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Nothing happens. The orbit of a planet is not dependent on its mass, only the mass of the sun.
anshul singh asked the Naked Scientists: Hi the naked scientists,What happens if mass of a planet reduces to its half without exerting any thrust (force) on it, what will happen to its orbit?ThanksWhat do you think?
Is the sun and the earth act as a binary star system? What happens to the rest of the planets?
I was assuming that the planet is much lighter than the Sun. However I think it fair to say that, in the spirit of the question (I thought), that you could define the orbit of a body around the sun to be relative to the sun. In this case the orbit still does not depend on the mass of the planet. If you take a solar system, with multiple bodies, the problem if analysed very strictly and to high accuracy, is indeed complex and probably cannot actually be analysed mathematically at all, but a solution would be reliant on computer modelling. Gm1m2/r2 = m2rω2So ω2 = Gm1/r3where ω = 2π/T where T is the time for a complete orbit (1 year for the earth)Note that m2 (the mass of the planet) cancels out.This is the relationship between distance to the the sun and orbit time that was derived empirically by Kepler.