While establishing relation of escape velocity and radius , I confronted a problem .
(i) $$v_e=\sqrt{\frac{2GM}{R}}$$
This states that $v_e$ is inversely proportional to the square root of radius .
(i) $$v_e=\sqrt{2gR}$$
This states that $v_e$ is directly proportional to the square root of radius .
Whoch one’s correct?
Best Answer
The problem is solved when you realize that $g$ in your second formula is a function of $R$: if
$$F = \frac{GMm}{r^2}$$
is rewritten as
$$F = mg$$
Then it follows that
$$g = \frac{GM}{r^2}$$
When you substitute that in your second equation, you get the first...