# Patched conics

1. May 7, 2013

### Dustinsfl

I have been trying to find a hyperbolic trajectory that has hyperbolic excess speed of 3.944 km/s.

However, I can only find ones that would start inside the Earth's crust.

mue = 398600

energy = mue / (2 * a)

ve = 29.78

vinf = 3.944 = \sqrt{mue / a}

I have at least 30 more equations that are relevant but they have all lead no where.

2. May 8, 2013

### Filip Larsen

The excess speed determines a, but you still have e to play with for a given perigee radius. Among your 30 equations you may find one that relates perigee radius rp, semi-major axis a, and eccentricity e. If not not, then look for a relevant equation that gives radius r as a function of true anomaly f and then set f to zero.

[Later] It has occurred to me that the orbital eccentricity probably is not that interesting a parameter for you. If so you may instead want to use the vis viva equation with your last equation above in order to get the (desired) velocity at perigee as a function of perigee orbital radius and the hyperbolic excess speed. The difference between the actual and desired perigee speed is then the maneuver speed needed at perigee to enter the desired hyperbolic orbit.

Last edited: May 8, 2013