Question

A black hole is an object with mass, but no spatial extent. It truly is a particle. A black hole may form from a dead star. Such a black hole has a mass several times the mass of the Sun. Imagine a black hole whose mass is eighty-two times the mass of the Sun.
(a) Would you expect the period of an object orbiting the black hole with a semimajor axis of 1 AU to have a period greater than, less than, or equal to 1 yr?
greater than
less than
equal to

(b) Use the equation
T2 =

4π2
GM

a3
to calculate this period.

yr

Answer 1

wouldn't the centripetal force to keep in orbit be greater due to the increased mass? If that force is greater, it must be traveling faster (remember v^2/r ?)

Answer 2

For a, it is less than and for b,itis The square root of 1^3/82=.110yr