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:
[tex]Roche\ limit=2.423\times R_{P}\times\sqrt[3]{\frac{D_{P} }{D_{M} } }[/tex] ....(1)
Here [tex]R_{P}[/tex] is radius of planet and [tex]D_{P}\ and\ D_{M}[/tex] are density of planet and moon respectively.
According to the problem,
Density of Earth,[tex]D_{P}[/tex] = 5.5 g/cm³
Density of Moon,[tex]D_{M}[/tex] = 3.34 g/cm³
Consider [tex]R_{E}[/tex] be the radius of the Earth.
Substitute the suitable values in the equation (1).
[tex]Roche\ limit=2.423\times R_{E}\times\sqrt[3]{\frac{5.5 }{3.34 } }[/tex]
[tex]Roche\ limit= 2.86R_{P}[/tex]
