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本帖最后由 polar_bear 于 2015-1-9 13:22 编辑 # h! Y7 `8 }( u$ L2 Y7 Z y. ?
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http://curious.astro.cornell.edu/question.php?number=467
* l. [4 c( j8 K: Q/ S! dWhy do planets have elliptical orbits?
! x1 ], c( j+ d9 lWhy do planets have elliptical orbits and why do some satellites when launched in lower orbits, go around earth in elliptical orbits? ; i6 Y o; ^ I
- _1 a3 X$ m# L1 Z$ w JAt first glance it may seem odd that a force such as gravity, which pulls the planets straight in toward the center of mass, should result in elliptical orbits! But in fact it is quite straightforward to understand why this should be so.
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It is certainly possible to set up a satellite so that it has a circular orbit (a circle is just an ellipse whose foci coincide). Gravity can only pull in the direction toward the planet. The inertia of the satellite makes it want to travel in a straight line, but if it does so, its velocity is no longer perfectly perpendicular to the pull of gravity, so gravity pulls it in; this will remove part of the velocity, but as the satellite is also falling inward, it gets a new component of velocity due to the acceleration of gravity. In a circular orbit, we know that the ground speed is constant, so these two effects must perfectly cancel one another out to leave the speed of the satellite unchanged. Now imagine that we fire the satellite's boosters so that its ground speed increases. Now the desire of the satellite to go straight is stronger, so the two effects do not cancel perfectly, and the ground speed will vary. You can see how this corresponds to an elliptical orbit, and how a planet orbiting the Sun behaves in the same way. (Of course, planets have no boosters, but think about what effect the initial velocity of the planet due to the process of its formation would have--what happens if a planet is formed with only a small initial velocity, far from the Sun, or if it is formed with a large velocity, very near to the Sun? What happens if the inital velocity of the planet
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http://curious.astro.cornell.edu/question.php?number=461
! [0 o: [* X ]( {* y" \" m2 |Does the Sun orbit the Earth as well as the Earth orbiting the Sun?5 ?# [/ M* T, V
Is it true that Sun also revolves around the Earth? If yes, apart from convenience, is there another reason why we use the Solar-centered coordinate system ?9 m; _4 u9 Y, s1 v7 D
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Technically, what is going on is that the Earth, Sun and all the planets are orbiting around the center of mass of the solar system. This is actually how planets orbiting other stars are often detected, by searching for the motion of the stars they orbit that is caused by the fact that the star is orbiting the center of mass of the system, causing it to wobble on the sky. " z* k" Y4 }, O4 l7 l6 J
6 B) L1 g8 R( \5 z3 h1 X* t+ J. ^% OThe center of mass of our solar system very close to the Sun itself, but not exactly at the Sun's center (it is actually a little bit outside the radius of the Sun). However, since almost all of the mass within the solar system is contained in the Sun, its motion is only a slight wobble in comparison to the motion of the planets. Therefore, assuming that the Sun is stationary and the planets revolve around its center is a good enough approximation for most purposes.
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http://curious.astro.cornell.edu/question.php?number=334
9 Q- _0 ~- V! nWhat is the significance of the second focus of elliptical orbits of planets in our Solar System?
4 }4 y8 G7 L1 G% E& S SI just watched a PBS show on planetary motion and Kepler's Laws and had a couple of questions. According to Kepler's first law, the planets travel on an elliptical path with the Sun located at one of the two foci. Is there any significance to the other focus? I would think the gravitional pull of the Sun would contribute to the elliptical path, and that some other gravitional pull from the second focus would result in the elliptical orbit.
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Actually, both the Sun and the planets move around each other with their center of mass lying at the focus of the elliptical orbits. However, since the Sun contains 99.9% of the mass of the solar system, the center of mass is located almost at the Sun and so it looks like the planets are going around the Sun.
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# M" T9 v" t6 G; tThere is no real significance to the foci of the elliptical orbits. The same laws that govern the orbits of planets around the Sun also govern the motion of binary stars and in that case since the masses of the two stars may be roughly equal, the foci of the elliptical orbits may not correspond physically to any object. As I explained earlier, the Sun appears at one focus ony because it is so much more massive than any of the planets and so its center lies close to the focus (which is the actual location of the center of mass).
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Are each of the planetaryt orbits on a different plane? I would guess so, yet they each share a common focus (the Sun) in their elliptical orbits, a single point of intersection for each planer orbit, right? & k! B8 F1 k0 D _+ T4 w* P2 M
( {; ?9 j T- i- V, M4 J2 FStrictly speaking, you are correct and each orbit is in a different plane. However, because of the physics of planetary formation, all the planets are roughly in the same plane. There are of course slight differences, but to within about 10 degrees, all the planets are in the same plane. This is the reason why the planets appear to line up in the sky (when you can see many of them at the same time), and is also the reason why the planets are always found in one of the zodiac constellations.
7 C: A6 l# J, _3 q* z+ a虽然有些问题，不过可以一读。 |
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发表于 2015-1-9 16:20:49
发表于 2015-1-9 18:36:44
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