Two stars each of one solar mass (= 2× 10³⁰ kg) are approaching each other for a head on collision. When they are a distance 109 km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 104 km. Assume the stars to remain undistorted until they collide. (Use the known value of G).

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Solution

Mass of each star, M = 2 × 10³⁰kg

Radius of each star, R = 10⁴ km = 10⁷ m

Distance between the stars, r = 10⁹ km = 10¹²m

For negligible speeds, v = 0 total energy of two stars separated at distance r

Now, consider the case when the stars are about to collide:

Velocity of the stars = v

Distance between the centers of the stars = 2R

Total kinetic energy of both stars

Total potential energy of both stars

Total energy of the two stars =

Using the law of conservation of energy, we can write:

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