A large asteroid of mass 87900 kg is at rest far away from any planets or stars.

Question

A large asteroid of mass 87900 kg is at rest far away from any planets or stars. A much smaller asteroid, of mass 9.0 times 102 kg, is in a circular orbit about the first at a distance of 366 meters as a result of their mutual gravitational attraction. What is the speed of the second asteroid? Now suppose that the first and second asteroids carry charges of +3.68 C and -3.68 C, respectively. How fast would the second asteroid have to be moving in order to occupy the same circular orbit as before?

Explanation / Answer

a)for gravity we have

GMm/r2= mv2/r where M=87900kg and m=900kg

r=366meter G=6.673*10^(-11)

so we get v=(GM/r)

=1.26*10^(-4) m/s

b) k*q2/r2= mv2/r as electrodynamic force is much greater than gravitational force

where k=9*10^(9), q=3.68

substituting we get v=(k*q2/mr)

=608.28 m/s

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