{"id":170,"date":"2022-02-07T23:03:54","date_gmt":"2022-02-07T23:03:54","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/astronomy\/?post_type=chapter&#038;p=170"},"modified":"2022-04-22T16:01:25","modified_gmt":"2022-04-22T16:01:25","slug":"3-2-newtons-great-synthesis","status":"publish","type":"chapter","link":"https:\/\/pressbooks.ccconline.org\/astronomy\/chapter\/3-2-newtons-great-synthesis\/","title":{"raw":"3.2 Newton's Great Synthesis","rendered":"3.2 Newton&#8217;s Great Synthesis"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Learning Objectives<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168979446101\" class=\" \">By the end of this section, you will be able to:<\/p>\r\n\r\n<ul>\r\n \t<li style=\"list-style-type: none\">\r\n<ul>\r\n \t<li>Describe Newton\u2019s three laws of motion<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<ul id=\"fs-id1163976438349\">\r\n \t<li>Explain how Newton\u2019s three laws of motion relate to momentum<\/li>\r\n \t<li>Define mass, volume, and density and how they differ<\/li>\r\n \t<li>Define angular momentum<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1163976420462\" class=\" \">It was the genius of Isaac\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term91\" class=\"no-emphasis\" data-type=\"term\">Newton<\/span>\u00a0that found a conceptual framework that completely explained the observations and rules assembled by Galileo, Brahe, Kepler, and others. Newton was born in Lincolnshire, England, in the year after Galileo\u2019s death (Figure 3.6). Against the advice of his mother, who wanted him to stay home and help with the family farm, he entered Trinity College at Cambridge in 1661 and eight years later was appointed professor of mathematics. Among Newton\u2019s contemporaries in England were architect Christopher Wren, authors Aphra Behn and Daniel Defoe, and composer G. F. Handel.<\/p>\r\n\r\n<div id=\"OSC_Astro_03_02_Newton\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_03_02_Newton\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"325\"]<img id=\"2\" src=\"https:\/\/openstax.org\/apps\/archive\/20210823.155019\/resources\/3db40569e39c17b63a0d74e7da3dc2bbf2d382dd\" alt=\"Portrait of Isaac Newton.\" width=\"325\" height=\"446\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a03.6<\/strong>\u00a0Isaac Newton (1643\u20131727), 1689 Portrait by Sir Godfrey Kneller.\u00a0Isaac Newton\u2019s work on the laws of motion, gravity, optics, and mathematics laid the foundations for much of physical science.[\/caption]<\/figure>\r\n<\/div>\r\n<section id=\"fs-id1163976439987\" data-depth=\"1\">\r\n<h3 data-type=\"title\">Newton\u2019s Laws of Motion<\/h3>\r\n<p id=\"fs-id1163976520304\" class=\" \">As a young man in college, Newton became interested in natural philosophy, as science was then called. He worked out some of his first ideas on machines and optics during the plague years of 1665 and 1666, when students were sent home from college. Newton, a moody and often difficult man, continued to work on his ideas in private, even inventing new mathematical tools to help him deal with the complexities involved. Eventually, his friend Edmund\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term92\" class=\"no-emphasis\" data-type=\"term\">Halley<\/span>\u00a0(profiled in\u00a0Comets and Asteroids: Debris of the Solar System) prevailed on him to collect and publish the results of his remarkable investigations on motion and gravity. The result was a volume that set out the underlying system of the physical world,\u00a0<em data-effect=\"italics\">Philosophiae Naturalis Principia Mathematica<\/em>. The\u00a0<em data-effect=\"italics\">Principia<\/em>, as the book is generally known, was published at Halley\u2019s expense in 1687.<\/p>\r\n<p id=\"fs-id1163976472518\" class=\" \">At the very beginning of the\u00a0<em data-effect=\"italics\">Principia<\/em>, Newton proposes three laws that would govern the motions of all objects:<\/p>\r\n\r\n<ul id=\"fs-id1163976453716\" data-bullet-style=\"bullet\">\r\n \t<li><span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term93\" data-type=\"term\">Newton\u2019s first law<\/span>: Every object will continue to be in a state of rest or move at a constant speed in a straight line unless it is compelled to change by an outside force.<\/li>\r\n \t<li><span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term94\" data-type=\"term\">Newton\u2019s second law<\/span>: The change of motion of a body is proportional to and in the direction of the force acting on it.<\/li>\r\n \t<li><span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term95\" data-type=\"term\">Newton\u2019s third law<\/span>: For every action there is an equal and opposite reaction (<em data-effect=\"italics\">or:<\/em>\u00a0the mutual actions of two bodies upon each other are always equal and act in opposite directions).<\/li>\r\n<\/ul>\r\n<p id=\"fs-id1163976462693\" class=\" \">In the original Latin, the three laws contain only 59 words, but those few words set the stage for modern science. Let us examine them more carefully.<\/p>\r\n\r\n<\/section><section id=\"fs-id1163976458539\" data-depth=\"1\">\r\n<h3 data-type=\"title\">Interpretation of Newton\u2019s Laws<\/h3>\r\n<p id=\"fs-id1163976427461\" class=\" \">Newton\u2019s first law is a restatement of one of Galileo\u2019s discoveries, called the\u00a0<em data-effect=\"italics\">conservation of momentum<\/em>. The law states that in the absence of any outside influence, there is a measure of a body\u2019s motion, called its\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term96\" data-type=\"term\">momentum<\/span>, that remains unchanged. You may have heard the term momentum used in everyday expressions, such as \u201cThis bill in Congress has a lot of momentum; it\u2019s going to be hard to stop.\u201d<\/p>\r\n<p id=\"fs-id1163976443348\" class=\" \">Newton\u2019s first law is sometimes called the\u00a0<em data-effect=\"italics\">law of inertia<\/em>, where inertia is the tendency of objects (and legislatures) to keep doing what they are already doing. In other words, a stationary object stays put, and a moving object keeps moving unless some force intervenes.<\/p>\r\n<p id=\"fs-id1163976520021\" class=\" \">Let\u2019s define the precise meaning of momentum\u2014it depends on three factors: (1) speed\u2014how fast a body moves (zero if it is stationary), (2) the direction of its motion, and (3) its mass\u2014a measure of the amount of matter in a body, which we will discuss later. Scientists use the term\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term97\" data-type=\"term\">velocity<\/span>\u00a0to describe the speed and direction of motion. For example, 20 kilometers per hour due south is velocity, whereas 20 kilometers per hour just by itself is speed. Momentum then can be defined as an object\u2019s mass times its velocity.<\/p>\r\n<p id=\"fs-id1163976443052\" class=\" \">It\u2019s not so easy to see this rule in action in the everyday world because of the many forces acting on a body at any one time. One important force is friction, which generally slows things down. If you roll a ball along the sidewalk, it eventually comes to a stop because the sidewalk exerts a rubbing force on the ball. But in the space between the stars, where there is so little matter that friction is insignificant, objects can in fact continue to move (to coast) indefinitely.<\/p>\r\n<p id=\"fs-id1163976523775\" class=\" \">The momentum of a body can change only under the action of an outside influence. Newton\u2019s second law expresses\u00a0<em data-effect=\"italics\">force<\/em>\u00a0in terms of its ability to change momentum with time. A force (a push or a pull) has both size and direction. When a force is applied to a body, the momentum changes in the direction of the applied force. This means that a force is required to change either the speed or the direction of a body, or both\u2014that is, to start it moving, to speed it up, to slow it down, to stop it, or to change its direction.<\/p>\r\n<p id=\"fs-id1163976439808\" class=\" \">As you learned in\u00a0Observing the Sky: The Birth of Astronomy, the rate of change in an object\u2019s velocity is called\u00a0<em data-effect=\"italics\">acceleration<\/em>. Newton showed that the acceleration of a body was proportional to the force being applied to it. Suppose that after a long period of reading, you push an astronomy book away from you on a long, smooth table. (We use a smooth table so we can ignore friction.) If you push the book steadily, it will continue to speed up as long as you are pushing it. The harder you push the book, the larger its acceleration will be. How much a force will accelerate an object is also determined by the object\u2019s mass. If you kept pushing a pen with the same force with which you pushed the textbook, the pen\u2014having less mass\u2014would be accelerated to a greater speed.<\/p>\r\n<p id=\"fs-id1163976559032\" class=\" \">Newton\u2019s third law is perhaps the most profound of the rules he discovered. Basically, it is a generalization of the first law, but it also gives us a way to define mass. If we consider a system of two or more objects isolated from outside influences, Newton\u2019s first law says that the total momentum of the objects should remain constant. Therefore, any change of momentum within the system must be balanced by another change that is equal and opposite so that the momentum of the entire system is not changed.<\/p>\r\n<p id=\"fs-id1163976542721\" class=\" \">This means that forces in nature do not occur alone: we find that in each situation there is always a\u00a0<em data-effect=\"italics\">pair<\/em>\u00a0of forces that are equal to and opposite each other. If a force is exerted on an object, it must be exerted by something else, and the object will exert an equal and opposite force back on that something. We can look at a simple example to demonstrate this.<\/p>\r\n<p id=\"fs-id1163976443974\" class=\" \">Suppose that a daredevil astronomy student\u2014and avid skateboarder\u2014wants to jump from his second-story dorm window onto his board below (we don\u2019t recommend trying this!). The force pulling him down after jumping (as we will see in the next section) is the force of gravity between him and Earth. Both he and Earth must experience the same total change of momentum because of the influence of these mutual forces. So, both the student and Earth are accelerated by each other\u2019s pull. However, the student does much more of the moving. Because Earth has enormously greater mass, it can experience the same change of momentum by accelerating only a very small amount. Things fall toward Earth all the time, but the acceleration of our planet as a result is far too small to be measured.<\/p>\r\n<p id=\"fs-id1163976530595\" class=\" \">A more obvious example of the mutual nature of forces between objects is familiar to all who have batted a baseball. The recoil you feel as you swing your bat shows that the ball exerts a force on it during the impact, just as the bat does on the ball. Similarly, when a rifle you are bracing on your shoulder is discharged, the force pushing the bullet out of the muzzle is equal to the force pushing backward upon the gun and your shoulder.<\/p>\r\n<p id=\"fs-id1163976538164\" class=\" \">This is the principle behind jet engines and rockets: the force that discharges the exhaust gases from the rear of the rocket is accompanied by the force that pushes the rocket forward. The exhaust gases need not push against air or Earth; a rocket actually operates best in a vacuum (Figure 3.7).<\/p>\r\n\r\n<div id=\"OSC_Astro_03_02_ThirdLaw\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_03_02_ThirdLaw\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]<img id=\"4\" src=\"https:\/\/openstax.org\/apps\/archive\/20210823.155019\/resources\/e2d21ffda8a5b4a13055eb8eea1f738e3f5253c9\" alt=\"Photograph of the Space Shuttle Discovery at liftoff.\" width=\"487\" height=\"387\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a03.7\u00a0<\/strong>Demonstrating Newton\u2019s Third Law.\u00a0The U.S. Space Shuttle (here launching\u00a0Discovery), powered by three fuel engines burning liquid oxygen and liquid hydrogen, with two solid fuel boosters, demonstrates Newton\u2019s third law. (credit: modification of work by NASA)[\/caption]<\/figure>\r\n<div class=\"os-caption-container\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFor more about Isaac Newton\u2019s life and work, check out this\u00a0<a href=\"https:\/\/openstax.org\/l\/30IsaacNewTime\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">timeline page<\/a>\u00a0with snapshots from his career, produced by the British Broadcasting Corporation (BBC).\r\n\r\n<\/div>\r\n<\/div>\r\n<h3 data-type=\"title\">Mass, Volume, and Density<\/h3>\r\n<p id=\"fs-id1163976444185\" class=\" \">Before we go on to discuss Newton\u2019s other work, we want to take a brief look at some terms that will be important to sort out clearly. We begin with\u00a0<em data-effect=\"italics\">mass,<\/em>\u00a0which is a measure of the amount of material within an object.<\/p>\r\n<p id=\"fs-id1163976466092\" class=\" \">The\u00a0<em data-effect=\"italics\">volume<\/em>\u00a0of an object is the measure of the physical space it occupies. Volume is measured in cubic units, such as cubic centimeters or liters. The\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term98\" class=\"no-emphasis\" data-type=\"term\">volume<\/span>\u00a0is the \u201csize\u201d of an object. A penny and an inflated balloon may both have the same\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term99\" class=\"no-emphasis\" data-type=\"term\">mass<\/span>, but they have very different volumes. The reason is that they also have very different\u00a0<em data-effect=\"italics\">densities<\/em>, which is a measure of how much mass there is per unit volume. Specifically,\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term100\" data-type=\"term\">density<\/span>\u00a0is the mass divided by the volume. Note that in everyday language we often use \u201cheavy\u201d and \u201clight\u201d as indications of density (rather than weight) as, for instance, when we say that iron is heavy or that whipped cream is light.<\/p>\r\n<p id=\"fs-id1163976529854\" class=\" has-noteref\">The units of density that will be used in this book are grams per cubic centimeter ([latex]{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex]).<sup id=\"footnote-ref1\" data-type=\"footnote-number\"><a role=\"doc-noteref\" href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/3-2-newtons-great-synthesis#fs-id1163976455934\" data-type=\"footnote-link\">1<\/a><\/sup>\u00a0If a block of some material has a mass of 300 grams and a volume of 100 [latex]{\\rm{c}}{{\\rm{m}}^3}[\/latex] , its density is [latex]3{\\rm{ g}}\/{\\rm{c}}{{\\rm{m}}^3}[\/latex]. Familiar materials span a considerable range in density, from artificial materials such as plastic insulating foam (less than [latex]0.1{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex]) to gold ([latex]19.3{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex]).\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/3-2-newtons-great-synthesis#fs-id1163976527872\">Table 3.1<\/a>\u00a0gives the densities of some familiar materials. In the astronomical universe, much more remarkable densities can be found, all the way from a comet\u2019s tail ([latex]{10^{ - 16}}{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex]) to a collapsed \u201cstar corpse\u201d called a neutron star ([latex]{10^{15}}{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex]).<\/p>\r\n\r\n<div class=\"os-table os-top-titled-container\">\r\n<div class=\"os-table-title\"><\/div>\r\n<table id=\"fs-id1163976527872\" class=\"grid landscape aligncenter\" summary=\"Table 3.1 \"><caption>Table 3.1 Densities of Common Materials<\/caption>\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Material<\/th>\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Density ([latex]{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex])<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Gold<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">19.3<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Lead<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">11.3<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Iron<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">7.9<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Earth (bulk)<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">5.5<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Rock (typical)<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">2.5<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Water<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">1<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Wood (typical)<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.8<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Insulating foam<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.1<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Silica gel<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.02<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">To sum up, mass is <\/span><em style=\"text-align: initial;font-size: 1em\" data-effect=\"italics\">how much<\/em><span style=\"text-align: initial;font-size: 1em\">, volume is\u00a0<\/span><em style=\"text-align: initial;font-size: 1em\" data-effect=\"italics\">how big<\/em><span style=\"text-align: initial;font-size: 1em\">, and density is\u00a0<\/span><em style=\"text-align: initial;font-size: 1em\" data-effect=\"italics\">how tightly packed<\/em><span style=\"text-align: initial;font-size: 1em\">.<\/span><\/div>\r\n<\/div>\r\n<div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nYou can play with a\u00a0<a href=\"https:\/\/openstax.org\/l\/30phetsimdenmas\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">simple animation<\/a>\u00a0demonstrating the relationship between the concepts of density, mass, and volume, and find out why objects like wood float in water.\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"page_8dc7024f-0626-4a47-9ddb-34ecd15db2f6\" class=\" chapter-content-module\" data-type=\"page\" data-cnxml-to-html-ver=\"2.1.2\"><section id=\"fs-id1163976451019\" data-depth=\"1\">\r\n<h3 data-type=\"title\">Angular Momentum<\/h3>\r\n<p id=\"fs-id1163976553331\" class=\" \">A concept that is a bit more complex, but important for understanding many astronomical objects, is\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term101\" data-type=\"term\">angular momentum<\/span>, which is a measure of the rotation of a body as it revolves around some fixed point (an example is a planet orbiting the Sun). The angular momentum of an object is defined as the product of its mass, its velocity, and its distance from the fixed point around which it revolves.<\/p>\r\n<p id=\"fs-id1163976404199\" class=\" \">If these three quantities remain constant\u2014that is, if the motion of a particular object takes place at a constant velocity at a fixed distance from the spin center\u2014then the angular momentum is also a constant. Kepler\u2019s second law is a consequence of the\u00a0<em data-effect=\"italics\">conservation of angular momentum<\/em>. As a planet approaches the Sun on its elliptical orbit and the distance to the spin center decreases, the planet speeds up to conserve the angular momentum. Similarly, when the planet is farther from the Sun, it moves more slowly.<\/p>\r\n<p id=\"fs-id1163976518154\" class=\" \">The\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term102\" class=\"no-emphasis\" data-type=\"term\">conservation of angular momentum<\/span>\u00a0is illustrated by figure skaters, who bring their arms and legs in to spin more rapidly, and extend their arms and legs to slow down (Figure 3.8). You can duplicate this yourself on a well-oiled swivel stool by starting yourself spinning slowly with your arms extended and then pulling your arms in. Another example of the conservation of angular momentum is a shrinking cloud of dust or a star collapsing on itself (both are situations that you will learn about as you read on). As material moves to a lesser distance from the spin center, the speed of the material increases to conserve angular momentum.<\/p>\r\n\r\n<div id=\"OSC_Astro_03_02_Angular\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_03_02_Angular\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"731\"]<img id=\"6\" src=\"https:\/\/openstax.org\/apps\/archive\/20210823.155019\/resources\/d78cefc9fa06b3c77258aecc5c6c55d9966c95ec\" alt=\"Illustration of Conservation of Angular Momentum. At left a skater is illustrated with her arms and right leg outstretched, with cartoon motion lines indicating slow rotation. At right the skater has her arms folded across her chest and right leg crossed over her left. The motion lines now indicate a faster rotation.\" width=\"731\" height=\"463\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a03.8<\/strong>\u00a0Conservation of Angular Momentum.\u00a0When a spinning figure skater brings in her arms, their distance from her spin center is smaller, so her speed increases. When her arms are out, their distance from the spin center is greater, so she slows down.[\/caption]<\/figure>\r\n<\/div>\r\n<\/section><\/div>\r\n<div data-type=\"footnote-refs\">\r\n<h3 data-type=\"footnote-refs-title\">Footnotes<\/h3>\r\n<ul data-list-type=\"bulleted\" data-bullet-style=\"none\">\r\n \t<li id=\"fs-id1163976455934\" data-type=\"footnote-ref\"><a role=\"doc-backlink\" href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/3-2-newtons-great-synthesis#footnote-ref1\">1<\/a> <span data-type=\"footnote-ref-content\">Generally we use standard metric (or SI) units in this book. The proper metric unit of density in that system is [latex]{\\rm{kg\/}}{{\\rm{m}}^3}[\/latex]. But to most people, [latex]{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex]\u00a0provides a more meaningful unit because the density of water is exactly [latex]1{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex], and this is useful information for comparison. Density expressed in [latex]{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex]\u00a0is sometimes called specific density or specific weight.<\/span><\/li>\r\n<\/ul>\r\n<div class=\"textbox\">This book was adapted from the following: Fraknoi, A., Morrison, D., &amp; Wolff, S. C. (2016). 3.2 Newton\u2019s Great Synthesis. In <i>Astronomy<\/i>. OpenStax. https:\/\/openstax.org\/books\/astronomy\/pages\/3-2-newtons-great-synthesis under a <a href=\"http:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Creative Commons Attribution License 4.0<\/a><\/div>\r\n<div>Access the entire book for free at <a href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction\">https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction<\/a><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Learning Objectives<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168979446101\" class=\"\">By the end of this section, you will be able to:<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>Describe Newton\u2019s three laws of motion<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul id=\"fs-id1163976438349\">\n<li>Explain how Newton\u2019s three laws of motion relate to momentum<\/li>\n<li>Define mass, volume, and density and how they differ<\/li>\n<li>Define angular momentum<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1163976420462\" class=\"\">It was the genius of Isaac\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term91\" class=\"no-emphasis\" data-type=\"term\">Newton<\/span>\u00a0that found a conceptual framework that completely explained the observations and rules assembled by Galileo, Brahe, Kepler, and others. Newton was born in Lincolnshire, England, in the year after Galileo\u2019s death (Figure 3.6). Against the advice of his mother, who wanted him to stay home and help with the family farm, he entered Trinity College at Cambridge in 1661 and eight years later was appointed professor of mathematics. Among Newton\u2019s contemporaries in England were architect Christopher Wren, authors Aphra Behn and Daniel Defoe, and composer G. F. Handel.<\/p>\n<div id=\"OSC_Astro_03_02_Newton\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_03_02_Newton\">\n<figure style=\"width: 325px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"2\" src=\"https:\/\/openstax.org\/apps\/archive\/20210823.155019\/resources\/3db40569e39c17b63a0d74e7da3dc2bbf2d382dd\" alt=\"Portrait of Isaac Newton.\" width=\"325\" height=\"446\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a03.6<\/strong>\u00a0Isaac Newton (1643\u20131727), 1689 Portrait by Sir Godfrey Kneller.\u00a0Isaac Newton\u2019s work on the laws of motion, gravity, optics, and mathematics laid the foundations for much of physical science.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<section id=\"fs-id1163976439987\" data-depth=\"1\">\n<h3 data-type=\"title\">Newton\u2019s Laws of Motion<\/h3>\n<p id=\"fs-id1163976520304\" class=\"\">As a young man in college, Newton became interested in natural philosophy, as science was then called. He worked out some of his first ideas on machines and optics during the plague years of 1665 and 1666, when students were sent home from college. Newton, a moody and often difficult man, continued to work on his ideas in private, even inventing new mathematical tools to help him deal with the complexities involved. Eventually, his friend Edmund\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term92\" class=\"no-emphasis\" data-type=\"term\">Halley<\/span>\u00a0(profiled in\u00a0Comets and Asteroids: Debris of the Solar System) prevailed on him to collect and publish the results of his remarkable investigations on motion and gravity. The result was a volume that set out the underlying system of the physical world,\u00a0<em data-effect=\"italics\">Philosophiae Naturalis Principia Mathematica<\/em>. The\u00a0<em data-effect=\"italics\">Principia<\/em>, as the book is generally known, was published at Halley\u2019s expense in 1687.<\/p>\n<p id=\"fs-id1163976472518\" class=\"\">At the very beginning of the\u00a0<em data-effect=\"italics\">Principia<\/em>, Newton proposes three laws that would govern the motions of all objects:<\/p>\n<ul id=\"fs-id1163976453716\" data-bullet-style=\"bullet\">\n<li><span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term93\" data-type=\"term\">Newton\u2019s first law<\/span>: Every object will continue to be in a state of rest or move at a constant speed in a straight line unless it is compelled to change by an outside force.<\/li>\n<li><span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term94\" data-type=\"term\">Newton\u2019s second law<\/span>: The change of motion of a body is proportional to and in the direction of the force acting on it.<\/li>\n<li><span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term95\" data-type=\"term\">Newton\u2019s third law<\/span>: For every action there is an equal and opposite reaction (<em data-effect=\"italics\">or:<\/em>\u00a0the mutual actions of two bodies upon each other are always equal and act in opposite directions).<\/li>\n<\/ul>\n<p id=\"fs-id1163976462693\" class=\"\">In the original Latin, the three laws contain only 59 words, but those few words set the stage for modern science. Let us examine them more carefully.<\/p>\n<\/section>\n<section id=\"fs-id1163976458539\" data-depth=\"1\">\n<h3 data-type=\"title\">Interpretation of Newton\u2019s Laws<\/h3>\n<p id=\"fs-id1163976427461\" class=\"\">Newton\u2019s first law is a restatement of one of Galileo\u2019s discoveries, called the\u00a0<em data-effect=\"italics\">conservation of momentum<\/em>. The law states that in the absence of any outside influence, there is a measure of a body\u2019s motion, called its\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term96\" data-type=\"term\">momentum<\/span>, that remains unchanged. You may have heard the term momentum used in everyday expressions, such as \u201cThis bill in Congress has a lot of momentum; it\u2019s going to be hard to stop.\u201d<\/p>\n<p id=\"fs-id1163976443348\" class=\"\">Newton\u2019s first law is sometimes called the\u00a0<em data-effect=\"italics\">law of inertia<\/em>, where inertia is the tendency of objects (and legislatures) to keep doing what they are already doing. In other words, a stationary object stays put, and a moving object keeps moving unless some force intervenes.<\/p>\n<p id=\"fs-id1163976520021\" class=\"\">Let\u2019s define the precise meaning of momentum\u2014it depends on three factors: (1) speed\u2014how fast a body moves (zero if it is stationary), (2) the direction of its motion, and (3) its mass\u2014a measure of the amount of matter in a body, which we will discuss later. Scientists use the term\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term97\" data-type=\"term\">velocity<\/span>\u00a0to describe the speed and direction of motion. For example, 20 kilometers per hour due south is velocity, whereas 20 kilometers per hour just by itself is speed. Momentum then can be defined as an object\u2019s mass times its velocity.<\/p>\n<p id=\"fs-id1163976443052\" class=\"\">It\u2019s not so easy to see this rule in action in the everyday world because of the many forces acting on a body at any one time. One important force is friction, which generally slows things down. If you roll a ball along the sidewalk, it eventually comes to a stop because the sidewalk exerts a rubbing force on the ball. But in the space between the stars, where there is so little matter that friction is insignificant, objects can in fact continue to move (to coast) indefinitely.<\/p>\n<p id=\"fs-id1163976523775\" class=\"\">The momentum of a body can change only under the action of an outside influence. Newton\u2019s second law expresses\u00a0<em data-effect=\"italics\">force<\/em>\u00a0in terms of its ability to change momentum with time. A force (a push or a pull) has both size and direction. When a force is applied to a body, the momentum changes in the direction of the applied force. This means that a force is required to change either the speed or the direction of a body, or both\u2014that is, to start it moving, to speed it up, to slow it down, to stop it, or to change its direction.<\/p>\n<p id=\"fs-id1163976439808\" class=\"\">As you learned in\u00a0Observing the Sky: The Birth of Astronomy, the rate of change in an object\u2019s velocity is called\u00a0<em data-effect=\"italics\">acceleration<\/em>. Newton showed that the acceleration of a body was proportional to the force being applied to it. Suppose that after a long period of reading, you push an astronomy book away from you on a long, smooth table. (We use a smooth table so we can ignore friction.) If you push the book steadily, it will continue to speed up as long as you are pushing it. The harder you push the book, the larger its acceleration will be. How much a force will accelerate an object is also determined by the object\u2019s mass. If you kept pushing a pen with the same force with which you pushed the textbook, the pen\u2014having less mass\u2014would be accelerated to a greater speed.<\/p>\n<p id=\"fs-id1163976559032\" class=\"\">Newton\u2019s third law is perhaps the most profound of the rules he discovered. Basically, it is a generalization of the first law, but it also gives us a way to define mass. If we consider a system of two or more objects isolated from outside influences, Newton\u2019s first law says that the total momentum of the objects should remain constant. Therefore, any change of momentum within the system must be balanced by another change that is equal and opposite so that the momentum of the entire system is not changed.<\/p>\n<p id=\"fs-id1163976542721\" class=\"\">This means that forces in nature do not occur alone: we find that in each situation there is always a\u00a0<em data-effect=\"italics\">pair<\/em>\u00a0of forces that are equal to and opposite each other. If a force is exerted on an object, it must be exerted by something else, and the object will exert an equal and opposite force back on that something. We can look at a simple example to demonstrate this.<\/p>\n<p id=\"fs-id1163976443974\" class=\"\">Suppose that a daredevil astronomy student\u2014and avid skateboarder\u2014wants to jump from his second-story dorm window onto his board below (we don\u2019t recommend trying this!). The force pulling him down after jumping (as we will see in the next section) is the force of gravity between him and Earth. Both he and Earth must experience the same total change of momentum because of the influence of these mutual forces. So, both the student and Earth are accelerated by each other\u2019s pull. However, the student does much more of the moving. Because Earth has enormously greater mass, it can experience the same change of momentum by accelerating only a very small amount. Things fall toward Earth all the time, but the acceleration of our planet as a result is far too small to be measured.<\/p>\n<p id=\"fs-id1163976530595\" class=\"\">A more obvious example of the mutual nature of forces between objects is familiar to all who have batted a baseball. The recoil you feel as you swing your bat shows that the ball exerts a force on it during the impact, just as the bat does on the ball. Similarly, when a rifle you are bracing on your shoulder is discharged, the force pushing the bullet out of the muzzle is equal to the force pushing backward upon the gun and your shoulder.<\/p>\n<p id=\"fs-id1163976538164\" class=\"\">This is the principle behind jet engines and rockets: the force that discharges the exhaust gases from the rear of the rocket is accompanied by the force that pushes the rocket forward. The exhaust gases need not push against air or Earth; a rocket actually operates best in a vacuum (Figure 3.7).<\/p>\n<div id=\"OSC_Astro_03_02_ThirdLaw\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_03_02_ThirdLaw\">\n<figure style=\"width: 487px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"4\" src=\"https:\/\/openstax.org\/apps\/archive\/20210823.155019\/resources\/e2d21ffda8a5b4a13055eb8eea1f738e3f5253c9\" alt=\"Photograph of the Space Shuttle Discovery at liftoff.\" width=\"487\" height=\"387\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a03.7\u00a0<\/strong>Demonstrating Newton\u2019s Third Law.\u00a0The U.S. Space Shuttle (here launching\u00a0Discovery), powered by three fuel engines burning liquid oxygen and liquid hydrogen, with two solid fuel boosters, demonstrates Newton\u2019s third law. (credit: modification of work by NASA)<\/figcaption><\/figure>\n<\/figure>\n<div class=\"os-caption-container\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<p>For more about Isaac Newton\u2019s life and work, check out this\u00a0<a href=\"https:\/\/openstax.org\/l\/30IsaacNewTime\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">timeline page<\/a>\u00a0with snapshots from his career, produced by the British Broadcasting Corporation (BBC).<\/p>\n<\/div>\n<\/div>\n<h3 data-type=\"title\">Mass, Volume, and Density<\/h3>\n<p id=\"fs-id1163976444185\" class=\"\">Before we go on to discuss Newton\u2019s other work, we want to take a brief look at some terms that will be important to sort out clearly. We begin with\u00a0<em data-effect=\"italics\">mass,<\/em>\u00a0which is a measure of the amount of material within an object.<\/p>\n<p id=\"fs-id1163976466092\" class=\"\">The\u00a0<em data-effect=\"italics\">volume<\/em>\u00a0of an object is the measure of the physical space it occupies. Volume is measured in cubic units, such as cubic centimeters or liters. The\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term98\" class=\"no-emphasis\" data-type=\"term\">volume<\/span>\u00a0is the \u201csize\u201d of an object. A penny and an inflated balloon may both have the same\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term99\" class=\"no-emphasis\" data-type=\"term\">mass<\/span>, but they have very different volumes. The reason is that they also have very different\u00a0<em data-effect=\"italics\">densities<\/em>, which is a measure of how much mass there is per unit volume. Specifically,\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term100\" data-type=\"term\">density<\/span>\u00a0is the mass divided by the volume. Note that in everyday language we often use \u201cheavy\u201d and \u201clight\u201d as indications of density (rather than weight) as, for instance, when we say that iron is heavy or that whipped cream is light.<\/p>\n<p id=\"fs-id1163976529854\" class=\"has-noteref\">The units of density that will be used in this book are grams per cubic centimeter ([latex]{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex]).<sup id=\"footnote-ref1\" data-type=\"footnote-number\"><a role=\"doc-noteref\" href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/3-2-newtons-great-synthesis#fs-id1163976455934\" data-type=\"footnote-link\">1<\/a><\/sup>\u00a0If a block of some material has a mass of 300 grams and a volume of 100 [latex]{\\rm{c}}{{\\rm{m}}^3}[\/latex] , its density is [latex]3{\\rm{ g}}\/{\\rm{c}}{{\\rm{m}}^3}[\/latex]. Familiar materials span a considerable range in density, from artificial materials such as plastic insulating foam (less than [latex]0.1{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex]) to gold ([latex]19.3{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex]).\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/3-2-newtons-great-synthesis#fs-id1163976527872\">Table 3.1<\/a>\u00a0gives the densities of some familiar materials. In the astronomical universe, much more remarkable densities can be found, all the way from a comet\u2019s tail ([latex]{10^{ - 16}}{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex]) to a collapsed \u201cstar corpse\u201d called a neutron star ([latex]{10^{15}}{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex]).<\/p>\n<div class=\"os-table os-top-titled-container\">\n<div class=\"os-table-title\"><\/div>\n<table id=\"fs-id1163976527872\" class=\"grid landscape aligncenter\" summary=\"Table 3.1\">\n<caption>Table 3.1 Densities of Common Materials<\/caption>\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Material<\/th>\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Density ([latex]{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex])<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Gold<\/td>\n<td data-valign=\"top\" data-align=\"left\">19.3<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Lead<\/td>\n<td data-valign=\"top\" data-align=\"left\">11.3<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Iron<\/td>\n<td data-valign=\"top\" data-align=\"left\">7.9<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Earth (bulk)<\/td>\n<td data-valign=\"top\" data-align=\"left\">5.5<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Rock (typical)<\/td>\n<td data-valign=\"top\" data-align=\"left\">2.5<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Water<\/td>\n<td data-valign=\"top\" data-align=\"left\">1<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Wood (typical)<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.8<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Insulating foam<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.1<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Silica gel<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.02<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">To sum up, mass is <\/span><em style=\"text-align: initial;font-size: 1em\" data-effect=\"italics\">how much<\/em><span style=\"text-align: initial;font-size: 1em\">, volume is\u00a0<\/span><em style=\"text-align: initial;font-size: 1em\" data-effect=\"italics\">how big<\/em><span style=\"text-align: initial;font-size: 1em\">, and density is\u00a0<\/span><em style=\"text-align: initial;font-size: 1em\" data-effect=\"italics\">how tightly packed<\/em><span style=\"text-align: initial;font-size: 1em\">.<\/span><\/div>\n<\/div>\n<div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<p>You can play with a\u00a0<a href=\"https:\/\/openstax.org\/l\/30phetsimdenmas\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">simple animation<\/a>\u00a0demonstrating the relationship between the concepts of density, mass, and volume, and find out why objects like wood float in water.<\/p>\n<\/div>\n<\/div>\n<div id=\"page_8dc7024f-0626-4a47-9ddb-34ecd15db2f6\" class=\"chapter-content-module\" data-type=\"page\" data-cnxml-to-html-ver=\"2.1.2\">\n<section id=\"fs-id1163976451019\" data-depth=\"1\">\n<h3 data-type=\"title\">Angular Momentum<\/h3>\n<p id=\"fs-id1163976553331\" class=\"\">A concept that is a bit more complex, but important for understanding many astronomical objects, is\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term101\" data-type=\"term\">angular momentum<\/span>, which is a measure of the rotation of a body as it revolves around some fixed point (an example is a planet orbiting the Sun). The angular momentum of an object is defined as the product of its mass, its velocity, and its distance from the fixed point around which it revolves.<\/p>\n<p id=\"fs-id1163976404199\" class=\"\">If these three quantities remain constant\u2014that is, if the motion of a particular object takes place at a constant velocity at a fixed distance from the spin center\u2014then the angular momentum is also a constant. Kepler\u2019s second law is a consequence of the\u00a0<em data-effect=\"italics\">conservation of angular momentum<\/em>. As a planet approaches the Sun on its elliptical orbit and the distance to the spin center decreases, the planet speeds up to conserve the angular momentum. Similarly, when the planet is farther from the Sun, it moves more slowly.<\/p>\n<p id=\"fs-id1163976518154\" class=\"\">The\u00a0<span id=\"8dc7024f-0626-4a47-9ddb-34ecd15db2f6_term102\" class=\"no-emphasis\" data-type=\"term\">conservation of angular momentum<\/span>\u00a0is illustrated by figure skaters, who bring their arms and legs in to spin more rapidly, and extend their arms and legs to slow down (Figure 3.8). You can duplicate this yourself on a well-oiled swivel stool by starting yourself spinning slowly with your arms extended and then pulling your arms in. Another example of the conservation of angular momentum is a shrinking cloud of dust or a star collapsing on itself (both are situations that you will learn about as you read on). As material moves to a lesser distance from the spin center, the speed of the material increases to conserve angular momentum.<\/p>\n<div id=\"OSC_Astro_03_02_Angular\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_03_02_Angular\">\n<figure style=\"width: 731px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"6\" src=\"https:\/\/openstax.org\/apps\/archive\/20210823.155019\/resources\/d78cefc9fa06b3c77258aecc5c6c55d9966c95ec\" alt=\"Illustration of Conservation of Angular Momentum. At left a skater is illustrated with her arms and right leg outstretched, with cartoon motion lines indicating slow rotation. At right the skater has her arms folded across her chest and right leg crossed over her left. The motion lines now indicate a faster rotation.\" width=\"731\" height=\"463\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a03.8<\/strong>\u00a0Conservation of Angular Momentum.\u00a0When a spinning figure skater brings in her arms, their distance from her spin center is smaller, so her speed increases. When her arms are out, their distance from the spin center is greater, so she slows down.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/section>\n<\/div>\n<div data-type=\"footnote-refs\">\n<h3 data-type=\"footnote-refs-title\">Footnotes<\/h3>\n<ul data-list-type=\"bulleted\" data-bullet-style=\"none\">\n<li id=\"fs-id1163976455934\" data-type=\"footnote-ref\"><a role=\"doc-backlink\" href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/3-2-newtons-great-synthesis#footnote-ref1\">1<\/a> <span data-type=\"footnote-ref-content\">Generally we use standard metric (or SI) units in this book. The proper metric unit of density in that system is [latex]{\\rm{kg\/}}{{\\rm{m}}^3}[\/latex]. But to most people, [latex]{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex]\u00a0provides a more meaningful unit because the density of water is exactly [latex]1{\\rm{ g\/c}}{{\\rm{m}}^3}[\/latex], and this is useful information for comparison. Density expressed in [latex]{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex]\u00a0is sometimes called specific density or specific weight.<\/span><\/li>\n<\/ul>\n<div class=\"textbox\">This book was adapted from the following: Fraknoi, A., Morrison, D., &amp; Wolff, S. C. (2016). 3.2 Newton\u2019s Great Synthesis. In <i>Astronomy<\/i>. OpenStax. https:\/\/openstax.org\/books\/astronomy\/pages\/3-2-newtons-great-synthesis under a <a href=\"http:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Creative Commons Attribution License 4.0<\/a><\/div>\n<div>Access the entire book for free at <a href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction\">https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"author":33,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-170","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":148,"_links":{"self":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/170","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/users\/33"}],"version-history":[{"count":14,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/170\/revisions"}],"predecessor-version":[{"id":765,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/170\/revisions\/765"}],"part":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/parts\/148"}],"metadata":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/170\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/media?parent=170"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapter-type?post=170"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/contributor?post=170"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/license?post=170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}