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. (a) What should the orbital period of that star be? (b) If its period is 6.0×107 instead, what is the mass of the galaxy? 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.
Step 1 of 6</p>
The mass of the milky way galaxy is given to be times solar mass, using the given distance of star from the center we need to calculate the orbital period of the star. Also, in the part(b) we need to calculate the mass of the galaxy for the given value to time period of star as . By using the value of distance traveled by the light in 1 year as .
Step 2 of 6</p>
Given data,Mass of milky way galaxy,
Using mass of sun or solar mass
Distance of star from the center of galaxy,
Step 3 of 6</p>
Using kepler’s third law, we can arrive at a relation that can be used to determine the orbital time period of star using the mass of the galaxy.
Let and be the radius and time period of revolution of star, M be the mass of the galaxy around which star is revolving. The relation obtained from Kepler’s third law, that gives the relation between above quantities is given by,
In terms of years, using