How could a spacecraft reduce an orbital insertion burn after a Hohmann transfer using gravity assists?

I want to calculate a mission to Saturn, and my theoretical spacecraft has a total Delta-V of about 10,000 m/s. I have seen using different tools that it will take about 6000 m/s for the initial transfer using multiple Mars and one Jupiter gravity assist, and have been wondering if there are any ways to reduce the amount of Delta-V used for Saturn orbit insertion after the transfer. For example, Aerocapture or other methods. I'm not really a math person, so if you have any equations to help determine anything, I might not understand it, but I am willing to learn how it works!

Edit: Assuming starting from a 300 KM circular orbit to clear some confusion.

• The escape velocity of Earth is according to this site: nasa.gov/audience/foreducators/k-4/features/… 11 km/s. That means that with your 10 km/s, you will not be able to even escape Earth's gravity, let alone going to Saturn. Maybe, with 10 km/s, you could do a flyby around the moon to escape Earth's gravity and start there. Jun 12 at 16:45
• If you escaped Earth's gravitational field, then you could do multiple flybys around Earth, slowly making your way upwards. However, such a thing would require many years to ever reach Saturn. You would also have to get lucky with the planetary alignment to make it to Saturn. Jun 12 at 16:49
• You could dip into the atmosphere of Saturn at your periapsis and bleed off velocity using drag, then when your apoapsis is low enough, do a burn there to bring the periapsis up out of the atmosphere. Might take multiple orbits to bleed off enough speed. (note: knowledge from KSP, not actual rocket science ;) ) Jun 12 at 20:37
• @TheRocketfan I would guess that the OP might mean a 10 km/s budget from LEO-ish based on the estimate of 6 km/s for the initial transfer Jun 12 at 22:52
• related: Did the spacecrafts Galileo or Juno use the Galilean moons for a gravity assist before entering Jovian orbit? and also Delta-v obtained from Titan by the Cassini spacecraft; just how much of a "gas tank" was it? and Wikipedia's Timeline of Cassini–Huygens While initial capture to a high orbit was propulsive only(?) Titan was used for orbit lowering and certainly for inclination changes
– uhoh
Jun 12 at 23:47

2 Answers

Note: I'm not in a position to do any of the math right now, so I'm more addressing the "wondering if there are any ways to reduce the amount of Delta-V used" part of the question.

Gravity assists can go both ways (acceleration or deceleration) depending on the geometry of the approach. Note that entering orbit using a gravity assist probably requires you to drop into a retrograde orbit, which may be undesirable depending on what you're trying to accomplish. For example, if you mean to intercept a moon, a gravity assist would be counterproductive because you'd wind up going the wrong way around the planet and approaching all the moons head-on. But we believe that's how some planets ended up with retrograde moons -- they just happened to fall in on a trajectory where the gravity assist slowed them into a stable orbit going the "wrong" way.

Another trick is the Oberth effect. For some complicated physics reasons, fuel becomes more efficient the deeper you are in a gravity well. This doesn't change the delta-V required, but it increases how much delta-V a given mass of fuel is worth. For example, Jupiter has an incredibly huge gravity well, so thrusters are extremely efficient when used during a close, high speed pass. That efficiency counts whether you're using the thrusters to speed up or slow down, so aiming for a close initial approach is a good strategy even if your target orbit is much further out. The price you pay is that close approach will be very fast, which means you don't stay there for very long, so you need to use thrusters that have a very high impulse. In other words, Oberth makes it more efficient if you can blast out a lot of fuel very fast, but highly efficient thrusters usually throw out a very small amount of fuel at a time, so there's a balancing act there to get your approach as close as possible while still staying close long enough to fire the thrusters for the necessary time. (If it's Jupiter, you also run into issues where the space environment gets significantly more dangerous in terms of radiation/plasma fields the closer you get to the planet, so you have to also consider how that's going to impact your craft.)

Aerobraking is also an option, and in theory you can bleed off any arbitrary amount of velocity that way, given a sufficiently thick atmosphere. However, it's a surprisingly tricky problem, especially with very large planets, because tiny changes in the approach angle can have a huge effect on the distance traveled through the atmosphere. There are other issues with aerobraking, depending on how aggressively you're going to do it, like shaping the craft and adding thermal shielding to ensure you don't damage anything in the process (which may end up making aerobraking less effective than just loading a bit more fuel). Actual aerocapture is probably so tricky that it isn't worth the effort as compared to aerobraking down to a reasonable speed and using thrusters to finish the orbital capture.

• If Saturn is your target, remember that you have Titan as a nice aerobraking candidate. Jun 14 at 15:26
• Maybe so; I don't know whether a low pass over Titan is a better or worse candidate for aerobraking as compared to a long high pass over Saturn, but either way the aerobraking still becomes a major design constraint. Jun 15 at 13:56

I've made a spreadsheet that I hope you will find helpful. Link

so far as I know the minimum burn for a capture orbit is to have periapsis as close as possible to the planet with apoapsis at the edge of the planet's sphere of influence.

See attached illustration

Setting periapsis at 300 km and apoapsis at about 54 million kilometers the insertion burn is about .44 km/s

However...

This parking orbit has a period of about 1685 days! If you don't want to wait nearly five years to start your aerobraking drag passes you will want to bring the apoapsis closer to Saturn. Which you can do in my spreadsheet. All the colored cells accept input.