EXAM QUESTION black hole force?

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SUMMARY

The discussion centers on calculating the gravitational force acting on a star in circular motion around a supermassive black hole, with a radius of 1014 m and a period of 15 years (4.7 x 108 s). The gravitational force is derived using the formula F = (Gm1m2)/r2, where G is the gravitational constant (6.7 x 10-11 N m2/kg2). Participants suggest using centripetal force (mv2/r) to find the velocity and ultimately solve for the gravitational force.

PREREQUISITES
  • Understanding of gravitational force calculations
  • Familiarity with centripetal force concepts
  • Knowledge of the gravitational constant (G = 6.7 x 10-11 N m2/kg2)
  • Ability to convert units (e.g., meters to kilometers)
NEXT STEPS
  • Learn how to derive gravitational force using F = (Gm1m2)/r2
  • Study centripetal force and its application in orbital mechanics
  • Explore the concept of orbital velocity and its calculation
  • Review gravitational interactions in astrophysics, particularly around black holes
USEFUL FOR

Students preparing for physics exams, particularly those studying gravitational forces and orbital mechanics, as well as educators looking for practical examples in astrophysics.

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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
 
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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?
 


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!
 


you too, thanks
 

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