Question

A satellite is to be launched into an orbit of radius,r Show that v = 2gr, where V is the

Answer 1

Explanation:

We start by using the conservation law of energy:

$\Delta{K} + \Delta{U} = 0$

or

$\dfrac{1}{2}mv^2 - G\dfrac{mM}{r} = 0$

Simplifying the above equation, we get

$v^2 = 2G\dfrac{M}{r}$

We can rewrite this as

$v^2 = 2\left(G\dfrac{M}{r^2}\right)r$

Note that the expression inside the parenthesis is simply the acceleration due to gravity $g$ so we can write

$v^2 = 2gr$

where $v$ is the launch velocity.