# Keplers Law

Gold Member
A star has a mass approximately 100 times that of our sun. If a planet with the same mass as the earth is oribiting at a radius similar to that of the earths radius around the sun, how long would it take the planet to revolve around the star once?

Ok, the period of the earths rotation is given by:
$$T_e = \sqrt {\frac{{4\pi ^2 r^3 }}{{Gm_e}}}$$

If the radius remains the same, and the mass increases by a factor of 100, the period in comparison to the earths period is given by:

$$T_p = \frac{1}{{10}}\sqrt {\frac{{4\pi ^2 r^3 }}{{Gm_e}}}$$

Comparing these two, we see that $$T_p = \frac{1}{{10}}T_e$$

If the period of the earths revolution around the sun is 1 year i.e. 365 days, then the period of the other planet is one tenth of that i.e. 36.5 days.

It was an exam question and that was my working, and i got no marks for it. Where have i gone wrong?

Thanks,
Dan.

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learningphysics
Homework Helper
Looks right to me... only thing that maybe could be seen as a mistake is that you used "me"... with the subscript e... giving the impression that you might mean mass of the earth... instead of mass of the sun.