Question

If earth radius is doubled what is effect on escape velocity?

Answer 1

Escape velocity happens when your kinetic energy, 12mv2, is equal in magnitude to your gravitational potential energy, GMmr.

Setting these equal and solving for v gives you escape velocity:

ve=√ 2GM/r

The key fact to take away from that is that escape velocity is proportional to the square root of mass, and inversely proportional to the square root of the radius.

So, if by doubling the Earth’s size you mean doubling the radius, then your escape velocity will increase by a factor of:

21/2 21/2=1. So doubling both the mass and the radius causes no change to escape velocity.

If, by doubling, you mean doubling the Earth’s volume (which would happen if you increased the radius by the cube root of two), then escape velocity would change by a factor of:

21/2(21/3)1/2=21/3≈1.26

So doubling the volume and the mass increases escape velocity to about 14 km/s.

Brainliest plz