A large asteroid of mass 77100 kg is at rest far away from any planets or stars.

Question

A large asteroid of mass 77100 kg is at rest far away from any planets or stars. A much smaller asteroid, of mass 610 kg, is in a circular orbit about the first at a distance of 311 meters as a result of their mutual gravitational attraction. What is the speed of the second asteroid? ____________m/s Now suppose that the first and second asteroids carry charges of 3.18 C and -3.18 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)for gravity we have

GMm/r2= mv2/r where M=77100kg and m=610kg

r=311meter G=6.673*10^(-11)

so we get v=(GM/r)

=1.29*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=3.18

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

=692.63 m/s

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