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.

If you were on a parabolic escape, you'd leave the origin planet's sphere of influence at zero relative speed, and then you could execute the Hohmann, but in practice you combine the escape burn with the Hohmann ascent burn, which I believe is more efficient than doing two separate burns: you spend less time being dragged back by the origin planet because you're going faster than you would for parabolic escape alone.

So the cost of the parabolic escape burn, plus the Hohmann, plus the destination capture burn (symmetrical with the parabolic escape), should be a reasonably close conservative estimate (overestimate) of the actual burn cost. Remember to add the origin planet's sphere of influence to the starting altitude for the Hohmann, and subtract the destination planet's SOI from the ending altitude; this assumes you leave each body in the most favorable direction.

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 -- this one is a slight underestimate if the burn isn't instantaneous, but since you're not trying to be very precise I think you can pretend that this neatly cancels out the overestimate on the other part.

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.

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.

If you were on a parabolic escape, you'd leave the origin planet's sphere of influence at zero relative speed, and then you could execute the Hohmann, but in practice you combine the escape burn with the Hohmann ascent burn, which I believe is more efficient than doing two separate burns, because you spend less time being dragged back by the origin planet.

So the cost of the parabolic escape burn, plus the Hohmann, plus the destination capture burn (symmetrical with the parabolic escape), should be a reasonably close conservative estimate of the actual burn cost. Remember to add the origin planet's sphere of influence to the starting altitude for the Hohmann, and subtract the destination planet's SOI from the ending altitude -- assuming you leave each body in the right direction.

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 -- this one is a slight underestimate if the burn isn't instantaneous, but since you're not trying to be very precise I think you can ignore both this and the efficiency gain of combining the escape/capture and transfer burns.

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.

If you were on a parabolic escape, you'd leave the origin planet's sphere of influence at zero relative speed, and then you could execute the Hohmann, but in practice you combine the escape burn with the Hohmann ascent burn, which I believe is more efficient than doing two separate burns: you spend less time being dragged back by the origin planet because you're going faster than you would for parabolic escape alone.

So the cost of the parabolic escape burn, plus the Hohmann, plus the destination capture burn (symmetrical with the parabolic escape), should be a reasonably close conservative estimate (overestimate) of the actual burn cost. Remember to add the origin planet's sphere of influence to the starting altitude for the Hohmann, and subtract the destination planet's SOI from the ending altitude; this assumes you leave each body in the most favorable direction.

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 -- this one is a slight underestimate if the burn isn't instantaneous, but since you're not trying to be very precise I think you can pretend that this neatly cancels out the overestimate on the other part.