18]

    The writing style of the Analects also inspired future Confucian writers. For example, Sui Dynasty writer Wang Tong's 中说 (Explanation of the Mean) [19] was purposely written to emulate the style of the Analects, a practice praised by Ming Dynasty philosopher Wang Yangming. [20]

    Commentaries Edit

    Since the Han dynasty, Chinese readers have interpreted the Analects by reading scholars' commentaries on the book. There have been many commentaries on the Analects since the Han dynasty, but the two which have been most influential have been the Collected Explanations of the Analects (Lunyu Jijie) by He Yan (c. 195–249) and several colleagues, and the Collected Commentaries of the Analects (Lunyu Jizhu) by Zhu Xi (1130–1200). In his work, He Yan collected, selected, summarized, and rationalized what he believed to be the most insightful of all preceding commentaries on the Analects which had been produced by earlier Han and Wei dynasty (220–265 AD) scholars. [21]

    He Yan's personal interpretation of the Lunyu was guided by his belief that Daoism and Confucianism complemented each other, so that by studying both in a correct manner a scholar could arrive at a single, unified truth. Arguing for the ultimate compatibility of Daoist and Confucian teachings, he argued that "Laozi [in fact] was in agreement with the Sage" (sic). The Explanations was written in 248 AD, was quickly recognized as authoritative, and remained the standard guide to interpreting the Analects for nearly 1,000 years, until the early Yuan dynasty (1271–1368). It is the oldest complete commentary on the Analects that still exists. [21]

    He Yan's commentary was eventually displaced as the definitive, standard commentary by Zhu Xi's commentary. Zhu Xi's work also brought together the commentaries of earlier scholars (mostly from the Song dynasty), along with his own interpretations. Zhu's work took part in the context of a period of renewed interest in Confucian studies, in which Chinese scholars were interested in producing a single "correct" intellectual orthodoxy that would "save" Chinese traditions and protect them from foreign influences, and in which scholars were increasingly interested in metaphysical speculation. [22]

    In his commentary Zhu made a great effort to interpret the Analects by using theories elaborated in the other Four Books, something that He Yan had not done. Zhu attempted to give an added coherence and unity to the message of the Analects, demonstrating that the individual books of the Confucian canon gave meaning to the whole, just as the whole of the canon gave meaning to its parts. In his preface, Zhu Xi stated, "[T]he Analects and the Mencius are the most important works for students pursuing the Way [. ] The words of the Analects are all inclusive what they teach is nothing but the essentials of preserving the mind and cultivating [one's] nature." [23]

    From the first publication of the Commentaries, Zhu continued to refine his interpretation for the last thirty years of his life. In the fourteenth century, the Chinese government endorsed Zhu's commentary. Until 1905 it was read and memorized along with the Analects by all Chinese aspiring to literacy and employment as government officials. [23]

    Very few reliable sources about Confucius exist besides that of the Analects. The principal biography available to historians is included in Sima Qian's Shiji, but because the Shiji contains a large amount of (possibly legendary) material not confirmed by extant sources, the biographical material on Confucius found in the Analects makes the Analects arguably the most reliable source of biographical information about Confucius. [24] Confucius viewed himself as a "transmitter" of social and political traditions originating in the early Zhou dynasty (c. 1000–800 BC), and claimed not to have originated anything (Analects 7.1), but Confucius's social and political ideals were not popular in his time. [25]

    Social philosophy Edit

    Confucius' discussions on the nature of the supernatural (Analects 3.12 6.20 11.11) indicate his belief that while "ghosts" and "spirits" should be respected, they are best kept at a distance. Instead human beings should base their values and social ideals on moral philosophy, tradition, and a natural love for others. Confucius' social philosophy largely depended on the cultivation of ren by every individual in a community. [25]

    Later Confucian philosophers explained ren as the quality of having a kind manner, similar to the English words "humane", "altruistic", or "benevolent", but, of the sixty instances in which Confucius discusses ren in the Analects, very few have these later meanings. Confucius instead used the term ren to describe an extremely general and all-encompassing state of virtue, one which no living person had attained completely. (This use of the term ren is peculiar to the Analects.) [26]

    Throughout the Analects, Confucius's students frequently request that Confucius define ren and give examples of people who embody it, but Confucius generally responds indirectly to his students' questions, instead offering illustrations and examples of behaviours that are associated with ren and explaining how a person could achieve it. According to Confucius, a person with a well-cultivated sense of ren would speak carefully and modestly (Analects 12.3) be resolute and firm (Analects 12.20), courageous (Analects 14.4), free from worry, unhappiness, and insecurity (Analects 9.28 6.21) moderate their desires and return to propriety (Analects 12.1) be respectful, tolerant, diligent, trustworthy and kind (Analects 17.6) and love others (Analects 12.22). Confucius recognized his followers' disappointment that he would not give them a more comprehensive definition of ren, but assured them that he was sharing all that he could (Analects 7.24). [27]

    To Confucius, the cultivation of ren involved depreciating oneself through modesty while avoiding artful speech and ingratiating manners that would create a false impression of one's own character (Analects 1.3). Confucius said that those who had cultivated ren could be distinguished by their being "simple in manner and slow of speech." He believed that people could cultivate their sense of ren through exercising the inverted Golden Rule: "Do not do to others what you would not like done to yourself" "a man with ren, desiring to establish himself, helps others establish themselves desiring to succeed himself, helps others to succeed" (Analects 12.2 6.28). [25]

    Confucius taught that the ability of people to imagine and project themselves into the places of others was a crucial quality for the pursuit of moral self-cultivation (Analects 4.15 see also 5.12 6.30 15.24). [28] Confucius regarded the exercise of devotion to one's parents and older siblings as the simplest, most basic way to cultivate ren. (Analects 1.2). [25]

    Confucius believed that ren could best be cultivated by those who had already learned self-discipline, and that self-discipline was best learned by practicing and cultivating one's understanding of li: rituals and forms of propriety through which people demonstrate their respect for others and their responsible roles in society (Analects 3.3). Confucius said that one's understanding of li should inform everything that one says and does (Analects 12.1). He believed that subjecting oneself to li did not mean suppressing one's desires, but learning to reconcile them with the needs of one's family and broader community. [25]

    By leading individuals to express their desires within the context of social responsibility, Confucius and his followers taught that the public cultivation of li was the basis of a well-ordered society (Analects 2.3). [25] Confucius taught his students that an important aspect of li was observing the practical social differences that exist between people in daily life. In Confucian philosophy these "five relationships" include: ruler to ruled father to son husband to wife elder brother to younger brother and friend to friend. [25]

    Ren and li have a special relationship in the Analects: li manages one's relationship with one's family and close community, while ren is practiced broadly and informs one's interactions with all people. Confucius did not believe that ethical self-cultivation meant unquestioned loyalty to an evil ruler. He argued that the demands of ren and li meant that rulers could oppress their subjects only at their own peril: "You may rob the Three Armies of their commander, but you cannot deprive the humblest peasant of his opinion" (Analects 9.26). Confucius said that a morally well-cultivated individual would regard his devotion to loving others as a mission for which he would be willing to die (Analects 15.8). [25]

    Political philosophy Edit

    Confucius' political beliefs were rooted in his belief that a good ruler would be self-disciplined, would govern his subjects through education and by his own example, and would seek to correct his subjects with love and concern rather than punishment and coercion. "If the people be led by laws, and uniformity among them be sought by punishments, they will try to escape punishment and have no sense of shame. If they are led by virtue, and uniformity sought among them through the practice of ritual propriety, they will possess a sense of shame and come to you of their own accord" (Analects 2.3 see also 13.6). Confucius' political theories were directly contradictory to the Legalistic political orientations of China's rulers, and he failed to popularize his ideals among China's leaders within his own lifetime. [29]

    Confucius believed that the social chaos of his time was largely due to China's ruling elite aspiring to, and claiming, titles of which they were unworthy. When the ruler of the large state of Qi asked Confucius about the principles of good government, Confucius responded: "Good government consists in the ruler being a ruler, the minister being a minister, the father being a father, and the son being a son" (Analects 12.11).

    The analysis of the need to raise officials' behavior to reflect the way that they identify and describe themselves is known as the rectification of names, and he stated that the rectification of names should be the first responsibility of a ruler upon taking office (Analects 13.3). Confucius believed that, because the ruler was the model for all who were under him in society, the rectification of names had to begin with the ruler, and that afterwards others would change to imitate him (Analects 12.19). [29]

    Confucius judged a good ruler by his possession of de ("virtue"): a sort of moral force that allows those in power to rule and gain the loyalty of others without the need for physical coercion (Analects 2.1). Confucius said that one of the most important ways that a ruler cultivates his sense of de is through a devotion to the correct practices of li. Examples of rituals identified by Confucius as important to cultivate a ruler's de include: sacrificial rites held at ancestral temples to express thankfulness and humility ceremonies of enfeoffment, toasting, and gift exchanges that bound nobility in complex hierarchical relationships of obligation and indebtedness and, acts of formal politeness and decorum (i.e. bowing and yielding) that identify the performers as morally well-cultivated. [29]

    Education Edit

    The importance of education and study is a fundamental theme of the Analects. For Confucius, a good student respects and learns from the words and deeds of his teacher, and a good teacher is someone older who is familiar with the ways of the past and the practices of antiquity (Analects 7.22). Confucius emphasized the need to find balance between formal study and intuitive self-reflection (Analects 2.15). When teaching he is never cited in the Analects as lecturing at length about any subject, but instead challenges his students to discover the truth through asking direct questions, citing passages from the classics, and using analogies (Analects 7.8). [30] He sometimes required his students to demonstrate their understanding of subjects by making intuitive conceptual leaps before accepting their understanding and discussing those subjects at greater levels of depth. (Analects 3.8) [31]

    His primary goal in educating his students was to produce ethically well-cultivated men who would carry themselves with gravity, speak correctly, and demonstrate consummate integrity in all things (Analects 12.11 see also 13.3). He was willing to teach anyone regardless of social class, as long as they were sincere, eager, and tireless to learn (Analects 7.7 15.38). He is traditionally credited with teaching three thousand students, though only seventy are said to have mastered what he taught. He taught practical skills, but regarded moral self-cultivation as his most important subject. [30]

    Chapters Edit

    The traditional titles given to each chapter are mostly an initial two or three incipits. In some cases a title may indicate a central theme of a chapter, but it is inappropriate to regard a title as a description or generalization of the content of a chapter. Chapters in the Analects are grouped by individual themes, but the chapters are not arranged in a way as to carry a continuous stream of thoughts or ideas. The themes of adjacent chapters are completely unrelated to each other. Central themes recur repeatedly in different chapters, sometimes in exactly the same wording and sometimes with small variations.

    Chapter 10 contains detailed descriptions of Confucius's behaviors in various daily activities. Voltaire and Ezra Pound believed that this chapter demonstrated how Confucius was a mere human. Simon Leys, who recently translated the Analects into English and French, said that the book may have been the first in human history to describe the life of an individual, historic personage. Elias Canetti wrote: "Confucius's Analects is the oldest complete intellectual and spiritual portrait of a man. It strikes one as a modern book everything it contains and indeed everything it lacks is important." [32]

    Chapter 20, "Yao Yue", particularly the first verse, is bizarre in terms of both language and content. In terms of language, the text appears to be archaic (or a deliberate imitation of the archaic language of the Western Zhou) and bears some similarity with the language of the speeches in the Shujing. [33] [34] In terms of the content, the passage appears to be an admonition by Yao to Shun on the eve of Yao's abdication, which seems to be only tangentially related to Confucius and his philosophy. Moreover, there appear to be some problems with the text's continuity, and scholars have speculated that parts of the text were lost in the process of transmission and possibly transmitted with errors in the order. [35] The fragmentary nature of the final chapter of the received Lu text has been explained by the "accretion theory", in which the text of the Analects was gradually accreted over a 230-year period, beginning with the death of Confucius and ending suddenly with the conquest of Lu in 249 BCE. [36]

    Within these incipits a large number of passages in the Analects begin with the formulaic ziyue, "The Master said," but without punctuation marks in classical Chinese, this does not confirm whether what follows ziyue is direct quotation of actual sayings of Confucius, or simply to be understood as "the Master said that.." and the paraphrase of Confucius by the compilers of the Analects. [37]


    Contents

    Matter should not be confused with mass, as the two are not the same in modern physics. [9] Matter is a general term describing any 'physical substance'. By contrast, mass is not a substance but rather a quantitative property of matter and other substances or systems various types of mass are defined within physics – including but not limited to rest mass, inertial mass, relativistic mass, mass–energy.

    While there are different views on what should be considered matter, the mass of a substance has exact scientific definitions. Another difference is that matter has an "opposite" called antimatter, but mass has no opposite—there is no such thing as "anti-mass" or negative mass, so far as is known, although scientists do discuss the concept. Antimatter has the same (i.e. positive) mass property as its normal matter counterpart.

    Different fields of science use the term matter in different, and sometimes incompatible, ways. Some of these ways are based on loose historical meanings, from a time when there was no reason to distinguish mass from simply a quantity of matter. As such, there is no single universally agreed scientific meaning of the word "matter". Scientifically, the term "mass" is well-defined, but "matter" can be defined in several ways. Sometimes in the field of physics "matter" is simply equated with particles that exhibit rest mass (i.e., that cannot travel at the speed of light), such as quarks and leptons. However, in both physics and chemistry, matter exhibits both wave-like and particle-like properties, the so-called wave–particle duality. [10] [11] [12]

    Based on atoms

    A definition of "matter" based on its physical and chemical structure is: matter is made up of atoms. [13] Such atomic matter is also sometimes termed ordinary matter. As an example, deoxyribonucleic acid molecules (DNA) are matter under this definition because they are made of atoms. This definition can be extended to include charged atoms and molecules, so as to include plasmas (gases of ions) and electrolytes (ionic solutions), which are not obviously included in the atoms definition. Alternatively, one can adopt the protons, neutrons, and electrons definition.

    Based on protons, neutrons and electrons

    A definition of "matter" more fine-scale than the atoms and molecules definition is: matter is made up of what atoms and molecules are made of, meaning anything made of positively charged protons, neutral neutrons, and negatively charged electrons. [14] This definition goes beyond atoms and molecules, however, to include substances made from these building blocks that are not simply atoms or molecules, for example electron beams in an old cathode ray tube television, or white dwarf matter—typically, carbon and oxygen nuclei in a sea of degenerate electrons. At a microscopic level, the constituent "particles" of matter such as protons, neutrons, and electrons obey the laws of quantum mechanics and exhibit wave–particle duality. At an even deeper level, protons and neutrons are made up of quarks and the force fields (gluons) that bind them together, leading to the next definition.

    Based on quarks and leptons

    As seen in the above discussion, many early definitions of what can be called "ordinary matter" were based upon its structure or "building blocks". On the scale of elementary particles, a definition that follows this tradition can be stated as: "ordinary matter is everything that is composed of quarks and leptons", or "ordinary matter is everything that is composed of any elementary fermions except antiquarks and antileptons". [15] [16] [17] The connection between these formulations follows.

    Leptons (the most famous being the electron), and quarks (of which baryons, such as protons and neutrons, are made) combine to form atoms, which in turn form molecules. Because atoms and molecules are said to be matter, it is natural to phrase the definition as: "ordinary matter is anything that is made of the same things that atoms and molecules are made of". (However, notice that one also can make from these building blocks matter that is not atoms or molecules.) Then, because electrons are leptons, and protons, and neutrons are made of quarks, this definition in turn leads to the definition of matter as being "quarks and leptons", which are two of the four types of elementary fermions (the other two being antiquarks and antileptons, which can be considered antimatter as described later). Carithers and Grannis state: "Ordinary matter is composed entirely of first-generation particles, namely the [up] and [down] quarks, plus the electron and its neutrino." [16] (Higher generations particles quickly decay into first-generation particles, and thus are not commonly encountered. [18] )

    This definition of ordinary matter is more subtle than it first appears. All the particles that make up ordinary matter (leptons and quarks) are elementary fermions, while all the force carriers are elementary bosons. [19] The W and Z bosons that mediate the weak force are not made of quarks or leptons, and so are not ordinary matter, even if they have mass. [20] In other words, mass is not something that is exclusive to ordinary matter.

    The quark–lepton definition of ordinary matter, however, identifies not only the elementary building blocks of matter, but also includes composites made from the constituents (atoms and molecules, for example). Such composites contain an interaction energy that holds the constituents together, and may constitute the bulk of the mass of the composite. As an example, to a great extent, the mass of an atom is simply the sum of the masses of its constituent protons, neutrons and electrons. However, digging deeper, the protons and neutrons are made up of quarks bound together by gluon fields (see dynamics of quantum chromodynamics) and these gluons fields contribute significantly to the mass of hadrons. [21] In other words, most of what composes the "mass" of ordinary matter is due to the binding energy of quarks within protons and neutrons. [22] For example, the sum of the mass of the three quarks in a nucleon is approximately 12.5 MeV/c 2 , which is low compared to the mass of a nucleon (approximately 938 MeV/c 2 ). [23] [24] The bottom line is that most of the mass of everyday objects comes from the interaction energy of its elementary components.

    The Standard Model groups matter particles into three generations, where each generation consists of two quarks and two leptons. The first generation is the up and down quarks, the electron and the electron neutrino the second includes the charm and strange quarks, the muon and the muon neutrino the third generation consists of the top and bottom quarks and the tau and tau neutrino. [25] The most natural explanation for this would be that quarks and leptons of higher generations are excited states of the first generations. If this turns out to be the case, it would imply that quarks and leptons are composite particles, rather than elementary particles. [26]

    This quark–lepton definition of matter also leads to what can be described as "conservation of (net) matter" laws—discussed later below. Alternatively, one could return to the mass–volume–space concept of matter, leading to the next definition, in which antimatter becomes included as a subclass of matter.

    Based on elementary fermions (mass, volume, and space)

    A common or traditional definition of matter is "anything that has mass and volume (occupies space)". [27] [28] For example, a car would be said to be made of matter, as it has mass and volume (occupies space).

    The observation that matter occupies space goes back to antiquity. However, an explanation for why matter occupies space is recent, and is argued to be a result of the phenomenon described in the Pauli exclusion principle, [29] [30] which applies to fermions. Two particular examples where the exclusion principle clearly relates matter to the occupation of space are white dwarf stars and neutron stars, discussed further below.

    Thus, matter can be defined as everything composed of elementary fermions. Although we don't encounter them in everyday life, antiquarks (such as the antiproton) and antileptons (such as the positron) are the antiparticles of the quark and the lepton, are elementary fermions as well, and have essentially the same properties as quarks and leptons, including the applicability of the Pauli exclusion principle which can be said to prevent two particles from being in the same place at the same time (in the same state), i.e. makes each particle "take up space". This particular definition leads to matter being defined to include anything made of these antimatter particles as well as the ordinary quark and lepton, and thus also anything made of mesons, which are unstable particles made up of a quark and an antiquark.

    In general relativity and cosmology

    In the context of relativity, mass is not an additive quantity, in the sense that one can not add the rest masses of particles in a system to get the total rest mass of the system. [1] : 21 Thus, in relativity usually a more general view is that it is not the sum of rest masses, but the energy–momentum tensor that quantifies the amount of matter. This tensor gives the rest mass for the entire system. "Matter" therefore is sometimes considered as anything that contributes to the energy–momentum of a system, that is, anything that is not purely gravity. [31] [32] This view is commonly held in fields that deal with general relativity such as cosmology. In this view, light and other massless particles and fields are all part of "matter".

    In particle physics, fermions are particles that obey Fermi–Dirac statistics. Fermions can be elementary, like the electron—or composite, like the proton and neutron. In the Standard Model, there are two types of elementary fermions: quarks and leptons, which are discussed next.


    Contents

    For most of history, humanity did not recognize or understand the concept of the Solar System. Most people up to the Late Middle Ages–Renaissance believed Earth to be stationary at the centre of the universe and categorically different from the divine or ethereal objects that moved through the sky. Although the Greek philosopher Aristarchus of Samos had speculated on a heliocentric reordering of the cosmos, Nicolaus Copernicus was the first to develop a mathematically predictive heliocentric system. [11] [12]

    In the 17th century, Galileo discovered that the Sun was marked with sunspots, and that Jupiter had four satellites in orbit around it. [13] Christiaan Huygens followed on from Galileo's discoveries by discovering Saturn's moon Titan and the shape of the rings of Saturn. [14] Around 1677, Edmond Halley observed a transit of Mercury across the Sun, leading him to realise that observations of the solar parallax of a planet (more ideally using the transit of Venus) could be used to trigonometrically determine the distances between Earth, Venus, and the Sun. [15] In 1705, Halley realised that repeated sightings of a comet were of the same object, returning regularly once every 75–76 years. This was the first evidence that anything other than the planets orbited the Sun, [16] though this had been theorized about comets in the 1st century by Seneca. [17] Around 1704, the term "Solar System" first appeared in English. [18] In 1838, Friedrich Bessel successfully measured a stellar parallax, an apparent shift in the position of a star created by Earth's motion around the Sun, providing the first direct, experimental proof of heliocentrism. [19] Improvements in observational astronomy and the use of uncrewed spacecraft have since enabled the detailed investigation of other bodies orbiting the Sun.

    The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99.86% of the system's known mass and dominates it gravitationally. [20] The Sun's four largest orbiting bodies, the giant planets, account for 99% of the remaining mass, with Jupiter and Saturn together comprising more than 90%. The remaining objects of the Solar System (including the four terrestrial planets, the dwarf planets, moons, asteroids, and comets) together comprise less than 0.002% of the Solar System's total mass. [g]

    Most large objects in orbit around the Sun lie near the plane of Earth's orbit, known as the ecliptic. The planets are very close to the ecliptic, whereas comets and Kuiper belt objects are frequently at significantly greater angles to it. [24] [25] As a result of the formation of the Solar System, planets (and most other objects) orbit the Sun in the same direction that the Sun is rotating (counter-clockwise, as viewed from above Earth's north pole). [26] There are exceptions, such as Halley's Comet. Most of the larger moons orbit their planets in this prograde direction (with Triton being the largest retrograde exception) and most larger objects rotate themselves in the same direction (with Venus being a notable retrograde exception).

    The overall structure of the charted regions of the Solar System consists of the Sun, four relatively small inner planets surrounded by a belt of mostly rocky asteroids, and four giant planets surrounded by the Kuiper belt of mostly icy objects. Astronomers sometimes informally divide this structure into separate regions. The inner Solar System includes the four terrestrial planets and the asteroid belt. The outer Solar System is beyond the asteroids, including the four giant planets. [27] Since the discovery of the Kuiper belt, the outermost parts of the Solar System are considered a distinct region consisting of the objects beyond Neptune. [28]

    Most of the planets in the Solar System have secondary systems of their own, being orbited by planetary objects called natural satellites, or moons (two of which, Titan and Ganymede, are larger than the planet Mercury). The four giant planets have planetary rings, thin bands of tiny particles that orbit them in unison. Most of the largest natural satellites are in synchronous rotation, with one face permanently turned toward their parent. [29]

    Kepler's laws of planetary motion describe the orbits of objects about the Sun. Following Kepler's laws, each object travels along an ellipse with the Sun at one focus. Objects closer to the Sun (with smaller semi-major axes) travel more quickly because they are more affected by the Sun's gravity. On an elliptical orbit, a body's distance from the Sun varies over the course of its year. A body's closest approach to the Sun is called its perihelion, whereas its most distant point from the Sun is called its aphelion. The orbits of the planets are nearly circular, but many comets, asteroids, and Kuiper belt objects follow highly elliptical orbits. The positions of the bodies in the Solar System can be predicted using numerical models.

    Although the Sun dominates the system by mass, it accounts for only about 2% of the angular momentum. [30] [31] The planets, dominated by Jupiter, account for most of the rest of the angular momentum due to the combination of their mass, orbit, and distance from the Sun, with a possibly significant contribution from comets. [30]

    The Sun, which comprises nearly all the matter in the Solar System, is composed of roughly 98% hydrogen and helium. [32] Jupiter and Saturn, which comprise nearly all the remaining matter, are also primarily composed of hydrogen and helium. [33] [34] A composition gradient exists in the Solar System, created by heat and light pressure from the Sun those objects closer to the Sun, which are more affected by heat and light pressure, are composed of elements with high melting points. Objects farther from the Sun are composed largely of materials with lower melting points. [35] The boundary in the Solar System beyond which those volatile substances could condense is known as the frost line, and it lies at roughly 5 AU from the Sun. [4]

    The objects of the inner Solar System are composed mostly of rock, [36] the collective name for compounds with high melting points, such as silicates, iron or nickel, that remained solid under almost all conditions in the protoplanetary nebula. [37] Jupiter and Saturn are composed mainly of gases, the astronomical term for materials with extremely low melting points and high vapour pressure, such as hydrogen, helium, and neon, which were always in the gaseous phase in the nebula. [37] Ices, like water, methane, ammonia, hydrogen sulfide, and carbon dioxide, [36] have melting points up to a few hundred kelvins. [37] They can be found as ices, liquids, or gases in various places in the Solar System, whereas in the nebula they were either in the solid or gaseous phase. [37] Icy substances comprise the majority of the satellites of the giant planets, as well as most of Uranus and Neptune (the so-called "ice giants") and the numerous small objects that lie beyond Neptune's orbit. [36] [38] Together, gases and ices are referred to as volatiles. [39]

    Distances and scales

    The distance from Earth to the Sun is 1 astronomical unit [AU] (150,000,000 km 93,000,000 mi). For comparison, the radius of the Sun is 0.0047 AU (700,000 km). Thus, the Sun occupies 0.00001% (10 −5 %) of the volume of a sphere with a radius the size of Earth's orbit, whereas Earth's volume is roughly one millionth (10 −6 ) that of the Sun. Jupiter, the largest planet, is 5.2 astronomical units (780,000,000 km) from the Sun and has a radius of 71,000 km (0.00047 AU), whereas the most distant planet, Neptune, is 30 AU (4.5 × 10 9 km) from the Sun.

    With a few exceptions, the farther a planet or belt is from the Sun, the larger the distance between its orbit and the orbit of the next nearer object to the Sun. For example, Venus is approximately 0.33 AU farther out from the Sun than Mercury, whereas Saturn is 4.3 AU out from Jupiter, and Neptune lies 10.5 AU out from Uranus. Attempts have been made to determine a relationship between these orbital distances (for example, the Titius–Bode law), [40] but no such theory has been accepted.

    Some Solar System models attempt to convey the relative scales involved in the Solar System on human terms. Some are small in scale (and may be mechanical—called orreries)—whereas others extend across cities or regional areas. [41] The largest such scale model, the Sweden Solar System, uses the 110-metre (361 ft) Ericsson Globe in Stockholm as its substitute Sun, and, following the scale, Jupiter is a 7.5-metre (25-foot) sphere at Stockholm Arlanda Airport, 40 km (25 mi) away, whereas the farthest current object, Sedna, is a 10 cm (4 in) sphere in Luleå, 912 km (567 mi) away. [42] [43]

    If the Sun–Neptune distance is scaled to 100 metres, then the Sun would be about 3 cm in diameter (roughly two-thirds the diameter of a golf ball), the giant planets would be all smaller than about 3 mm, and Earth's diameter along with that of the other terrestrial planets would be smaller than a flea (0.3 mm) at this scale. [44]

    Distances of selected bodies of the Solar System from the Sun. The left and right edges of each bar correspond to the perihelion and aphelion of the body, respectively, hence long bars denote high orbital eccentricity. The radius of the Sun is 0.7 million km, and the radius of Jupiter (the largest planet) is 0.07 million km, both too small to resolve on this image.

    The Solar System formed 4.568 billion years ago from the gravitational collapse of a region within a large molecular cloud. [h] This initial cloud was likely several light-years across and probably birthed several stars. [46] As is typical of molecular clouds, this one consisted mostly of hydrogen, with some helium, and small amounts of heavier elements fused by previous generations of stars. As the region that would become the Solar System, known as the pre-solar nebula, [47] collapsed, conservation of angular momentum caused it to rotate faster. The centre, where most of the mass collected, became increasingly hotter than the surrounding disc. [46] As the contracting nebula rotated faster, it began to flatten into a protoplanetary disc with a diameter of roughly 200 AU [46] and a hot, dense protostar at the centre. [48] [49] The planets formed by accretion from this disc, [50] in which dust and gas gravitationally attracted each other, coalescing to form ever larger bodies. Hundreds of protoplanets may have existed in the early Solar System, but they either merged or were destroyed, leaving the planets, dwarf planets, and leftover minor bodies. [51]

    Due to their higher boiling points, only metals and silicates could exist in solid form in the warm inner Solar System close to the Sun, and these would eventually form the rocky planets of Mercury, Venus, Earth, and Mars. Because metallic elements only comprised a very small fraction of the solar nebula, the terrestrial planets could not grow very large. The giant planets (Jupiter, Saturn, Uranus, and Neptune) formed further out, beyond the frost line, the point between the orbits of Mars and Jupiter where material is cool enough for volatile icy compounds to remain solid. The ices that formed these planets were more plentiful than the metals and silicates that formed the terrestrial inner planets, allowing them to grow massive enough to capture large atmospheres of hydrogen and helium, the lightest and most abundant elements. Leftover debris that never became planets congregated in regions such as the asteroid belt, Kuiper belt, and Oort cloud. [51] The Nice model is an explanation for the creation of these regions and how the outer planets could have formed in different positions and migrated to their current orbits through various gravitational interactions. [53]

    Within 50 million years, the pressure and density of hydrogen in the centre of the protostar became great enough for it to begin thermonuclear fusion. [54] The temperature, reaction rate, pressure, and density increased until hydrostatic equilibrium was achieved: the thermal pressure equalled the force of gravity. At this point, the Sun became a main-sequence star. [55] The main-sequence phase, from beginning to end, will last about 10 billion years for the Sun compared to around two billion years for all other phases of the Sun's pre-remnant life combined. [56] Solar wind from the Sun created the heliosphere and swept away the remaining gas and dust from the protoplanetary disc into interstellar space, ending the planetary formation process. The Sun is growing brighter early in its main-sequence life its brightness was 70% that of what it is today. [57]

    The Solar System will remain roughly as we know it today until the hydrogen in the core of the Sun has been entirely converted to helium, which will occur roughly 5 billion years from now. This will mark the end of the Sun's main-sequence life. At that time, the core of the Sun will contract with hydrogen fusion occurring along a shell surrounding the inert helium, and the energy output will be much greater than at present. The outer layers of the Sun will expand to roughly 260 times its current diameter, and the Sun will become a red giant. Because of its vastly increased surface area, the surface of the Sun will be considerably cooler (2,600 K at its coolest) than it is on the main sequence. [56] The expanding Sun is expected to vaporize Mercury and render Earth uninhabitable. Eventually, the core will be hot enough for helium fusion the Sun will burn helium for a fraction of the time it burned hydrogen in the core. The Sun is not massive enough to commence the fusion of heavier elements, and nuclear reactions in the core will dwindle. Its outer layers will move away into space, leaving a white dwarf, an extraordinarily dense object, half the original mass of the Sun but only the size of Earth. [58] The ejected outer layers will form what is known as a planetary nebula, returning some of the material that formed the Sun—but now enriched with heavier elements like carbon—to the interstellar medium.

    The Sun is the Solar System's star and by far its most massive component. Its large mass (332,900 Earth masses), [59] which comprises 99.86% of all the mass in the Solar System, [60] produces temperatures and densities in its core high enough to sustain nuclear fusion of hydrogen into helium, making it a main-sequence star. [61] This releases an enormous amount of energy, mostly radiated into space as electromagnetic radiation peaking in visible light. [62]

    The Sun is a G2-type main-sequence star. Hotter main-sequence stars are more luminous. The Sun's temperature is intermediate between that of the hottest stars and that of the coolest stars. Stars brighter and hotter than the Sun are rare, whereas substantially dimmer and cooler stars, known as red dwarfs, make up 85% of the stars in the Milky Way. [63] [64]

    The Sun is a population I star it has a higher abundance of elements heavier than hydrogen and helium ("metals" in astronomical parlance) than the older population II stars. [65] Elements heavier than hydrogen and helium were formed in the cores of ancient and exploding stars, so the first generation of stars had to die before the universe could be enriched with these atoms. The oldest stars contain few metals, whereas stars born later have more. This high metallicity is thought to have been crucial to the Sun's development of a planetary system because the planets form from the accretion of "metals". [66]

    The vast majority of the Solar System consists of a near-vacuum known as the interplanetary medium. Along with light, the Sun radiates a continuous stream of charged particles (a plasma) known as the solar wind. This stream of particles spreads outwards at roughly 1.5 million kilometres per hour, [67] creating a tenuous atmosphere that permeates the interplanetary medium out to at least 100 AU (see § Heliosphere). [68] Activity on the Sun's surface, such as solar flares and coronal mass ejections, disturbs the heliosphere, creating space weather and causing geomagnetic storms. [69] The largest structure within the heliosphere is the heliospheric current sheet, a spiral form created by the actions of the Sun's rotating magnetic field on the interplanetary medium. [70] [71]

    Earth's magnetic field stops its atmosphere from being stripped away by the solar wind. [72] Venus and Mars do not have magnetic fields, and as a result the solar wind is causing their atmospheres to gradually bleed away into space. [73] Coronal mass ejections and similar events blow a magnetic field and huge quantities of material from the surface of the Sun. The interaction of this magnetic field and material with Earth's magnetic field funnels charged particles into Earth's upper atmosphere, where its interactions create aurorae seen near the magnetic poles.

    The heliosphere and planetary magnetic fields (for those planets that have them) partially shield the Solar System from high-energy interstellar particles called cosmic rays. The density of cosmic rays in the interstellar medium and the strength of the Sun's magnetic field change on very long timescales, so the level of cosmic-ray penetration in the Solar System varies, though by how much is unknown. [74]

    The interplanetary medium is home to at least two disc-like regions of cosmic dust. The first, the zodiacal dust cloud, lies in the inner Solar System and causes the zodiacal light. It was likely formed by collisions within the asteroid belt brought on by gravitational interactions with the planets. [75] The second dust cloud extends from about 10 AU to about 40 AU, and was probably created by similar collisions within the Kuiper belt. [76] [77]

    The inner Solar System is the region comprising the terrestrial planets and the asteroid belt. [78] Composed mainly of silicates and metals, the objects of the inner Solar System are relatively close to the Sun the radius of this entire region is less than the distance between the orbits of Jupiter and Saturn. This region is also within the frost line, which is a little less than 5 AU (about 700 million km) from the Sun. [79]

    Inner planets

    The four terrestrial or inner planets have dense, rocky compositions, few or no moons, and no ring systems. They are composed largely of refractory minerals such as the silicates—which form their crusts and mantles—and metals such as iron and nickel which form their cores. Three of the four inner planets (Venus, Earth and Mars) have atmospheres substantial enough to generate weather all have impact craters and tectonic surface features, such as rift valleys and volcanoes. The term inner planet should not be confused with inferior planet, which designates those planets that are closer to the Sun than Earth is (i.e. Mercury and Venus).

    Mercury

    Mercury ( 0.4 AU from the Sun) is the closest planet to the Sun and on average, all seven other planets. [80] [81] The smallest planet in the Solar System (0.055 M ), Mercury has no natural satellites. Besides impact craters, its only known geological features are lobed ridges or rupes that were probably produced by a period of contraction early in its history. [82] Mercury's very tenuous atmosphere consists of atoms blasted off its surface by the solar wind. [83] Its relatively large iron core and thin mantle have not yet been adequately explained. Hypotheses include that its outer layers were stripped off by a giant impact, or that it was prevented from fully accreting by the young Sun's energy. [84] [85]

    Venus

    Venus (0.7 AU from the Sun) is close in size to Earth (0.815 M ) and, like Earth, has a thick silicate mantle around an iron core, a substantial atmosphere, and evidence of internal geological activity. It is much drier than Earth, and its atmosphere is ninety times as dense. Venus has no natural satellites. It is the hottest planet, with surface temperatures over 400 °C (752 °F), most likely due to the amount of greenhouse gases in the atmosphere. [86] No definitive evidence of current geological activity has been detected on Venus, but it has no magnetic field that would prevent depletion of its substantial atmosphere, which suggests that its atmosphere is being replenished by volcanic eruptions. [87]

    Earth

    Earth (1 AU from the Sun) is the largest and densest of the inner planets, the only one known to have current geological activity, and the only place where life is known to exist. [88] Its liquid hydrosphere is unique among the terrestrial planets, and it is the only planet where plate tectonics has been observed. Earth's atmosphere is radically different from those of the other planets, having been altered by the presence of life to contain 21% free oxygen. [89] It has one natural satellite, the Moon, the only large satellite of a terrestrial planet in the Solar System.

    Mars (1.5 AU from the Sun) is smaller than Earth and Venus (0.107 M ). It has an atmosphere of mostly carbon dioxide with a surface pressure of 6.1 millibars (roughly 0.6% of that of Earth). [90] Its surface, peppered with vast volcanoes, such as Olympus Mons, and rift valleys, such as Valles Marineris, shows geological activity that may have persisted until as recently as 2 million years ago. [91] Its red colour comes from iron oxide (rust) in its soil. [92] Mars has two tiny natural satellites (Deimos and Phobos) thought to be either captured asteroids, [93] or ejected debris from a massive impact early in Mars's history. [94]

    Asteroid belt

    • Sun
    • Jupiter trojans
    • Planetary orbit
    • Asteroid belt
    • Hilda asteroids
    • NEOs(selection)

    Asteroids except for the largest, Ceres, are classified as small Solar System bodies [f] and are composed mainly of refractory rocky and metallic minerals, with some ice. [95] [96] They range from a few metres to hundreds of kilometres in size. Asteroids smaller than one meter are usually called meteoroids and micrometeoroids (grain-sized), depending on different, somewhat arbitrary definitions.

    The asteroid belt occupies the orbit between Mars and Jupiter, between 2.3 and 3.3 AU from the Sun. It is thought to be remnants from the Solar System's formation that failed to coalesce because of the gravitational interference of Jupiter. [97] The asteroid belt contains tens of thousands, possibly millions, of objects over one kilometre in diameter. [98] Despite this, the total mass of the asteroid belt is unlikely to be more than a thousandth of that of Earth. [23] The asteroid belt is very sparsely populated spacecraft routinely pass through without incident. [99]

    Ceres

    Ceres (2.77 AU) is the largest asteroid, a protoplanet, and a dwarf planet. [f] It has a diameter of slightly under 1000 km , and a mass large enough for its own gravity to pull it into a spherical shape. Ceres was considered a planet when it was discovered in 1801 and was reclassified to asteroid in the 1850s as further observations revealed additional asteroids. [100] It was classified as a dwarf planet in 2006 when the definition of a planet was created.

    Asteroid groups

    Asteroids in the asteroid belt are divided into asteroid groups and families based on their orbital characteristics. Asteroid moons are asteroids that orbit larger asteroids. They are not as clearly distinguished as planetary moons, sometimes being almost as large as their partners. The asteroid belt also contains main-belt comets, which may have been the source of Earth's water. [101]

    Jupiter trojans are located in either of Jupiter's L4 or L5 points (gravitationally stable regions leading and trailing a planet in its orbit) the term trojan is also used for small bodies in any other planetary or satellite Lagrange point. Hilda asteroids are in a 2:3 resonance with Jupiter that is, they go around the Sun three times for every two Jupiter orbits. [102]

    The inner Solar System also contains near-Earth asteroids, many of which cross the orbits of the inner planets. [103] Some of them are potentially hazardous objects.

    The outer region of the Solar System is home to the giant planets and their large moons. The centaurs and many short-period comets also orbit in this region. Due to their greater distance from the Sun, the solid objects in the outer Solar System contain a higher proportion of volatiles, such as water, ammonia, and methane than those of the inner Solar System because the lower temperatures allow these compounds to remain solid. [51]

    Outer planets

    The four outer planets, or giant planets (sometimes called Jovian planets), collectively make up 99% of the mass known to orbit the Sun. [g] Jupiter and Saturn are together more than 400 times the mass of Earth and consist overwhelmingly of the gases hydrogen and helium, hence their designation as gas giants. [104] Uranus and Neptune are far less massive—less than 20 Earth masses ( M ) each—and are composed primarily of ices. For these reasons, some astronomers suggest they belong in their own category, ice giants. [105] All four giant planets have rings, although only Saturn's ring system is easily observed from Earth. The term superior planet designates planets outside Earth's orbit and thus includes both the outer planets and Mars.

    Jupiter

    Jupiter (5.2 AU), at 318 M , is 2.5 times the mass of all the other planets put together. It is composed largely of hydrogen and helium. Jupiter's strong internal heat creates semi-permanent features in its atmosphere, such as cloud bands and the Great Red Spot. Jupiter has 79 known satellites. The four largest, Ganymede, Callisto, Io, and Europa, show similarities to the terrestrial planets, such as volcanism and internal heating. [106] Ganymede, the largest satellite in the Solar System, is larger than Mercury.

    Saturn

    Saturn (9.5 AU), distinguished by its extensive ring system, has several similarities to Jupiter, such as its atmospheric composition and magnetosphere. Although Saturn has 60% of Jupiter's volume, it is less than a third as massive, at 95 M . Saturn is the only planet of the Solar System that is less dense than water. [107] The rings of Saturn are made up of small ice and rock particles. Saturn has 82 confirmed satellites composed largely of ice. Two of these, Titan and Enceladus, show signs of geological activity. [108] Titan, the second-largest moon in the Solar System, is larger than Mercury and the only satellite in the Solar System with a substantial atmosphere.

    Uranus

    Uranus (19.2 AU), at 14 M , is the lightest of the outer planets. Uniquely among the planets, it orbits the Sun on its side its axial tilt is over ninety degrees to the ecliptic. It has a much colder core than the other giant planets and radiates very little heat into space. [109] Uranus has 27 known satellites, the largest ones being Titania, Oberon, Umbriel, Ariel, and Miranda. [110]

    Neptune

    Neptune ( 30.1 AU ), though slightly smaller than Uranus, is more massive (17 M ) and hence more dense. It radiates more internal heat, but not as much as Jupiter or Saturn. [111] Neptune has 14 known satellites. The largest, Triton, is geologically active, with geysers of liquid nitrogen. [112] Triton is the only large satellite with a retrograde orbit. Neptune is accompanied in its orbit by several minor planets, termed Neptune trojans, that are in 1:1 resonance with it.

    Centaurs

    The centaurs are icy comet-like bodies whose orbits have semi-major axes greater than Jupiter's (5.5 AU) and less than Neptune's (30 AU). The largest known centaur, 10199 Chariklo, has a diameter of about 250 km. [113] The first centaur discovered, 2060 Chiron, has also been classified as a comet (95P) because it develops a coma just as comets do when they approach the Sun. [114]

    Comets are small Solar System bodies, [f] typically only a few kilometres across, composed largely of volatile ices. They have highly eccentric orbits, generally a perihelion within the orbits of the inner planets and an aphelion far beyond Pluto. When a comet enters the inner Solar System, its proximity to the Sun causes its icy surface to sublimate and ionise, creating a coma: a long tail of gas and dust often visible to the naked eye.

    Short-period comets have orbits lasting less than two hundred years. Long-period comets have orbits lasting thousands of years. Short-period comets are thought to originate in the Kuiper belt, whereas long-period comets, such as Hale–Bopp, are thought to originate in the Oort cloud. Many comet groups, such as the Kreutz Sungrazers, formed from the breakup of a single parent. [115] Some comets with hyperbolic orbits may originate outside the Solar System, but determining their precise orbits is difficult. [116] Old comets whose volatiles have mostly been driven out by solar warming are often categorised as asteroids. [117]

    Beyond the orbit of Neptune lies the area of the "trans-Neptunian region", with the doughnut-shaped Kuiper belt, home of Pluto and several other dwarf planets, and an overlapping disc of scattered objects, which is tilted toward the plane of the Solar System and reaches much further out than the Kuiper belt. The entire region is still largely unexplored. It appears to consist overwhelmingly of many thousands of small worlds—the largest having a diameter only a fifth that of Earth and a mass far smaller than that of the Moon—composed mainly of rock and ice. This region is sometimes described as the "third zone of the Solar System", enclosing the inner and the outer Solar System. [118]

    Kuiper belt

    • Sun
    • Jupiter trojans
    • Giant planets
    • Kuiper belt
    • Scattered disc
    • Neptune trojans

    The Kuiper belt is a great ring of debris similar to the asteroid belt, but consisting mainly of objects composed primarily of ice. [119] It extends between 30 and 50 AU from the Sun. Though it is estimated to contain anything from dozens to thousands of dwarf planets, it is composed mainly of small Solar System bodies. Many of the larger Kuiper belt objects, such as Quaoar, Varuna, and Orcus, may prove to be dwarf planets with further data. There are estimated to be over 100,000 Kuiper belt objects with a diameter greater than 50 km, but the total mass of the Kuiper belt is thought to be only a tenth or even a hundredth the mass of Earth. [22] Many Kuiper belt objects have multiple satellites, [120] and most have orbits that take them outside the plane of the ecliptic. [121]

    The Kuiper belt can be roughly divided into the "classical" belt and the resonances. [119] Resonances are orbits linked to that of Neptune (e.g. twice for every three Neptune orbits, or once for every two). The first resonance begins within the orbit of Neptune itself. The classical belt consists of objects having no resonance with Neptune, and extends from roughly 39.4 AU to 47.7 AU. [122] Members of the classical Kuiper belt are classified as cubewanos, after the first of their kind to be discovered, 15760 Albion (which previously had the provisional designation 1992 QB1), and are still in near primordial, low-eccentricity orbits. [123]

    Pluto and Charon

    The dwarf planet Pluto (with an average orbit of 39 AU) is the largest known object in the Kuiper belt. When discovered in 1930, it was considered to be the ninth planet this changed in 2006 with the adoption of a formal definition of planet. Pluto has a relatively eccentric orbit inclined 17 degrees to the ecliptic plane and ranging from 29.7 AU from the Sun at perihelion (within the orbit of Neptune) to 49.5 AU at aphelion. Pluto has a 3:2 resonance with Neptune, meaning that Pluto orbits twice round the Sun for every three Neptunian orbits. Kuiper belt objects whose orbits share this resonance are called plutinos. [124]

    Charon, the largest of Pluto's moons, is sometimes described as part of a binary system with Pluto, as the two bodies orbit a barycentre of gravity above their surfaces (i.e. they appear to "orbit each other"). Beyond Charon, four much smaller moons, Styx, Nix, Kerberos, and Hydra, orbit within the system.

    Makemake and Haumea

    Makemake (45.79 AU average), although smaller than Pluto, is the largest known object in the classical Kuiper belt (that is, a Kuiper belt object not in a confirmed resonance with Neptune). Makemake is the brightest object in the Kuiper belt after Pluto. It was assigned a naming committee under the expectation that it would prove to be a dwarf planet in 2008. [6] Its orbit is far more inclined than Pluto's, at 29°. [125]

    Haumea (43.13 AU average) is in an orbit similar to Makemake, except that it is in a temporary 7:12 orbital resonance with Neptune. [126] It was named under the same expectation that it would prove to be a dwarf planet, though subsequent observations have indicated that it may not be a dwarf planet after all. [127]

    Scattered disc

    The scattered disc, which overlaps the Kuiper belt but extends out to about 200 AU, is thought to be the source of short-period comets. Scattered-disc objects are thought to have been ejected into erratic orbits by the gravitational influence of Neptune's early outward migration. Most scattered disc objects (SDOs) have perihelia within the Kuiper belt but aphelia far beyond it (some more than 150 AU from the Sun). SDOs' orbits are also highly inclined to the ecliptic plane and are often almost perpendicular to it. Some astronomers consider the scattered disc to be merely another region of the Kuiper belt and describe scattered disc objects as "scattered Kuiper belt objects". [128] Some astronomers also classify centaurs as inward-scattered Kuiper belt objects along with the outward-scattered residents of the scattered disc. [129]

    Eris (with an average orbit of 68 AU) is the largest known scattered disc object, and caused a debate about what constitutes a planet, because it is 25% more massive than Pluto [130] and about the same diameter. It is the most massive of the known dwarf planets. It has one known moon, Dysnomia. Like Pluto, its orbit is highly eccentric, with a perihelion of 38.2 AU (roughly Pluto's distance from the Sun) and an aphelion of 97.6 AU, and steeply inclined to the ecliptic plane.

    The point at which the Solar System ends and interstellar space begins is not precisely defined because its outer boundaries are shaped by two forces, the solar wind and the Sun's gravity. The limit of the solar wind's influence is roughly four times Pluto's distance from the Sun this heliopause, the outer boundary of the heliosphere, is considered the beginning of the interstellar medium. [68] The Sun's Hill sphere, the effective range of its gravitational dominance, is thought to extend up to a thousand times farther and encompasses the hypothetical Oort cloud. [131]

    Heliosphere

    The heliosphere is a stellar-wind bubble, a region of space dominated by the Sun, in which it radiates its solar wind at approximately 400 km/s, a stream of charged particles, until it collides with the wind of the interstellar medium.

    The collision occurs at the termination shock, which is roughly 80–100 AU from the Sun upwind of the interstellar medium and roughly 200 AU from the Sun downwind. [132] Here the wind slows dramatically, condenses and becomes more turbulent, [132] forming a great oval structure known as the heliosheath. This structure is thought to look and behave very much like a comet's tail, extending outward for a further 40 AU on the upwind side but tailing many times that distance downwind evidence from the Cassini and Interstellar Boundary Explorer spacecraft has suggested that it is forced into a bubble shape by the constraining action of the interstellar magnetic field. [133]

    The outer boundary of the heliosphere, the heliopause, is the point at which the solar wind finally terminates and is the beginning of interstellar space. [68] Voyager 1 and Voyager 2 are reported to have passed the termination shock and entered the heliosheath, at 94 and 84 AU from the Sun, respectively. [134] [135] Voyager 1 is reported to have crossed the heliopause in August 2012. [136]

    The shape and form of the outer edge of the heliosphere is likely affected by the fluid dynamics of interactions with the interstellar medium as well as solar magnetic fields prevailing to the south, e.g. it is bluntly shaped with the northern hemisphere extending 9 AU farther than the southern hemisphere. [132] Beyond the heliopause, at around 230 AU, lies the bow shock, a plasma "wake" left by the Sun as it travels through the Milky Way. [137]

    • inner Solar System and Jupiter
    • outer Solar System and Pluto
    • orbit of Sedna (detached object)
    • inner part of the Oort Cloud

    Due to a lack of data, conditions in local interstellar space are not known for certain. It is expected that NASA's Voyager spacecraft, as they pass the heliopause, will transmit valuable data on radiation levels and solar wind to Earth. [138] How well the heliosphere shields the Solar System from cosmic rays is poorly understood. A NASA-funded team has developed a concept of a "Vision Mission" dedicated to sending a probe to the heliosphere. [139] [140]

    Detached objects

    90377 Sedna (with an average orbit of 520 AU) is a large, reddish object with a gigantic, highly elliptical orbit that takes it from about 76 AU at perihelion to 940 AU at aphelion and takes 11,400 years to complete. Mike Brown, who discovered the object in 2003, asserts that it cannot be part of the scattered disc or the Kuiper belt because its perihelion is too distant to have been affected by Neptune's migration. He and other astronomers consider it to be the first in an entirely new population, sometimes termed "distant detached objects" (DDOs), which also may include the object 2000 CR105 , which has a perihelion of 45 AU, an aphelion of 415 AU, and an orbital period of 3,420 years. [141] Brown terms this population the "inner Oort cloud" because it may have formed through a similar process, although it is far closer to the Sun. [142] Sedna is very likely a dwarf planet, though its shape has yet to be determined. The second unequivocally detached object, with a perihelion farther than Sedna's at roughly 81 AU, is 2012 VP 113 , discovered in 2012. Its aphelion is only half that of Sedna's, at 400–500 AU. [143] [144]

    Oort cloud

    The Oort cloud is a hypothetical spherical cloud of up to a trillion icy objects that is thought to be the source for all long-period comets and to surround the Solar System at roughly 50,000 AU (around 1 light-year (ly)), and possibly to as far as 100,000 AU (1.87 ly). It is thought to be composed of comets that were ejected from the inner Solar System by gravitational interactions with the outer planets. Oort cloud objects move very slowly, and can be perturbed by infrequent events, such as collisions, the gravitational effects of a passing star, or the galactic tide, the tidal force exerted by the Milky Way. [145] [146]

    Boundaries

    Much of the Solar System is still unknown. The Sun's gravitational field is estimated to dominate the gravitational forces of surrounding stars out to about two light-years (125,000 AU). Lower estimates for the radius of the Oort cloud, by contrast, do not place it farther than 50,000 AU. [147] Despite discoveries such as Sedna, the region between the Kuiper belt and the Oort cloud, an area tens of thousands of AU in radius, is still virtually unmapped. There are also ongoing studies of the region between Mercury and the Sun. [148] Objects may yet be discovered in the Solar System's uncharted regions.

    Currently, the furthest known objects, such as Comet West, have aphelia around 70,000 AU from the Sun, but as the Oort cloud becomes better known, this may change.

    The Solar System is located in the Milky Way, a barred spiral galaxy with a diameter of about 100,000 light-years containing more than 100 billion stars. [149] The Sun resides in one of the Milky Way's outer spiral arms, known as the Orion–Cygnus Arm or Local Spur. [150] The Sun lies about 26,660 light-years from the Galactic Centre, [151] and its speed around the center of the Milky Way is about 247 km/s, so that it completes one revolution every 210 million years. This revolution is known as the Solar System's galactic year. [152] The solar apex, the direction of the Sun's path through interstellar space, is near the constellation Hercules in the direction of the current location of the bright star Vega. [153] The plane of the ecliptic lies at an angle of about 60° to the galactic plane. [i]

    The Solar System's location in the Milky Way is a factor in the evolutionary history of life on Earth. Its orbit is close to circular, and orbits near the Sun are at roughly the same speed as that of the spiral arms. [155] [156] Therefore, the Sun passes through arms only rarely. Because spiral arms are home to a far larger concentration of supernovae, gravitational instabilities, and radiation that could disrupt the Solar System, this has given Earth long periods of stability for life to evolve. [155] However, the changing position of the Solar System relative to other parts of the Milky Way could explain periodic extinction events on Earth, according to the Shiva hypothesis or related theories. The Solar System lies well outside the star-crowded environs of the galactic centre. Near the centre, gravitational tugs from nearby stars could perturb bodies in the Oort cloud and send many comets into the inner Solar System, producing collisions with potentially catastrophic implications for life on Earth. The intense radiation of the galactic centre could also interfere with the development of complex life. [155] Even at the Solar System's current location, some scientists have speculated that recent supernovae may have adversely affected life in the last 35,000 years, by flinging pieces of expelled stellar core towards the Sun, as radioactive dust grains and larger, comet-like bodies. [157]

    Neighbourhood

    The Solar System is in the Local Interstellar Cloud or Local Fluff. It is thought to be near the neighbouring G-Cloud but it is not known if the Solar System is embedded in the Local Interstellar Cloud, or if it is in the region where the Local Interstellar Cloud and G-Cloud are interacting. [158] [159] The Local Interstellar Cloud is an area of denser cloud in an otherwise sparse region known as the Local Bubble, an hourglass-shaped cavity in the interstellar medium roughly 300 light-years (ly) across. The bubble is suffused with high-temperature plasma, that suggests it is the product of several recent supernovae. [160]

    There are relatively few stars within ten light-years of the Sun. The closest is the triple star system Alpha Centauri, which is about 4.4 light-years away. Alpha Centauri A and B are a closely tied pair of Sun-like stars, whereas the small red dwarf, Proxima Centauri, orbits the pair at a distance of 0.2 light-year. In 2016, a potentially habitable exoplanet was confirmed to be orbiting Proxima Centauri, called Proxima Centauri b, the closest confirmed exoplanet to the Sun. [161] The stars next closest to the Sun are the red dwarfs Barnard's Star (at 5.9 ly), Wolf 359 (7.8 ly), and Lalande 21185 (8.3 ly).

    The largest nearby star is Sirius, a bright main-sequence star roughly 8.6 light-years away and roughly twice the Sun's mass and that is orbited by a white dwarf, Sirius B. The nearest brown dwarfs are the binary Luhman 16 system at 6.6 light-years. Other systems within ten light-years are the binary red-dwarf system Luyten 726-8 (8.7 ly) and the solitary red dwarf Ross 154 (9.7 ly). [162] The closest solitary Sun-like star to the Solar System is Tau Ceti at 11.9 light-years. It has roughly 80% of the Sun's mass but only 60% of its luminosity. [163] The closest known free-floating planetary-mass object to the Sun is WISE 0855−0714, [164] an object with a mass less than 10 Jupiter masses roughly 7 light-years away.

    Comparison with extrasolar systems

    Compared to many other planetary systems, the Solar System stands out in lacking planets interior to the orbit of Mercury. [165] [166] The known Solar System also lacks super-Earths (Planet Nine could be a super-Earth beyond the known Solar System). [165] Uncommonly, it has only small rocky planets and large gas giants elsewhere planets of intermediate size are typical—both rocky and gas—so there is no "gap" as seen between the size of Earth and of Neptune (with a radius 3.8 times as large). Also, these super-Earths have closer orbits than Mercury. [165] This led to the hypothesis that all planetary systems start with many close-in planets, and that typically a sequence of their collisions causes consolidation of mass into few larger planets, but in case of the Solar System the collisions caused their destruction and ejection. [167] [168]

    The orbits of Solar System planets are nearly circular. Compared to other systems, they have smaller orbital eccentricity. [165] Although there are attempts to explain it partly with a bias in the radial-velocity detection method and partly with long interactions of a quite high number of planets, the exact causes remain undetermined. [165] [169]

    This section is a sampling of Solar System bodies, selected for size and quality of imagery, and sorted by volume. Some large objects are omitted here (notably Eris, Haumea, Makemake, and Nereid) because they have not been imaged in high quality.

    1. ^ ab As of August 27, 2019.
    2. ^Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar System" and "solar system" structures in their naming guidelines document. The name is commonly rendered in lower case ("solar system"), as, for example, in the Oxford English Dictionary and Merriam-Webster's 11th Collegiate Dictionary.
    3. ^ The natural satellites (moons) orbiting the Solar System's planets are an example of the latter.
    4. ^ Historically, several other bodies were once considered planets, including, from its discovery in 1930 until 2006, Pluto. See Former planets.
    5. ^ The two moons larger than Mercury are Ganymede, which orbits Jupiter, and Titan, which orbits Saturn. Although bigger than Mercury, both moons have less than half its mass. In addition, the radius of Jupiter's moon Callisto is over 98% that of Mercury.
    6. ^ abcde According to IAU definitions, objects orbiting the Sun are classified dynamically and physically into three categories: planets, dwarf planets, and small Solar System bodies.
      • A planet is any body orbiting the Sun whose mass is sufficient for gravity to have pulled it into a (near-)spherical shape and that has cleared its immediate neighbourhood of all smaller objects. By this definition, the Solar System has eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Because it has not cleared its neighbourhood of other Kuiper belt objects, Pluto does not fit this definition. [5]
      • A dwarf planet is a body orbiting the Sun that is massive enough to be made near-spherical by its own gravity but that has not cleared planetesimals from its neighbourhood and is also not a satellite. [5] Pluto is a dwarf planet and the IAU has recognized or named four other bodies in the Solar System under the expectation that they will turn out to be dwarf planets: Ceres, Haumea, Makemake, and Eris. [6] Other objects commonly expected to be dwarf planets include Gonggong, Sedna, Orcus, and Quaoar. [7] In a reference to Pluto, other dwarf planets orbiting in the trans-Neptunian region are sometimes called "plutoids", [8] though this term is seldom used.
      • The remaining objects orbiting the Sun are known as small Solar System bodies. [5]
    7. ^ ab The mass of the Solar System excluding the Sun, Jupiter and Saturn can be determined by adding together all the calculated masses for its largest objects and using rough calculations for the masses of the Oort cloud (estimated at roughly 3 Earth masses), [21] the Kuiper belt (estimated at roughly 0.1 Earth mass) [22] and the asteroid belt (estimated to be 0.0005 Earth mass) [23] for a total, rounded upwards, of

    37 Earth masses, or 8.1% of the mass in orbit around the Sun. With the combined masses of Uranus and Neptune (