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

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 ?)

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

To answer part (a) of the question, we need to determine whether the period of an object orbiting the black hole with a semimajor axis of 1 AU is greater than, less than, or equal to 1 year.

The period of an object in orbit is determined by the mass of the central object (in this case, the black hole) and the semimajor axis of the orbit. The period is given by the formula:

T^2 = (4π^2 * a^3) / G * M

where T is the period, a is the semimajor axis, G is the gravitational constant, and M is the mass of the central object (the black hole in this case).

To calculate the period for the given scenario in part (b) of the question, we substitute the values into the equation:

T^2 = (4π^2 * (1 AU)^3) / (G * (82 * mass of the Sun))

Since the mass of the Sun is approximately 1.989 x 10^30 kg, and G is the gravitational constant with a value of approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2, we can substitute these values into the equation to calculate the period in years.