Question

A meteorite approaching a planet of mass M collides with an automatic space station orbiting the planet in a circular trajectory of radius R. The mass of the station is ten times as large as the mass of the meteorite . As a result of the collision, the meteorite sticks with the station which goes over to a new orbit with the minimum distance R/2 from the planet. Speed of the meteorite just before it collides with the space station is

Answer 1

We are given with
M = mass of planet
R = radius of circular trajectory of the satellite
ms = mass of the station
mm = mass of the meteorite
ms = 10 mm
R/2 = new orbit distance

The speed of the meteorite can be solved using the law of conservation of momentum
ms vs + mm vm = (ms + mm) v
Since the new orbit distance is half the original
v = 2 vs

Substitute and solve for vs