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Say a spacecraft is arriving at Saturn, can aerobrake arbitrarily, and wishes to arrive at Hyperion. How much should it aerobrake (i.e. what should the SMA be after aerocapture) to minimize the Delta-V required afterwards?

I initially had the spacecraft aerobrake until its apochron matches Hyperion's SMA, but it takes over 3,600 m/s of Delta-V to match Hyperion's velocity. I realized that aerobraking was reducing my kinetic energy by so much, I had to increase it afterwards to match velocity with Hyperion. However, if I barely brake enough to capture (apochrone reaches out to Phoebe), the burns raising perichrone and matching velocity with Hyperion total to under 2,400 m/s.

So, my question is, how much should I aerobrake (i.e. what should the SMA be after aerocapture) to minimize the Delta-V needed to intercept Hyperion? I think it's likely between my two extremes, and I have a feeling it should be Hyperion's SMA, but that's just intuition.

For reference, Hyperion's SMA is 1,481,009 km and its orbital velocity is 5,060.8 m/s, Saturn's equatorial radius is 60,268 km, and there's a handy vis-viva solver here. I'm positive this has lots of similarities to a bi-elliptic transfer orbit, with the exception that the first 'burn' is free.

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  • $\begingroup$ Matching Hyperion's SMA seems like an intriguing hypothesis. I'm a filthy empiricist; have you tried bracketing that with e.g. 90% and 110% of Hyperion SMA and seeing if that's a local optimum? $\endgroup$ – Russell Borogove Jun 24 '17 at 2:33
  • $\begingroup$ @RussellBorogove Strangely, this does not appear to be the answer, since aerobraking to Hyperion SMA ends up requiring slightly over 3 km/s. It appears that, despite my earlier doubts, the less you aerobrake, the less delta-V you require. $\endgroup$ – Deimophobia Jun 24 '17 at 14:22
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Coming from an earth to Saturn Hohmann, it would take .435 km/s to brake into a 0 x 54104061 km capture orbit. 54104061 km is the altitude of Saturn's sphere of influence. Some or maybe all of that .435 km/s could be achieved by aerobraking. But the ship would enter Saturn's atmosphere at 36 km/s. That is pretty tough aerobraking.

At the 54104061 km apoapsis it will take a .154 km/s burn to raise periapsis to altitude of Hyperion's orbit (1420741 km).

Then it would take 2 km/s to circularize at Hyperion's orbit.

This is assuming circular, coplanar orbits.

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  • $\begingroup$ After some more calculations, this does appear to be the answer, since aerobraking to Hyperion SMA ends up requiring slightly over 3 km/s. It appears that, despite my earlier doubts, the less you aerobrake, the less delta-V is required. Kind of makes sense, if you imagine that you somehow start in a very low orbit and aerobraking gives you the first burn of a bi-elliptic transfer. $\endgroup$ – Deimophobia Jun 24 '17 at 14:25
  • $\begingroup$ @Deimophobia If radius of periapsis and destination orbits differ by more than a factor of 11, I go for a high apoapsis with a small apoapsis burn to raise periapsis. Then a circularize burn at the new periapsis. Based on the bi-elliptic transfer you mentioned. In this case 1,481,009/60,268=24.57. $\endgroup$ – HopDavid Jun 24 '17 at 18:02

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