# Orbits/angular momentum

1. Oct 11, 2007

### sitaras

1. The problem statement, all variables and given/known data
An object is approaching earth. When it reaches 5(10^6) m a rocket diverts it so that it is 6(10^8) m from earth at it's perihelion. What tangential velocity does the rocket have to impart so that this occurs. Assume that the object initially "falls" towards earth with some radial velocity.

2. Relevant equations
Angular momentum
conservation of energy

3. The attempt at a solution
V_1=velocity required to move the object to an orbit, solving for this.
V_2[/tex]=velocity at the perihelion.

Since there is no radial velocity at the perihelion, conservation of energy implies:
$$\frac12{}{}$$mV_r$$^2{}$$ + $$\frac12{}{}$$mV_1$$^2{}$$ - $$\frac{GMm}{5(10^6)}$$ = $$\frac12{}{}$$mv_2$$^2{}$$ - $$\frac{GMm}{6(10^8)}$$

m will cancel, and conservation of angular momentum says:
(v_1)5(10^6)=(v_2)(6(10^8))
But I have no idea how to solve for V_r.
Any ideas?

Thanks a lot