Exercise

• Exercise: How can we use knowledge of velocities to find the mass of the galaxy?

• This is the same as Kepler’s 3rd law, which can be derived from Newton’s laws:

• F = ma = G mM/R2; So a = G M/R2;

• Also a = v2/R , so v2 = G M/R

• Assuming the mass does not change with R, i.e., all the mass is well inside the radii R being considered, then the velocity can be used to find the mass, and the velocity is expected to decrease as 1/sqrt(R)

galaxy

R

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