Do you have to be on a parabolic escape orbit in reference to the origin planet to perform the first HT burn?
The Hohmann transfer ∆v equations normally assume you aren't in orbit around another body.
The following all assumes we're doing some sort of "patched conic" approximation, where we define a sphere of influence for each body and pretend it's the only significant gravitational influence within the sphere.
Consider doing it in three separate burns:
- a parabolic escape burn from a low circular parking orbit,
- a Hohmann transfer burn from edge of the origin planet's SOI to the edge of the destination planet's SOI,
- a capture burn from parabolic flyby to circular parking orbit at the destination (this is the same as an escape burn, but in reverse).
This is straightforward to compute. Note that the escape burn leaves you at 0 velocity at infinite distance from the departure planet; you still have considerable outbound velocity when you leave the SOI (which is just escape velocity at SOI's altitude), which you can apply toward the cost of the Hohmann, and likewise you can deduct the destination's escape-velocity-at-SOI from the cost of the Hohmann.
In practice, it's most efficient to combine the escape burn with the orbit-raising leg of the Hohmann, and to combine the capture burn with the second burn of the Hohmann. You get significant benefit from the Oberth effect, so the above is a gross overestimate.
What are the delta-v requirements for an escape burn from a circular orbit, and for a capture burn from an escape orbit?
The escape and capture burns are symmetrical, and should be just the difference between circular orbit velocity and escape velocity from a given parking orbit altitude.
