$\Delta V$ to aerocapture - reconciling conflicting data

Question

I'm working on some delta-V calcs for both Hohmann and non-Hohmann transfers, but the data I'm getting is conflicting.

While I'm looking for much broader applicability than transfer to Mars, since that's the most common case cited, let's use that. When I run the formula on Wikipedia, I get 3,45 km/s for the transfer. This of course assumes that neither Earth nor Mars are there. One can find more complicated formulae for including these, for example, How to calculate delta-v required for a planet-to-planet Hohmann transfer? Which you can find in spreadsheets like this or this.

But that's still not clear how you factor into account an aerocapture transfer. We can compare to datasets like Chris Hirata's, which make it look like from Earth escape (for which $\Delta V$ is easy to calculate), it's 0,6 km/s to Mars aerocapture outbound, and 0,9km/s to Earth aerocapture inbound. So where exactly do these numbers come from?

When I manually calculate Earth escape from a 250km LEO, I get 3,13 km/s additional $\Delta V$ needed. The difference between that and the "simple" Hohmann transfer formula is 0,3km/s, which matches no information I'm seeing elsewhere or calculating. For the spreadsheets, they have a number of periapses and apoapses to enter, but it's not clear what's being used for what. One spreadsheet suggests that for aerocapture "apoapsis should be within the planet's sphere of influence", so if I put in for Earth 250km for both periapsis and apoapsis, and for Mars a 50km periapsis / 570000km apoapsis (just barely within the sphere of influence), it gives

Departure Vinf 2,9448 km/s
Arrival Vinf 2,6490 km/s
Total DV 5,5937 km/s
Earth: Insertion burn from periapsis 3,6001 km/s
Mars: Insertion burn from periapsis 0.6749 km/s

If I change the Earth apoapsis to just under its sphere of influence (say, 911900km), I get the same except for "Earth: Insertion burn from periapsis 0,4279 km/s"

Soooooooo..... how am I supposed to interpret this? Where is this 0,6 km/s from Earth escape to Mars aerocapture, 0,9 km/s from Mars escape to Earth aerocapture supposed to come from?

I had actually spent some time trying to get real-world optimized transfer scenarios calculated in GMAT, but the built-in GMAT targeter is terrible (it always just gets stuck oscillating), and the better plugin targeters are a nightmare to try to compile.... :Þ

Answer 1

I would suggest starting with some of the precalculated solutions in https://trajbrowser.arc.nasa.gov/ if you're just getting started, that way you can be relatively certain you have a reasonable beginning point for any GMAT solution you get. But to answer your question the way I think you mean, the Mars Insertion Burn from Periapsis is the propulsive delta-V solution, so that nominally comes from your rocket engines. If you're doing an Aerocapture instead, then this is the equivalent amount of periapse velocity you need to shed during the Aerocapture. Actual velocity shed is slightly higher due to finite "burn" effects.

As for the discrepancies you may see, a lot of the variation in answers for things like "how much delta-V does it take to get to Mars" depends on what year you're talking about, what your initial and final orbits look like, and if you optimized for time, for delta-V, or for something else as you found the solution. The year variations are the biggest since earth and especially Mars aren't in the same relative positions in their orbits each time the minimum launch energy window opens. I hope this helps.