Question

Two equal-mass stars maintain a constant distance apart of 1.7×10¹¹ m and rotate about a point midway between them at a rate of one revolution every 21.6 yr .

A) Why don't the two stars crash into one another due to the gravitational force between them?

B) What must be the mass of each star? (Express your answer using two significant figures.)

Answer 1

a)

since the inward gravitational force is being balanced by centripetal force, hence due to equilibrium of forces, the net force acting on each mass is zero, so neither they comes close nor increase distance from each other.

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b)

using kepler's 3rdaw

T^2 = 4 pi^2 * R^3 / ( G M)

(21.6*365*24*3600)^2 = 4*3.14^2 * ( 1.7*10^11)^3 / ( 6.67*10^-11* M)

M = 6.3*10^27 kg

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