## anonymous 3 years ago 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?

1. anonymous

@satellite73

2. anonymous

@phi

3. anonymous

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 $E=\frac 12mv^2-\frac{GMm}{r}$ $E=\frac 12m\frac{GM}{r}-\frac{GMm}{r}$

4. anonymous

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

5. anonymous

@zepdrix

6. anonymous

@joemath314159

7. anonymous

I'm soo silly...nevermind

8. anonymous

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.

9. anonymous

THanks!