Double Star


Consider the double star:

It consists of two planets of mass M and m separated by distance 'R'. They revolve around their common center of mass.

What is the time period of revolution for 'm'? For 'M'?

Explain the observation.

8 comments:

  1. Sambhav GuptaMarch 13, 2011 at 11:41 PM

    2(pi)[(R)^(3/2)] divided by sqrt[GMm]

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  2. Sambhav GuptaMarch 13, 2011 at 11:43 PM

    sry its sqrt[G(M+m)]

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  3. Sambhav GuptaMarch 13, 2011 at 11:43 PM

    time period is same for both, follows from conservation of momentum

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  4. AnujMarch 14, 2011 at 9:42 AM

    be more precise.

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  5. AnujMarch 14, 2011 at 9:57 AM

    This comment has been removed by the author.

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  6. Sambhav GuptaMarch 14, 2011 at 10:32 AM

    i corrected my answer in the second comment, it was a 'typo' in the first, and i think dimensions are alright in the second one

    there is no net force on the COM, so, it must not be moving, if time period is different, relative positions of both the planets are different, hence, COM should move, by contradiction, time period is same

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  7. AnujMarch 14, 2011 at 1:22 PM

    This comment has been removed by the author.

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  8. AnujMarch 14, 2011 at 1:27 PM

    ok..got it. you could have written the complete answer in the 2nd comment..

    its probably right then..

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