Question

3. In this problem, we are going to examine the supermassive black hole in the center of our galaxy, Sagittarius A.. (a) (15 points) We can calculate its mass using the orbits of stars gravitationally bound to it in the same way that you can use the Earth's orbit to calculate the mass of the Sun). The orbit of a star, S2, has been fully mapped out. Its period is 15.24 yr and semi-major axis length is 980 AU. Using these measurements, calculate the mass of the supermassive black hole in solar masses (units of the mass of the Sun: 1 Mo = 1.99 x 10 kg).

Answer 1

Answer: Semi Major axis of s2 = 9.00 AU = 9 period of s2 = 15.24 yr =P From Keplevs god low - ip: ( ) as 47990.40) 1 15.24 y ear] 2 z = 159900261.0 1 year ME 1599 00861.0 Mo TM = 1.6 xro® MO © Mass of Milky way Mass of this blackhole . ~ 1.29x10 mo 19599 80 861 Mo = 0.206x109 = SORS ~ 0062.5

So this black hole- Schwarzchild radius of R = 2GM X1.67x16"x 1.6 Xrod X1.99 xlogo (3x108)2 1.101618 x10" m .. 1.49597871x108m R = = 0.789863X103 AU - (7.90 XIÓ AU) = 789.06 AU R Sdar system Oort Cloud the inner edge of solar system is about 1000 AD. So the event hosizon of Sga Aim will be nearly the Oort cloud.