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### 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

1. The calculation for each of the planets should result in a value for M of 2.0 x 1030 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.

2. Distance (kpc) Velocity (km/s) Mass (kg)
3.095.02.1 x 1040
10.0110.05.6 x 1040
15.0110.08.4 x 1040

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 1040 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 1030 kg. So this galaxy is at least 4.2 x 1010 times more massive than the sun.

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