I have been working on calculating all the the delta V needed to fly a rocket from one planet to another. I have worked out the delta V needed to raise the orbit to intercept the second planet, but once there, I cannot figure out how much delta V I would need to then circularize the orbit around the new planet.
I'll use Earth to Mars as an example.
Here's a quick and dirty pic of an Earth to mars Hohmann:
For sake of simplicity I'm rounding quite a bit here.
At Mars rendezvous you can see the speed difference is about 2.5 km/s. We'll call this 2.5 km/s Vinfinity.
When the ship enters Mars sphere of influence, the path is better modeled by a hyperbola about Mars rather than an ellipse about the sun.
A hyperbola's velocity:
$V_{hyperbola}=\sqrt{V_{infinity}^2 + V_{escape}^2}$
A good memory device for remembering hyperbola's speed is thinking of Vinf and Vesc as the legs of a right triangle and the hyperbola's speed as the hypotenuse.
Vescape, a.k.a. escape velocity varies depending on distance from planet. The 11 km/s earth escape velocity near earth perigee. The 5 km/s Mars escape velocity also assumes a periapsis near Mars' surface.
Low Mars orbit is about 3.5 km/s. So to enter low Mars orbit, you subtract 3.5 from 5.6 km/s. You'd need about a 2 km/s burn.
Now the periapsis speed of a 300 x 574,000 km Mars capture orbit is about 4.8 km/s. So if a capture orbit is all you need, .8 km/s would suffice.
To calculate speeds at different points of various orbits, use the vis viva equation
$V=\sqrt{\mu (2/r - 1/a)}$
Where a is semi major axis of an orbit, mu is GM and r is distance from center of gravitating body.
If you don't want to look up different quantities and work out equations, you can use my Hohmann spreadsheet
