Question

Given the Earth's density as 5.5 g/cm3 and the Moon's density as 3.34 g/cm3, determine the Roche limit for the Moon orbiting the Earth (in units of Earth radii).

Answer 1

Answer:

The Roche limit for the Moon orbiting the Earth is 2.86 times radius of Earth

Explanation:

The nearest distance between the planet and its satellite at where the planets gravitational pull does not torn apart the planets satellite is known as Roche limit.

The relation to determine Roche limit is:

$Roche\ limit=2.423\times R_{P}\times\sqrt[3]{\frac{D_{P} }{D_{M} } }$     ....(1)

Here $R_{P}$ is radius of planet and $D_{P}\ and\ D_{M}$ are density of planet and moon respectively.

According to the problem,

Density of Earth,$D_{P}$ = 5.5 g/cm³

Density of Moon,$D_{M}$ = 3.34 g/cm³

Consider $R_{E}$ be the radius of the Earth.

Substitute the suitable values in the equation (1).

$Roche\ limit=2.423\times R_{E}\times\sqrt[3]{\frac{5.5 }{3.34 } }$

$Roche\ limit= 2.86R_{P}$