A large asteroid of mass 66300 kg is at rest far away from any planets or stars.

Question

A large asteroid of mass 66300 kg is at rest far away from any planets or stars. A much smaller asteroid, of mass 690 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?

A large asteroid of mass 66300 kg is at rest far away from any planets or stars. A much smaller asteroid, of mass 690 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? Number m s Now suppose that the first and second asteroids carry charges of +1.18 C and -1.18 C, respectively. How fast would the second asteroid have to be moving in order to occupy the same circular orbit as before? Number m/s

Explanation / Answer

As given in the question,

Mass of large asteroid, m1 = 66300 kg

Mass of small asteroid, m2 = 690 kg

Distance, R = 366 m

Charge, q1 = q2 = 1.18 C

1) As force is given by, F = (G x m1 x m2) / R2 = (m2 x v2) / R

So velocity, v = sqrt(G x m1/R) = sqrt(6.67 x 10-11 x 66300 / 366) = 1.1 x 10-4 m/s

2) Again, force, F = [ (G x m1 x m2) /R2 ] + (k x q1 x q2 /R2) =m2 x v2 / R

(2.28 x 10-8) + (93550.12) = (690 x v2 / 366)

So, velocity comes out to be, v = 222.76 m/s

(Please rate my answer if you find it helpful. Good luck,..)

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