Astr 2100 Descriptive Astronomy
Fall 2017  Assignment 5  Answers

To keep Kepler's 3^{rd} Law simple (a³ = P²) then

all distances must be measured in Astronomical Units

all times must be measured in Earth years

Mercury is about 0.39 AU from the Sun. How many Earth days constitute its
year?

P² = a³ = 0.39³ = 0.0592

P = 0.244 years

P = 0.244 * 365 = 89 days

Jupiter is about 5.2 AU from the Sun. How long is its year?

P² = a³ = 5.2³ = 141

P = 11.9 years

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)?

M = a³ / P² = 5³ / 8² = 125/64
= 1.95 Solar Masses

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.

P = 187 days = 187/265 = 0.512 years

M = a³ / P²

6 = a³ / 0.512²

a³ = 6 * 0.512² = 1.57

a = 1.16 AU

Two moons are observed to be orbiting the same planet. Moon A is 3 x 10^{8}
m from the planet, and moon B is 7.5 x 10^{7} m from the planet.
If Moon A takes 11 days to make one orbit, how long does moon B take?

(P_{B} / P_{A})² = (a_{B}
/ a_{A})³

(P_{B} / P_{A})² = (7.5 x 10^{7}
/ 3 x 10^{8})³ = 0.25³ = 0.0156

P_{B} / P_{A} = 0.125

P_{B} = 0.125 * P_{A} = 0.125 * 11
= 1.38 days