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## Homework Statement

Suppose two stars are orbiting each other in circular orbits with angular speed ##\omega## .M1 is at distance r1 from CM wheras M2 is at distance r2 such that r1+r2=d where d is the distance between them . Now i have a little doubt whether the stars are orbiting around their common CM or they are orbiting each other . If we consider them orbiting CM then for M1 ##\frac{GM_1M_2}{d^2}=M_1\omega^2 r_1## .But it is wrong to write ##\frac{GM_1M_2}{d^2}=M_1\omega^2 d## .Could someone help me understand what is wrong with the latter expression ? Why can't we write centripetal acceleration to be ##M_1\omega^2 d##.Please pardon me for missing something obvious . Many thanks !

## Homework Equations

## The Attempt at a Solution

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