Escape velocity from a planet depends on:

The orbital speed of a satellite at height $h$ (with $h \ll R$) above the Earth is approximately:

The orbital period of a geostationary satellite is:

The orbital speed of a satellite just above the Earth's surface is approximately:

If Earth's mass were doubled and its radius halved, the escape velocity would become $k$ times the original. Find $k$.

The escape velocity from the surface of the Earth is about 11.2 km/s. If the radius of Earth were doubled (mass unchanged), the new escape…