1 00:00:01,800 --> 00:00:07,849 The first step towards resolving everything was gathering precise data and 2 00:00:07,849 --> 00:00:13,898 the name most commonly associated with this new data gathering is Tycho Brahe 3 00:00:13,898 --> 00:00:19,947 who in 1580 makes very, very detailed observations of planetary motion with an 4 00:00:19,947 --> 00:00:23,980 unprecedented accuracy, and these are very useful 5 00:00:23,980 --> 00:00:29,936 Interestingly Brahe got the brilliant equipment and the patronage he needed to 6 00:00:29,936 --> 00:00:35,391 make these observations by making a failed attempt to prove that comets and 7 00:00:35,391 --> 00:00:40,774 other such unpredictable changes in the sky are in fact terrestrial events. 8 00:00:40,774 --> 00:00:45,869 Things that happen on earth, not far like say meteors or shooting stars. 9 00:00:45,869 --> 00:00:50,750 they're not, but this didn't sit well with current world views. 10 00:00:50,750 --> 00:00:55,092 The important thing for us is that he made these very, very precise 11 00:00:55,092 --> 00:01:00,148 measurements and some of them he shared with Johannes Kepler, who came to work 12 00:01:00,148 --> 00:01:04,491 for him as an assistant. And in 1609 after playing with the data 13 00:01:04,491 --> 00:01:09,871 and playing with the data, this was very precise data, close good enough that you 14 00:01:09,871 --> 00:01:14,927 could take into account the angular measurements including the position of 15 00:01:14,927 --> 00:01:20,307 earth relative to the planets in this heliocentric model that we're that Kepler 16 00:01:20,307 --> 00:01:23,775 was pursuing, precise enough that you could use these, 17 00:01:23,775 --> 00:01:28,660 these angular measurements to actually not just make a 3-dimensional model with 18 00:01:28,660 --> 00:01:33,589 ordering of the planets, but actually find predict the ratios of their sizes in 19 00:01:33,589 --> 00:01:38,581 other words you could tell whether Mars' orbit was seven times that of Earth or 20 00:01:38,581 --> 00:01:42,950 three times that of Earth in radius rather than just that it's larger. 21 00:01:42,950 --> 00:01:47,692 And with this precise data Kepler discovers much to his surprise that three 22 00:01:47,692 --> 00:01:52,497 very, very simple rules describe all of the motions of all of the planets and 23 00:01:52,497 --> 00:01:56,000 these rules are important so let's go through them. 24 00:01:56,000 --> 00:02:01,805 Kepler's First Law says, that the orbits of planets, the trajectories that planets 25 00:02:01,805 --> 00:02:05,819 follow are not circles. They're not circles upon circles. 26 00:02:05,819 --> 00:02:10,406 They're a simple geometric figure, he found this very surprising. 27 00:02:10,406 --> 00:02:13,273 They are ellipses. So what is an ellipse? 28 00:02:13,273 --> 00:02:19,007 Well, an ellipse, is an oval, squashed circle type thing, and it's characterized 29 00:02:19,007 --> 00:02:22,520 by two special points called the focii, the focus. 30 00:02:22,520 --> 00:02:25,518 then plural, the full side of the ellipse. 31 00:02:25,518 --> 00:02:31,652 And an ellipse, is a sum, is a set of all the points in the plane such that the sum 32 00:02:31,652 --> 00:02:35,332 of their distances from the two full side, is the same. 33 00:02:35,332 --> 00:02:40,716 So if I take any point on this ellipse, it's distance from this point, plus it's 34 00:02:40,716 --> 00:02:46,033 distance from that point are always the same and if I take these two points to be 35 00:02:46,033 --> 00:02:50,810 on top of each other then I am thus designing a circle because then those are 36 00:02:50,810 --> 00:02:55,465 just twice the distance from that one point, so if the two focal points on a 37 00:02:55,465 --> 00:02:58,834 top of each other then the ellipse is in fact a circle. 38 00:02:58,834 --> 00:03:03,978 So this is what an ellipses and Kepler first law says the orbits of all planets 39 00:03:03,978 --> 00:03:07,960 or ellipses such that one of the focal points is in fact the Sun. 40 00:03:07,960 --> 00:03:11,943 What's in the other focal point? Well, the simulation here gives you a 41 00:03:11,943 --> 00:03:14,253 hint. The other focus is the empty focus. 42 00:03:14,253 --> 00:03:17,429 There is nothing there. It has no physical significance. 43 00:03:17,429 --> 00:03:21,066 It's just a punked in space. It's not even the same for all the 44 00:03:21,066 --> 00:03:23,895 planets. So, the empty focus of Mercury's orbit is 45 00:03:23,895 --> 00:03:28,514 nowhere near Venus' orbit but they both share one focal point and that is where 46 00:03:28,514 --> 00:03:31,956 the sun is. So we need to know a little bit about the 47 00:03:31,956 --> 00:03:36,233 geometry of an ellipse. So again an ellipse is characterized you 48 00:03:36,233 --> 00:03:42,247 see as I run here by this effect, the sum of these two distances is always the same 49 00:03:42,247 --> 00:03:47,392 and I get some particular size and we characterize an ellipse by the size of 50 00:03:47,392 --> 00:03:50,450 its. Semi minor axis to the half of the 51 00:03:50,450 --> 00:03:55,213 diameter if you will, of the ellipse. Perpendicular, aligned through the 52 00:03:55,213 --> 00:03:58,275 center. Perpendicular to the line between the 53 00:03:58,275 --> 00:04:03,107 focii, that's the shorter axis. So that's why it's a minor axis and this 54 00:04:03,107 --> 00:04:06,669 is half of it. And then the semi-major axis, which is 55 00:04:06,669 --> 00:04:10,583 the longer radius. If this is a circle, they'd both be the 56 00:04:10,583 --> 00:04:13,673 radius. The longer one is the semi-major axis. 57 00:04:13,673 --> 00:04:19,023 That's along the line between the focii. And an eclip, ellipse is characterized, 58 00:04:19,023 --> 00:04:23,531 either by giving these two numbers, or alternatively, giving one of them. 59 00:04:23,531 --> 00:04:28,356 Typically we give the semi-major axis. And the parameter called eccentricity 60 00:04:28,356 --> 00:04:32,356 that measures how different the two axises are from each other. 61 00:04:32,356 --> 00:04:37,500 So eccentricity zero is when the focii are on top of each other, and you have a 62 00:04:37,500 --> 00:04:43,431 circle in fact, an eccentricity one which this won't allow me to achieve, is the 63 00:04:43,431 --> 00:04:48,856 case where the eclip, ellipse is so smashed down that it becomes a straight 64 00:04:48,856 --> 00:04:54,570 line, and the semi minor axis vanishes. the eccentricities of, the planets, you 65 00:04:54,570 --> 00:05:00,140 can reproduce the most eccentric planetary orbit is Mercury's, and that it 66 00:05:00,140 --> 00:05:05,276 has an eccentricity of about 0.2. The eccentricity of the earth is closer 67 00:05:05,276 --> 00:05:08,913 to 02. which means that it's very close to a circle indeed. 68 00:05:08,913 --> 00:05:11,994 This is roughly what the earth's orbit looks like. 69 00:05:11,994 --> 00:05:17,107 So this is Kepler's first law, the orbit of any planet is an ellipse, and the sun 70 00:05:17,107 --> 00:05:19,880 is at one of the focal point of that ellipse. 71 00:05:19,880 --> 00:05:26,984 The second law states that as a planet, as a planet that we again exaggerate the 72 00:05:26,984 --> 00:05:34,088 electricity of this, as a planet orbits the Sun Kepler says it sweeps out, the 73 00:05:34,088 --> 00:05:40,679 line between the planet and the Sun sweeps out equal areas in equal times, so 74 00:05:40,679 --> 00:05:47,110 this will give us a demonstration. This turns on a sweep for 75 00:05:47,110 --> 00:05:52,430 particular amount of time and I can start it whenever I want and the point is that 76 00:05:52,430 --> 00:05:57,558 what this means is the areas of all these triangular shapes have to be the same, 77 00:05:57,558 --> 00:06:02,109 the implication is that when the planet is near the Sun, it needs to be 78 00:06:02,109 --> 00:06:07,238 travelling faster so the stubby triangles are abroad whereas when the planet is 79 00:06:07,238 --> 00:06:12,366 farther from the Sun, it can traverse slower because the longer triangles can 80 00:06:12,366 --> 00:06:16,137 be kind of narrow. So not only do Kepler's laws tell you the 81 00:06:16,137 --> 00:06:21,122 shape of the orbit but also the relative speed with which the planet goes, 82 00:06:21,122 --> 00:06:25,983 it goes fastest when it's nearest the sun, this point is called perihelion, the 83 00:06:25,983 --> 00:06:30,844 point of nearest approach to the sun. And it's always along the major axis you 84 00:06:30,844 --> 00:06:35,386 can see, and at the other end of the major axis is the point of farthest 85 00:06:35,386 --> 00:06:40,524 distance from the sun, aphelion, which is where the planet moves most slowly. 86 00:06:40,524 --> 00:06:46,100 So these are Kepler's first two laws. And let's go back and summarize that. 87 00:06:46,100 --> 00:06:50,771 So, we said Kepler's First Law was that the orbit of every planet is an ellipse. 88 00:06:50,771 --> 00:06:55,502 And these ellipses for the actual planets in the Solar System are very close to 89 00:06:55,502 --> 00:06:58,795 being circles. the second law tells us how a, planet, 90 00:06:58,795 --> 00:07:01,507 moves faster or slower as it orbits the sun. 91 00:07:01,507 --> 00:07:06,007 This is this law of equal areas. The implication is that the planet moves 92 00:07:06,007 --> 00:07:10,939 fastest near perihelion and slowest near aphelion when it's far from the sun. 93 00:07:10,939 --> 00:07:13,651 This is not very dramatic for, say the earth. 94 00:07:13,651 --> 00:07:18,644 For objects that might orbit the sun in for more eccentric orbit, which are 95 00:07:18,644 --> 00:07:23,760 sometimes very near the sun and sometimes very far from the sun, say comets this 96 00:07:23,760 --> 00:07:28,014 effect is much more dramatic. So when we get to, more eccentric orbits, 97 00:07:28,014 --> 00:07:31,937 which exist in the universe, we will have to consider this, aspect of 98 00:07:31,937 --> 00:07:36,503 Kepler's second law more seriously. And this is enough to determine all the 99 00:07:36,503 --> 00:07:40,533 orbits of the planets. And this leads to agreement with 100 00:07:40,533 --> 00:07:45,754 planetary positions to a precision, by now there were precise observations, that 101 00:07:45,754 --> 00:07:51,040 neither the Copernician model as it was stated nor the Ptolemaic model could 102 00:07:51,040 --> 00:07:53,617 achieve. And this is a very simple, very 103 00:07:53,617 --> 00:07:58,639 straightforward geometric construction. So Kepler was sure that he was on to 104 00:07:58,639 --> 00:08:01,961 something. Now the third law is different in the 105 00:08:01,961 --> 00:08:05,744 sense that it does not address the motion of a planet. 106 00:08:05,744 --> 00:08:10,718 It's a relation between the orbits of the, the motions of the different 107 00:08:10,718 --> 00:08:14,010 planets. Remember that Kepler by now had enough 108 00:08:14,010 --> 00:08:19,824 information to measure the actual size of the semi-major axes of the planets, at 109 00:08:19,824 --> 00:08:23,677 least their ratios. So one could decide, let us call the 110 00:08:23,677 --> 00:08:27,110 semi-major axis of earth's ellipse one something. 111 00:08:27,110 --> 00:08:31,826 We call it one astronomical unit. So by convention, the definition of 112 00:08:31,826 --> 00:08:37,582 something called an astronomical unit is that the semi-major axis of an ellipse is 113 00:08:37,582 --> 00:08:42,077 typically called a. We will often call this R because 114 00:08:42,077 --> 00:08:47,739 whenever possible, we'll be talking about circles, and for a circle, the semi-major 115 00:08:47,739 --> 00:08:52,352 axis as we saw, is the radius. The semi-major axis of Earth's orbit 116 00:08:52,352 --> 00:08:55,672 defines a unit of distance called an astronomical unit. 117 00:08:55,672 --> 00:08:59,765 And so we could always measure distances in astronomical units, and later figure 118 00:08:59,765 --> 00:09:02,220 out how many meters are in an astronomical unit. 119 00:09:02,220 --> 00:09:06,320 Something that was difficult for Kepler to do, though he had some measurements, 120 00:09:06,320 --> 00:09:09,699 we'll talk later about how precisely we know what an AU is. 121 00:09:09,699 --> 00:09:13,937 And what Kepler knows is he then knows the semi-major axes for all of the 122 00:09:13,937 --> 00:09:18,232 planets in units of an astronomical unit, or at least he knows their ratios. 123 00:09:18,232 --> 00:09:22,642 And what he also knows, their sidereal periods, because he has the motion down, 124 00:09:22,642 --> 00:09:26,937 and because if you want we can get it from the synodic period using the 125 00:09:26,937 --> 00:09:31,404 Copernican calculation, although since things are not circles you have to be a 126 00:09:31,404 --> 00:09:35,036 little more careful. And he notices the following relation. 127 00:09:35,036 --> 00:09:40,009 The square of the period, for any planet, and the cube, of, the semi major axis, 128 00:09:40,009 --> 00:09:42,953 are related by a constant of proportionality. 129 00:09:42,953 --> 00:09:47,534 Now I can always find a number, such that P squared is K times A cubed. 130 00:09:47,534 --> 00:09:52,441 Just divide P squared by A cubed. The point is that if you divide P squared 131 00:09:52,441 --> 00:09:57,741 by A cubed, for each of the five planets that Kepler knows about, you get the same 132 00:09:57,741 --> 00:10:00,102 answer. And this is very important because this 133 00:10:00,102 --> 00:10:03,813 is then not a property of the planet, some of the planet, property of the solar 134 00:10:03,813 --> 00:10:07,714 system, there is something that all these planets share and it's the value of this 135 00:10:07,714 --> 00:10:11,008 ratio. There might be something interesting here 136 00:10:11,008 --> 00:10:16,095 and it's worth expressing the same perhaps a different way. 137 00:10:16,095 --> 00:10:21,897 So remember that we can write the period of a planet that it the, of the planet's 138 00:10:21,897 --> 00:10:27,986 orbit, the sidereal period can be related to let me imagine that we are only doing 139 00:10:27,986 --> 00:10:32,930 circular orbit so R and a are the same thing and I will call AR. 140 00:10:32,930 --> 00:10:38,948 And so I can write the period, relate the period to the radius of the orbit and the 141 00:10:38,948 --> 00:10:44,314 speed, which I will assume uniform because it's a circle with which, the 142 00:10:44,314 --> 00:10:48,954 planet orbits the sun. So the period is simply the circumference 143 00:10:48,954 --> 00:10:55,822 of the orbit, two pi R divided by the speed with which the planet moves. 144 00:10:55,822 --> 00:11:03,785 So this is my expression for the period and A is simply R in this case so 145 00:11:03,785 --> 00:11:10,994 Keppler's Law becomes, well, I'd have to square this thing so 4 146 00:11:10,994 --> 00:11:17,020 pi squared R squared over V squared is K times R cubed. 147 00:11:17,020 --> 00:11:21,080 And I have some enticing cancellations here. 148 00:11:21,080 --> 00:11:25,831 I can cancel R squared and leave just one power of R over here. 149 00:11:25,831 --> 00:11:32,829 And what I can find is an equation that we might find use for later that says, if 150 00:11:32,829 --> 00:11:39,654 you know how far from the sun a planet orbits, from this you can figure out its 151 00:11:39,654 --> 00:11:43,628 period. From this, you can figure out the speed 152 00:11:43,628 --> 00:11:49,762 with which it's moving multiplying by v squared and dividing by KR, I find that V 153 00:11:49,762 --> 00:11:52,771 squared is 4. pi squared over KR, a relation, to which 154 00:11:52,771 --> 00:11:58,158 we will have a time to return. And, what is the numerical value of K? 155 00:11:58,158 --> 00:12:04,161 Well, K, is a kind of funny physical constant the first that, of its kind but 156 00:12:04,161 --> 00:12:09,164 we'll meet many of them. Remember that A is a length in, meters or 157 00:12:09,164 --> 00:12:15,243 astronomical units or whatever it is, P is a length of time, so K is some number 158 00:12:15,243 --> 00:12:18,630 of perhaps seconds squared per meters cubed. 159 00:12:18,630 --> 00:12:23,762 It is a completely different number of hours where per mile cubed, K is the 160 00:12:23,762 --> 00:12:29,300 physical constant which depends on the units you are using, you can always pick 161 00:12:29,300 --> 00:12:34,230 your units of distance and time to make K equal to 1 if you so desire. 162 00:12:34,230 --> 00:12:40,278 it natural units it, that of that we will try to use, seconds and meters it most 163 00:12:40,278 --> 00:12:44,690 certainly is not one. But the important thing for us is that K 164 00:12:44,690 --> 00:12:50,597 whatever it is, is the same for all the planets and that is hinting at some deep 165 00:12:50,597 --> 00:12:54,796 underlying physics. Because it's something that is true for 166 00:12:54,796 --> 00:12:59,017 all of them. Setting this aside for a minute we have 167 00:12:59,017 --> 00:13:03,951 other progress. Galileo about a year after Kepler obtains 168 00:13:03,951 --> 00:13:09,590 his laws, gets his hands on the newest technology, a telescope, a spyglass. 169 00:13:09,590 --> 00:13:12,084 And we don't know if he was the first to do it. 170 00:13:12,084 --> 00:13:16,011 But he was certainly the first to publish this and to become known for it. 171 00:13:16,011 --> 00:13:18,240 He used a telescope to look up in the sky. 172 00:13:18,240 --> 00:13:24,058 And, he finds many, many, many, many, exciting things when he looks up at the 173 00:13:24,058 --> 00:13:30,912 sky with this newfangled invention. the first thing he finds is he finds that 174 00:13:30,912 --> 00:13:34,340 Venus, the planet Venus, goes through phases. 175 00:13:34,340 --> 00:13:37,352 So it's not surprising to us. It's a chunk of rock. 176 00:13:37,352 --> 00:13:41,027 It's illuminated by the sun. It's angled to the sun's changes. 177 00:13:41,027 --> 00:13:45,366 So Venus goes through phases, but in particular the relation between the 178 00:13:45,366 --> 00:13:50,186 phases of Venus and its position in the sky show that sometimes Venus is closer 179 00:13:50,186 --> 00:13:54,765 to Earth than the Sun is, and we get the effect, effectively a new Venus, just 180 00:13:54,765 --> 00:13:58,500 like the new moon works. But on the other hand, unlike the full 181 00:13:58,500 --> 00:14:03,264 moon, which happens when the moon is on the other side of Earth from the sun 182 00:14:03,264 --> 00:14:08,127 Venus is never that twelve hours away from the sun in right ascension, Venus is 183 00:14:08,127 --> 00:14:12,498 always near the sun remember. A full Venus happens when Venus is on the 184 00:14:12,498 --> 00:14:17,767 other side of the sun from Earth. And what this means is this does not fit 185 00:14:17,767 --> 00:14:23,926 in with the precise parameters of the Ptolemaic Model, but it fits very nicely 186 00:14:23,926 --> 00:14:28,032 into the, Keplerian or even the Copernician model. 187 00:14:28,032 --> 00:14:31,665 Also, he discovers that Jupiter has satellites. 188 00:14:31,665 --> 00:14:37,508 He sees the four Galilean Moons, or as he, seeking patronage, calls them, the 189 00:14:37,508 --> 00:14:41,814 Medician Stars. moving back and forth around the image of 190 00:14:41,814 --> 00:14:47,198 Jupiter and he realizes quickly that what he is seeing is something, a collection 191 00:14:47,198 --> 00:14:51,364 of bodies orbiting Jupiter. Well they're clearly not orbiting the 192 00:14:51,364 --> 00:14:56,107 Earth so this is an important. A piece of breaking down the cultural 193 00:14:56,107 --> 00:15:00,393 objection to the earth. Moving, he sees various exciting things, 194 00:15:00,393 --> 00:15:05,785 he sees mountains on the moon, he sees sun spots on the sun, he sees some weird 195 00:15:05,785 --> 00:15:10,832 structure on Saturn that later Huygens discovers are the rings of Saturn. 196 00:15:10,832 --> 00:15:16,708 so Galileo finds many things with his telescope and in particular the evidence 197 00:15:16,708 --> 00:15:20,580 of the faces of Venus is really the smoking gun that 198 00:15:20,580 --> 00:15:24,689 Dooms the geocentric picture. Or the Ptolemaic Geocentric picture as 199 00:15:24,689 --> 00:15:28,451 we, we will talk about later. Whether you think that the whole, the 200 00:15:28,451 --> 00:15:32,791 Earth is stationary or the whole universe is doing a complicated motion, or 201 00:15:32,791 --> 00:15:35,870 something else. At the end of the day, that's very, 202 00:15:35,870 --> 00:15:38,498 difficult and almost philosophical question. 203 00:15:38,498 --> 00:15:43,396 We'll see what we can have to say about why we prefer one description over the 204 00:15:43,396 --> 00:15:47,935 other, but in particular the fact that Venus is sometimes behind the Sun and 205 00:15:47,935 --> 00:15:50,802 sometimes in front of the Sun, that's now a fact. 206 00:15:50,802 --> 00:15:53,789 and this does not fit with the Ptolemaic Model. 207 00:15:53,789 --> 00:15:58,388 Galileo also, applied himself to beginnings of the science of mechanics, 208 00:15:58,388 --> 00:16:03,166 the study of motion, and is well known for, formulating the, the, what is called 209 00:16:03,166 --> 00:16:06,795 the Principle of Inertia. As he put it, an object will retain its 210 00:16:06,795 --> 00:16:09,205 state of motion unless disturbed externally. 211 00:16:09,205 --> 00:16:12,765 Now, we are all familiar with this in the following painful sense. 212 00:16:12,765 --> 00:16:15,230 If you have a refrigerator that's not moving. 213 00:16:15,230 --> 00:16:19,506 And you want to set it in motion, you want to change its state of motion from 214 00:16:19,506 --> 00:16:22,812 rest to motion, you have to expend quite a bit of effort 215 00:16:22,812 --> 00:16:26,912 to move that refrigerator. But Galileo reminds us is but then if you 216 00:16:26,912 --> 00:16:31,615 let it go the refrigerator will stop. What Galileo realized is that this is an 217 00:16:31,615 --> 00:16:36,619 artifact of rubbing against the floor and if you put the refrigerator on ice or on 218 00:16:36,619 --> 00:16:41,141 roller skates and started it moving it would be just as hard to stop it or 219 00:16:41,141 --> 00:16:45,844 change its direction of motion as it was to get it started in the first place. 220 00:16:45,844 --> 00:16:49,281 And that is an abstraction that is, cannot be understated. 221 00:16:49,281 --> 00:16:53,140 Galileo made many, many, many Brilliant deductions. 222 00:16:53,140 --> 00:16:58,380 But he never really got mechanics right, what was missing for Galileo. 223 00:16:58,380 --> 00:17:02,930 Among many things but the technical ingredient that was missing was that the 224 00:17:02,930 --> 00:17:07,480 mathematics required to discuss mechanics correctly hadn't been invented yet. 225 00:17:07,480 --> 00:17:13,880 real progress await Isaac Newton. And Newton also didn't find the right 226 00:17:13,880 --> 00:17:18,764 mathematics, it hadn't been invented yet so Newton just ahead and invented it, 227 00:17:18,764 --> 00:17:23,458 that was calculus and we will have to work around it because we don't use 228 00:17:23,458 --> 00:17:26,185 calculus. So we've made incredible progress. 229 00:17:26,185 --> 00:17:30,688 Look, the planets have and, and in general the heavens have been removed 230 00:17:30,688 --> 00:17:35,890 from some our spiritual realm of spheres and in all have objects that are a given 231 00:17:35,890 --> 00:17:40,774 distance and a given position in the universe, its a 3D world out there, there 232 00:17:40,774 --> 00:17:44,770 are moons that orbit the planets. This is all a physical system. 233 00:17:44,770 --> 00:17:47,495 We can study it. We can observe it. 234 00:17:47,495 --> 00:17:49,980 Galileo observes the moon. As a. 235 00:17:49,980 --> 00:17:53,401 Moon, something to be observed, not some heavenly object. 236 00:17:53,401 --> 00:17:57,880 we have Kepler's laws, and the predictions of Kepler's laws from such 237 00:17:57,880 --> 00:18:00,991 simplicity, such precision, is extremely compelling. 238 00:18:00,991 --> 00:18:05,656 Moreover, it turns out that these laws are a lot more universal than Kepler 239 00:18:05,656 --> 00:18:09,451 could have imagined. In fact they govern orbiting, they govern 240 00:18:09,451 --> 00:18:12,997 any kind of orbiting system. They govern the Solar System. 241 00:18:12,997 --> 00:18:17,788 They govern the various moons of Jupiter, as was discovered not long after he 242 00:18:17,788 --> 00:18:21,256 published his book. They govern every orbiting system, in 243 00:18:21,256 --> 00:18:25,829 some sense electrons in an atom. Each system is characterized perhaps by a 244 00:18:25,829 --> 00:18:29,986 different Kepler constant K. That was a property of our solar system 245 00:18:29,986 --> 00:18:34,960 but their relation, the fact that objects are ellipses and the central objects is 246 00:18:34,960 --> 00:18:39,024 at one of the focal points. And that the semi-major axis and the 247 00:18:39,024 --> 00:18:43,573 periods are related by P squared equals a constant times A cube for object, 248 00:18:43,573 --> 00:18:48,365 different electrons orbiting a nucleus, or different moons orbiting the same 249 00:18:48,365 --> 00:18:51,251 planet. This, it turns out, goes way beyond what 250 00:18:51,251 --> 00:18:53,901 Kepler put into his model comes out of it. 251 00:18:53,901 --> 00:18:58,886 And in physics, when something is that universal, it tells you that there's some 252 00:18:58,886 --> 00:19:03,304 fundamental law underlying it. There's a reason why all of these thing 253 00:19:03,304 --> 00:19:06,270 share a behavior and again, these underlying, 254 00:19:06,270 --> 00:19:12,120 physical laws of which Kepler was just finding the manifestation in the Solar 255 00:19:12,120 --> 00:19:17,896 System, were, waiting discovery by Newton, so we're now ready to discuss Sir 256 00:19:17,896 --> 00:19:18,347 Isaac.