a) Newton’s universal law of gravitation describes the force of gravity acting on two masses. The correct equation is,
Fg = G m1m2
r2 .
Using dimensional analysis, determine the dimensions and SI units for the gravitational constant G. Here, Fg is a force, m1 and m2 are masses and r is a distance. (2 marks)
b) Someone then tells you that the equation for gravitational potential energy U (measured in Joules) is,
U = −G m1m2
r3 .
Using dimensional analysis, determine if they are correct. (1 mark)
c) An experiment determined that the time for a star to orbit a black hole T in a circular orbit depends on the distance from the black hole to the star r, the gravitational constant G and the mass of the black hole m. That is,
T = CrαGβmγ
where C is a dimensionless constant. Using only dimensional analysis, determine what the exponents α, β and γ must be for this equation to be correct. (3 marks)