Question

Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0×10¹¹ solar masses. A star orbiting on the galaxy’s periphery is about 6.0×10⁴ light years from its center. What should the orbital period in years of that star be? (You do not need to enter any units.)
2.61×10⁸ yr

¡Correcto! Su recibo es 160-1991

Intentos Anteriores

If its period is 5.0×10⁷ light years instead, what is the mass of the galaxy in solar mass? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. (You do not need to enter any units.)

Incorrecto.

Tries 9/40

Intentos Anteriores

Answer 1

A.) 8.3 X 10^15 S.

b.) 1.6 x 10^13 solar masses

First, we calculate the mass of the Milky Way Mmw, according to the astronomical observations. Then, we continue to convert the units of the distance r between the center of the galaxy and the star. Note that c is the speed of light. = Mmw = (8.0 · 1011) Ms = (8.0.1011) (1.9891 · 1030) = 1.6 · 1042 kg (6.0 · 104) (e) 365 days : (6.0 · 104 years) 1 year = 5.7 · 1020 m r = :) (14.x) (3606 ") (2.99792458 - 108 ) We now proceed to calculate the period T of the star using the orbital period formula. p3 T= 20 = 2V GMMW = (5.7 · 1020) 3 = 24V (6.67 - 10-11) (1.6 - 1042) = 8.3 · 1015 S Now, we solve for Mmw in the orbital period formula. It can be seen that this mass (1.6 - 1013 solar masses) is much greater than the one calculated according to the observations (8.0.1011 solar masses). 3600 s 1 year 1 h S 2 365 days 24 h T = 6.0.107 years 1 day = 1.89 · 1015 p3 27 MMW T (5.7 · 1020) 31 271 6.67 · 10-11 1.89 · 1015 3.1 · 1043 kg = 1.6 · 1013 solar masses (*) (*) 2 =