Question

The escape speed from the moon is much smaller than from earth. True or False

Answer 1

Answer:

True

The escape speed from the Moon is much smaller than from Earth.

Explanation:

The escape speed is defined as:

$v_{e} = \sqrt{\frac{2GM}{r}}$  (1)

Where G is the gravitational constant, M is the mass and r is the radius.

The mass of the Earth is $5.972x10^{24}kg$ and its radius is $6371000m$

Then, replacing those values in equation 1 it is gotten.

$v_{e} = \sqrt{\frac{(2)(6.67x10^{-11}N.m^{2}/kg^{2})(5.972x10^{24}kg)}{(6371000m)}}$  

$v_{e} = 11.18m/s$

For the case of the Moon:

$v_{e} = \sqrt{\frac{(2)(6.67x10^{-11}N.m^{2}/kg^{2})(7.347x10^{22}Kg)}{(1737000m)}}$  

$v_{e} = 2.38m/s$

Hence, the escape speed from the Moon is much smaller than from Earth.

Since it has a smaller mass and smaller radius compared to that from the Earth.