How Do You Calculate Slingshot Maneuver Dynamics for a Space Probe?

[noreally]

Really need help with this past exam question for revison:

Homework Statement

A probe performs slingshot maoeuvre around planet. Mass of planet is 9x10^22kg. Mass of probe is 4x10^2 kg and approaches planet from a great distance with relative speed 2x10^3 m/s and impact parameter 6x10^7. Using gravitational constant, G, determine:

1) Specific Energy, C and Specific Angular momentum L and alpha.
2) Closest approach distance of probe
3) Max speed of probe

I have the equations, but they involve the semi-major axis which can't be used as Rmax and Rmin arent given here so I'm a little lost on where to being with this, if anyone could help out I would be eternally greatfull! :D

 

[voko]

The only equations necessary here are those of conservation of energy and angular momentum.

 

[noreally]

I found parts 1 and 2 but am stuck on finding Vmax at my Rmin value without knowing the Rmax to be able to calculate the semi-major axis and eccentricity.

 

[voko]

Once you know (2), you can use both conservation of energy and conservation of angular momentum to obtain the max speed.