Two stars, each
of mass $M$, at a distance $d$ from each other are rotating in a circular path
around their center of mass. An asteroid with mass $m$ $(m<<M)$ moves
along the axis of the system perpendicular to the plane of the stars’ orbit.
Assuming that at a certain point on the z-axis, the net gravitational force
is zero, for a small displacement of the asteroid from that point, the time
period of its simple harmonic motion is $T_p $. The time period of motion of
the stars is $T_s$. Determine $\frac{T_s}{T_p} $. Hint: For small $x$, $(1+x)^n
\cong 1+nx $.

**Dhaka Regional-2023, Category : D**

Gravity Astrophysics Simple Harmonic Motion

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