 
Summary: ASTR 1120 Section 1 (3 credit hours): Spring 2006
SUMMARY OF KEY CONCEPTS: WEEK #7
Lecture #13 textbook 4.4 (4th
edition) or 5.3 (3rd
edition)
How can we measure the mass of the black hole at the Galactic Center? We start by noting that
if we know the mass call it M then we can work out the velocity v needed to stay in a
circular orbit at distance r. This is worked out in the textbook (check that) and leads to the
formula:
v2
=
GM
r
The orbital velocity is large for large masses and / or small radii. For the stars orbiting the
Galactic Center, we measure the velocity and the radius we can then rearrange the formula to
find the mass. This gives a result of about 4 million Solar masses, which must be packed into a
volume no larger than the Solar System! No ordinary star or cluster or stars can attain such a
high density, so a black hole is the only plausible explanation that satisfies known physical
laws.
