Question

Calculate the Roche limit of Phobos and explain the significance of this result. 

Density of Phobos = 1.90 g /cm³ 

Density of Mars = 3.94 g/cm³ 

Radius of Mars = 3394 km 

Radius of the orbit = 9.38 × 10³ km  of Phobos

Answer 1

r_R = 2.5(ρM/ρm)^1/3 x R

r_R = 2.5(3.94/1.90)^1/3 x 3398 = 8495(2.073)^1/3

r_R = 8495 x 1.2752 = 10, 832km

If the average radius of the orbit of Phobos is less than 10,832 km, the tidal force exerted by Mars could disrupt it.