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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. Gm_{1}m_{2}/r^{2} = m_{2}rω^{2}So ω^{2} = Gm_{1}/r^{3}where ω = 2π/T where T is the time for a complete orbit (1 year for the earth)Note that m_{2} (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.