Question

If you suddenly multiplied the mass of Earth by a factor of 4, how would the period of a satellite change, if the radius of its orbit did not change?

4 times as long

1/4 as long

2 times as long

1/2 as long

Unchanged

Answer 1

the centripetal force (gravity) is now 4 times as large

f = m v^2 / r

multiplying f by 4 (and keeping m and r constant) means that v is doubled

doubling the velocity would halve the period