## JenniferSmart1 Group Title 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? one year ago one year ago

1. JenniferSmart1 Group Title

@satellite73

2. JenniferSmart1 Group Title

@phi

3. JenniferSmart1 Group Title

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. JenniferSmart1 Group Title

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

5. JenniferSmart1 Group Title

@zepdrix

6. JenniferSmart1 Group Title

@joemath314159

7. JenniferSmart1 Group Title

I'm soo silly...nevermind

8. wio Group Title

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. JenniferSmart1 Group Title

THanks!