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When doing a Hohmann transfer, it takes a burn to change from a low orbit to the Hohmann Transfer Orbit (HTO), and a second burn to change from the HTO to a high orbit. I know how to find the delta-v required for both of those burns.

Do you have to be on a parabolic escape orbit in reference to the origin planet to perform the first HT burn? What about a capture burn for the destination? If that's true, what are the delta-v requirements for an escape burn from a circular orbit, and for a capture burn from an escape orbit? I'm not trying to be very precise.

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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.

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  • $\begingroup$ That answered my question, thank you. If it's okay, I would also like to ask if going from one moon directly to a seperate planet's moon in one escape/transfer/capture is reasonable, or should spacecraft always orbit the planet first before going interplanetary. $\endgroup$ – user36065 May 28 at 23:34
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    $\begingroup$ When performing the escape burn, it's typical to add the initial Hohmann transfer burn as well because then you can take advantage of the Oberth Effect (en.wikipedia.org/wiki/Oberth_effect) which greatly reduces the Delta-V one has to provide for the Hohmann burn. Don't forget small trajectory correction burns and a plane change in the middle to target the destination plane too. $\endgroup$ – Terrance Yee May 29 at 0:26
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    $\begingroup$ @user36065 You should ask that as a separate question. I suspect that in practice you’d want to do the destination moon encounter separately, at least the first time you do it, but it is certainly possible and efficient to go directly to the moon. $\endgroup$ – Russell Borogove May 29 at 1:13
  • $\begingroup$ You are seriously overestimating the total cost. For something like Mars the escape + transfer burn adds only 390m/s over just the escape burn. $\endgroup$ – Loren Pechtel May 29 at 14:57
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    $\begingroup$ @user36065 Loren is correct, my estimate is way off. Please do not use this answer to plan an interplanetary journey until I've had a chance to correct. $\endgroup$ – Russell Borogove May 29 at 16:53

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