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  1. What is the simplest explanation that provides enough evidence for the first Kepler law?

i.e. that planets around the Sun travel on ellipses with the Sun at one of the two foci.

  1. Are the three Kepler laws valid in every planetary system with planets moving around a star (not necessarily being the Sun)?
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  • $\begingroup$ Around one star? Yes, it'll be as with the Sun. But some exoplanets orbit two stars, which complicates matters. $\endgroup$
    – J.G.
    Jan 20, 2023 at 13:00

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The simplest explanation is given by Newton's theory of Universal Gravity.

He showed mathematically that if gravity is an instantaneous inverse-square force acting in proportion to mass, and assuming his three laws of motion, then two spherical bodies will orbit each other in ellipses around the common centre of mass.

Keplers' laws only apply in those conditions, and in reality, the solar system has more than two bodies. And Newton's laws are only an approximation to General Relativity (and quantum mechanics). Fortunately, in many situations, such as a planet orbiting a star, Kepler's laws are still a very good approximation, because Newton's laws are a very good approximation to relativity (at everyday speeds), and because the interactions between the planets are much smaller than the interactions between the sun and each planet. So it is a very good approximation for the motion of a planet to apply Kepler's Laws

Alternately, the motion of the planets in the sky fits the motion predicted by Kepler's laws. This provides empirical confirmation of Kepler's laws, and so indirectly it supports Newton's theory of Gravity.

In extrasolar planetary systems, Newton's laws will still hold, as an approximation to Relativity. And as systems in which there are significant interactions between three bodies at once are highly chaotic, and unstable, such systems won't exist for long.

Therefore one would expect that in all systems Kepler's laws will hold (in an approximate way as they do in the solar system).

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    $\begingroup$ And it even applies to moons: Kepler himself noticed that (en.m.wikipedia.org/wiki/…). Of course, the constant in that case is not 1 UA^3/year^2. $\endgroup$ Jan 19, 2023 at 21:29
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    $\begingroup$ The question does ask for evidence, not theory. We should remember that scientific theories are built upon evidence and not the other way around. Theories do not serve as evidence. $\endgroup$
    – user253751
    Jan 20, 2023 at 12:32
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    $\begingroup$ It should be noted that Mercury's orbit deviates a small but noticeable amount from the predictions of Kepler's Laws, and the deviation was explained by General Relativity. $\endgroup$
    – Barmar
    Jan 20, 2023 at 16:38
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    $\begingroup$ @Barmar The relativistic corrections to Mercury's orbit are much smaller than the Newtonian perturbations caused by the other planets. Kepler's laws correspond to the Newtonian orbital motion of a single body of negligible mass (relative to the mass of the body it's orbiting). $\endgroup$
    – PM 2Ring
    Jan 20, 2023 at 17:48
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    $\begingroup$ @user253751 It actually asks for "the simplest explanation" An explanation is given in terms of a more fundamental theory. But it also asks for evidence, which is somewhat contradictory, but I've tried to cover that alternate interpretation of what the OP wants in my fourth paragraph. However, in reference to the second question, my understanding is that the OP is really asking if the same reason that planets obey Kepler's laws in the solar system also applies to other planetary systems, so the discussion of Newton's gravity is appropriate. $\endgroup$
    – James K
    Jan 20, 2023 at 21:11
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Kepler's laws have been found to be accurate for the motion of planets in our Solar System and have been used to predict the positions of planets and other celestial bodies. However, these laws have been tested and verified only for the Solar System and it is not clear if they will hold true for other planetary systems. It is possible that other systems may have different dynamics and orbits, and therefore Kepler's laws may not be applicable.

It's important to mention that Kepler's laws are a first step in understanding the dynamics of planetary systems, but they are not the final answer. They are based on Newton's laws of motion and the law of universal gravitation, which are more general and accurate laws that explain the motion of objects in any system. Therefore, these laws are considered as a special case of the Newton's laws.

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    $\begingroup$ It's a bold statement that it is not clear if Kepler's law will hold true for other planetary systems. For them not to be true for simple systems (one heavy object/system) laws of gravity would have to be different. And I have jet to hear anyone claiming that. $\endgroup$
    – Negdo
    Jan 20, 2023 at 12:41
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    $\begingroup$ Kepler did not base his laws on Newton's laws as Kepler died in 1630 and Newton was not even born until 1643. $\endgroup$ Jan 20, 2023 at 17:09

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