EXAM QUESTION black hole force?

[fball558]

EXAM QUESTION black hole force??

Homework Statement

good morning everyone! just getting some last minute studying in before my final exam :(
ran into a question so hoping some one will help me understand it.

A star is observed to be in circular motion about a supermassive black hole at the center of
our galaxy. The radius of this orbit is 10^14 m (no prefix just 10 to the 14), and the period is T=15 years = 4.7 x 10^8s. If this
star has the mass of our Sun (M=2.0 x 10^30 kg), what is the magnitude of the force of gravity acting on it?

A. 4.9 x10^28 N
B. 3.6 x10^28 N
C. 2.0 x10^28 N
D. 1.3 x10^28 N
E. 8.8 x10^27 N
F. 6.5 x10^27 N

Homework Equations

F = (Gm1m2)/r^2
G = 6.7 x 10^-11

The Attempt at a Solution

i started using the formula but we do not know the final force (what we are trying to solve for) OR the mass of the black hole. two unknows and only one equation. i have to be missing something. any help would be great!
thanks

 

[hatinengr]

you use the centripetal force equation. mv^2/r. you find v by dividing the length of the orbit (2*pi*r) by T. i think i remember that you have to convert the radius to meters and then convert back to km for the answer.

on a side note, where you able to get problem 16? can you explain how to do that?

 

[fball558]

have not got that far yet.
will look at it now and let you know.
thanks for the help on this problem and good luck on the exam!

 

[fball558]

for problem 16 take a look at
https://www.physicsforums.com/showthread.php?t=204638
someone already posted it on here ;)

 

[hatinengr]

you too, thanks

 

[hatinengr]

for problem 16 take a look at
https://www.physicsforums.com/showthread.php?t=204638
someone already posted it on here ;)

Yeah, I saw that earlier but the approach confused me a bit. After thinking about it again, I've got it. Thanks a lot.