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The entire question is in the title .

It's the case for the solar system but is it always the case ? Can a planet do a revolution faster than another that is closer to the center ?

As far as I searched , it's not but I prefer ask here to be sure.

Of course I'm talking about similar orbits (all with the same eccentricity). (When I'm talking of the center, I mean the body in the center (in general a sun), even if it's not always the center)

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2 Answers 2

up vote 3 down vote accepted

You're talking about a year period, right? There is Kepler's Third Law:

$$ {S_1^3 \over S_2^3} = {P_1^2 \over P_2^2} .$$ where

  • S - is the distances between the 'center' and a planet
  • P - orbital period of the planet

Thus the further the planet is from the center (Sun), the longer its orbital period is. You can check that formula by taking examples of Earth (150million kilometers and 365days) and Mercury (58million kilometers, and you can calculate the length of its year).

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Kepler's Third Law says that the square of a planet's orbital period is proportional to the cube of its semi-major axis; $$ T^2 \propto a^3 $$ So if one planet has a larger semi-major axis than another, then its orbital period will necessarily be longer. Assuming that we define "closeness to the center" of a planet by the size of the semi-major axis of its orbit, the answer to your question is no.

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