Question

A binary star system has two stars, each with the same mass as our sun, separated by 1.50×1012 m . A comet is very far away and essentially at rest. Slowly but surely, gravity pulls the comet toward the stars. Suppose the comet travels along a straight line that passes through the midpoint between the two stars. What is the speed at the comet's midpoint?

Answer 1

When the comet is very far away, it's kinetic energy is zero (since it is at rest)

Also it's gravitational potential energy is zero (since it is far away)

So total energy is zero.

calculate total energy when the comet is at the mid point. Due to conservation of energy this energy also must be zero.

L = distance between the stars = 1.50 x 10¹² m

$\frac{1}{2}mv^2-2\frac{GMm}{L/2}=0$

using M = mass of sun = 2 x 10³⁰ kg

G = 6.67 x 10^-11 N.m²/kg²

$v = \sqrt{\frac{8GM}{L}}$

v = 2.7 x 10⁴ m/s