## The Hidden Lives of Galaxies - Classroom Activities

### Activity #6d - Weighing a Galaxy

Students will use Newton's Laws of Motion to determine the mass of the Sun from the motions of the planets. They will then use the same techniques to determine the mass of a galaxy. In doing so, students will convert among different measurement units used in astronomy.
**Worksheet Answers**

The calculation for each of the planets should result in a value for M of 2.0 x 10

^{30}kg, which is the mass of the Sun. It is the same for each because the central mass for the solar system is concentrated in the Sun.Distance (kpc) Velocity (km/s) Mass (kg) 3.0 95.0 2.1 x 10 ^{40}10.0 110.0 5.6 x 10 ^{40}15.0 110.0 8.4 x 10 ^{40}The mass increases as the distance from the center of the galaxy increases. This is because stars move under the gravitational influence of all the matter within their orbit. So stars at greater distances move under the influence of more mass than stars closer to the center.

The best estimate for the mass of the galaxy is the one which includes the most amount of mass. From this calculation, the largest value is 8.4 x 10

^{40}kg. The actual mass of the galaxy is likely to be more than this. From Part 1, we know the mass of the Sun is 2.0 x 10^{30}kg. So this galaxy is at least 4.2 x 10^{10}times more massive than the sun.