- #1

danago

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**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:

[tex]

T_e = \sqrt {\frac{{4\pi ^2 r^3 }}{{Gm_e}}}

[/tex]

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:

[tex]

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

[/tex]

Comparing these two, we see that [tex]T_p = \frac{1}{{10}}T_e [/tex]

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.