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A double star,with two star masses m1 & m2.They are rotating with constant angular speed. If max. distance of separation between them is R,find the angular speed of star in terms of m1,m2 & R
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2 years ago

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```                    Hi Shweta
The above ques will be done with the concept of reduced mass...

according to the concept of reduced mass when two  bodies rotate  about their common centre of mass such that a force of  attraction acts  between them and the dist.b/n the 2 bodies remains  constant then their  angular velocites are exactly same both in magnitude  and direction .the  results for  angular velocity and time period that u obtain for single  bodies can be  obtained by using the reduced mass of  2 body system .To  reduce the 2-body system to 1-body just consider 1 body of   mass=m(reduced mass) and consider its rotation about a fixed point at a   dist=dist between the 2 bodies.thus u get a simple circular motin whose   radius is known and the centrifugal force is balanced by the force of   attraction that was originally present between the bodies.

we can consider the 2-star system to be as 1 star having a massm=m1*m2/(m1+m2)  this will rotate in circular motion about a fixed  pt. and having  radius equal to the separation b/n the 2 bodies and the  force remaining  the same towards the centre as b4 which in this case is  the  gravitation force of interaction.

the equations will be
mw2R=Gm1m2/R2.   solving u get w=(1/R)(G(m1+m2)/R) ie 1/R*root(G(m1+m2)/R)

Hope it helps!

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2 years ago