Question

Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 1011 solar masses. A star orbiting near the galaxy's periphery is 5.7 x 104 light-years from its center. (a) What should the orbital period (in y) of that star be? 24.2e6 ху (b) If its period is 5.1 x 107 years instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way. solar masses

Answer 1

Gaj Orbital period of the stor: - T2=422 CMS - T'Ms R3 G - T²Ms TMs Rz 4h2 I constant R, 3 Ti= lyear. R = LAV=1-58x1075 & Ms = Isolax mass (1) ²x Ms Te’X 8x10"x Ms 11:58X105)3 (5.7x104)3 5) Tza: 5.7.2007) ㅗ (1.58x10-5j3 = 5.8694 X1016 8 x 10" T2² b) T2 = 2.4 226x108 years Given: Period Tz = 5:18107 (5:18107) 2 x nx Ms years -) (1) 2 x Ms (1-58x1095)3 n: (5.7 %104)3 (5.7x104) (1-58X10-5)3x (5.1X107) In = 1.807x 1013 solar mass