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=
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
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