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

Question

Gianna

Physics

9 July, 18:58

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

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Spencer Wiggins · 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