Question

The scape speed at the surface of a certain planet is twice that of the earth. What is it's mass in units of earth's mass

Answer 1

To find the mass of the planet, we can use the formula for escape velocity and set up an equation to solve for the mass. So, the mass of the planet is 4 times the mass of the Earth when the radius of the planet is twice that of the Earth.

Step-by-step explanation:

To find the mass of the planet, we can use the formula for escape velocity:

Vesc = √(2GM/r)

Where Vesc is the escape velocity, G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.

Given that the escape velocity at the surface of the planet is twice that of the Earth, we can set up the following equation:

2√(GM/rp) = √(GM/rEarth)

Squaring both sides of the equation, we get:

4(GM/rp) = (GM/rEarth)

Canceling out the G and rearranging the equation, we find:

M = 4(MEarth)(rp/rEarth)

So the mass of the planet is 4 times the mass of the Earth when the radius of the planet is twice that of the Earth.