Here's the question you clicked on:
JenniferSmart1
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?
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 \[E=\frac 12mv^2-\frac{GMm}{r}\] \[E=\frac 12m\frac{GM}{r}-\frac{GMm}{r}\]
@satellite73 @phi How does the above simplify to \[=-\frac{GMm}{2r}\]?
I'm soo silly...nevermind
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.