Question

A large asteroid of mass 71700 kg71700 kg is at rest far away from any planets or stars. A much smaller asteroid, of mass 830 kg,830 kg, is in a circular orbit about the large asteroid at a distance of 256 m256 m as a result of their mutual gravitational attraction. What is the speed ?2v2 of the second asteroid?

?₂

m/sm/s

Now suppose that the first and second asteroids carry charges of +1.68 C+1.68 C and −1.68 C,−1.68 C, respectively. How fast ?′₂ would the second asteroid have to be moving in order to occupy the same circular orbit as before?

?′₂=

Answer 1

a)

From Newton's second law ,gravitational force is balanced by centripetal force

GMm/r²  = mV₂²/r

=>V₂=sqrt(GM/r) =sqrt[(6.673*10^-11)(71700)/(256)]

V₂=1.367*10^-4 m/s

b)

From Newton's second law ,electrostatic force is balanced by centripetal force

KQ²/r²  = mV₂'²/r

=>V₂'=sqrt(KQ²/rm)=sqrt[(9*10⁹)(1.68)²/(256)(830)]

V₂'=345.76 m/s