I took a physics final and this question was on the test and would like to see h

Question

I took a physics final and this question was on the test and would like to see how someone who is better at physics would answer it: This is just a summarization of the key parts of the question:

                              It is thought that there is a massive black hole at the center of galaxies. It has been thought that there is one in the Milky Way in the region of Sagittarius A. The mass at the center has been thought to be 8.6E36 with a radius of 6.7E12. The constants are G=6.67E-11 and c=3.0E8 m/s..

a. based on the information can there be a black hole

b. if the mass could put in a tub of water, would it float

c. the mass has an orbit period of 15.6 years, with an eccentricy of .881, how large is the semi-axis.

Explanation / Answer

a) need to find escape speed

1/2 mv^2 - G M m/R

0.5*v^2 - 6.67E-11*8.6E36/6.7E12=0

v=1.3E7 m/s

so this is less than c so not a black hole

b) density = 8.6E36/(4/3*pi*6.7E12^3)=6.83E-3

so it can float

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