Question

When asked to calculate the energy required to launch a satellite into orbit, do I have to solve for E (E=K+U) or just potential U?

Answer 1

@satellite73

Answer 2

@phi

Answer 3

I think it's
E=K+U
\[K=\frac 12 mv^2\]
\[U=\frac{GMm}{r}\]
\[F=ma\]
\[a=\frac{v^2}r\]
\[F=m\frac{v^2}{r}\]
\[F=\frac{GMm}{r^2}\]
\[\frac{GMm}{r^2}=m\frac{v^2}{r}\]
\[\frac{GM\cancel m}{r^2}=\cancel m\frac{v^2}{r}\]
\[\frac{GM}{r}=v^2\]
E=K+U
\[E=\frac 12mv^2-\frac{GMm}{r}\]
\[E=\frac 12m\frac{GM}{r}-\frac{GMm}{r}\]

Answer 4

@satellite73 @phi
How does the above simplify to
\[=-\frac{GMm}{2r}\]?

Answer 5

@zepdrix

Answer 6

@joemath314159

Answer 7

I'm soo silly...nevermind

Answer 8

Orbits are elliptical so the potential energy is going to be changing, likewise kinetic energy is going to change. Clearly the amount of energy it took is constant.

Answer 9

THanks!