a) A large asteroid of mass 71700 kg is at rest far away from any planets or sta

Question

a) A large asteroid of mass 71700 kg is at rest far away from any planets or stars. A much smaller asteroid, of mass 930 kg, is in a circular orbit about the first at a distance of 256 meters as a result of their mutual gravitational attraction. What is the speed of the second asteroid?

_____ m/s

b) Now suppose that the first and second asteroids carry charges of 2.68 C and -2.68 C, respectively. How fast would the second asteroid have to be moving in order to occupy the same circular orbit as before?

_____ m/s

Explanation / Answer

a) force of attraction = G M m / r^2 =

= 6.67 x 10^-11 * 71700 * 930 / 256^2

= 6.7865 x 10^-8 N

This is the centrip force so

F = mv^2 / r

v^2 = Fr / m = 6.7865 x 10^-8 * 256 / 930 = 1.868 x 10^-8

v = 0.0001367 m/s

b) now the force of attraction has to include the electric force which is

elec force = k Q q / r^2 = 8.99 x 10^9 * 2.68 * 2.68 / 256^2 =

= 985257 Newtons this is huge compared to the grav force

So... v^2 = Fr / m = 985257 * 256 / 930 = 271210

v = 520.8 m/s

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