## Astr 2100 Descriptive Astronomy Fall 2017 - Assignment 5 - Answers

1. To keep Kepler's 3rd Law simple (a³ = P²) then
1. all distances must be measured in Astronomical Units
2. all times must be measured in Earth years
2. Mercury is about 0.39 AU from the Sun. How many Earth days constitute its year?
1. P² = a³ = 0.39³ = 0.0592
2. P = 0.244 years
3. P = 0.244 * 365 = 89 days
3. Jupiter is about 5.2 AU from the Sun. How long is its year?
1. P² = a³ = 5.2³ = 141
2. P = 11.9 years
4. A planet orbits its star at a distance of 5 AU, taking 8 Earth years to go around once. What is the mass of the star (in solar masses)?
1. M = a³ / P² = 5³ / 8² = 125/64 = 1.95 Solar Masses
5. A planet is observed to be orbiting a star of known mass equal to 6 solar masses. It is observed to make full orbit in 187 days. What is the radius of the orbit.
1. P = 187 days = 187/265 = 0.512 years
2. M = a³ / P²
3. 6 = a³ / 0.512²
4. a³ = 6 * 0.512² = 1.57
5. a = 1.16 AU
6. Two moons are observed to be orbiting the same planet. Moon A is 3 x 108 m from the planet, and moon B is 7.5 x 107 m from the planet. If Moon A takes 11 days to make one orbit, how long does moon B take?
1. (PB / PA)² = (aB / aA
2. (PB / PA)² = (7.5 x 107 / 3 x 108)³ = 0.25³ = 0.0156
3. PB / PA = 0.125
4. PB = 0.125 * PA = 0.125 * 11 = 1.38 days