1. The physics of Mars and its two moons.

Question

Mars has two moons, Phobos and Deimos (Fear and Panic, the companions of Mars, the god of war). Deimos has a period of 30 h, 18 min and a mean distance from the centre of Mars of 2.3 x 104 km. If the period of Phobos is 7 h, 39 min, what is the mean distance (in km) from the centre of Mars?

Answer 1

F = m a

G m Mmars/R^2 = m V^2/R

V^2 R = G Mmars
V = (G Mmars)^.5 R^-.5

period = 2 pi R/V
period = 2 pi R/(G Mmars)^.5 R^-.5
period = T = constant R^1.5 = k R^1.5

T1 = k R1^1.5
T2 = k R2^1.5

T2/T1 = R2^1.5/R1^1.5

so R2^1.5 = R1^1.5 (T2/T1)

Answer 2

9.2