Trying to wrap my brain around gravitational assists

[Decimator]

Ok, let's say we have "Mr. Big's Jupiter mining corporation." These guys mine stuff from Jupiter's moons and ship them back to Earth(and yes I know this is currently economically infeasible). Just how much delta-v can they save by using gravitational assists from Jupiter and its moons? How much delta-v can they save by doing the same with the Earth-Luna system?

If time isn't a major factor for the Earth-Jupiter trip(robot freighter, for example), can they burn off all their momentum using gravitational assist? How about the Jupiter-Earth trip?

 

[qraal]

I think you mean the Oberth gravity well maneuver, which is pretty handy around Jupiter. Can give payloads a big boost. Gravity assists on the way to Jupiter have been used for Galileo and Cassini, but it really depends on the propulsion system. What sort were you thinking?

 

[Decimator]

*looks up Oberth maneuver*

No, I don't think that's part of what I'm talking about. I didn't even know such a maneuver existed, so thank you for that. What I'm actually talking about is using the orbital energy of a multi-body system to accelerate and decelerate a spacecraft . Jupiter has numerous moons to slingshot around, and I'm curious if a spacecraft can save a massive amount of delta-v by using reverse-slingshot maneuvers around multiple moons on arrival at the Jupiter system.

For the drive, let's call it a solid core nuclear thermal rocket using hydrogen as remass.

This Oberth maneuver only work on departure trips, correct?


Edit: I should try to define exactly what I'm trying to do better.

Our robot freighter approaches Jupiter on an interplanetary trip from Earth. Our objective is to make the freighter enter a stable orbit around Jupiter so it can pick up cargo. The freighter performs a gravitational reverse-slingshot maneuver around Ganymede, then swings around Jupiter and performs another reverse-slingshot around Europa, then it swings around Jupiter yet again and reverse-slingshot around Io, and so on. Can the freighter dump all or nearly all of its momentum in this manner? Does this even work?

 

[qraal]

Hi Decimator
I realized the limitations of my reply afterwards. Both Galileo and Cassini missions rely heavily on multiple gravity assists to maneuver for minimal propellant around the moons of Jupiter and Saturn. While orbits can be shaped via such maneuvers I don't think they're very effective for initial capture.

Neither is aerobraking, oddly enough, in the case of Jupiter - gravity well is too steep. Saturn allows aerobraking for a fuel saving. When I first heard that about Jupiter I didn't believe it - I am a fan of "2010" and Arthur C. Clarke - but I ran the numbers and it's true. Try for yourself. Aerobraking from hyperbolic speed then orbit matching to Io's orbit (or any other Galilean) chews up as much propellant as braking direct into orbit.

In reply to your second questions, Oberth maneuvers are as effective on arrival as they are on departure. Arriving from "infinity" means your initial speed is hyperbolic and doing a burn at periapsis is the most effective way to be captured - in a sensible gravity well, the lower the periapsis, the better. After capture burn, then a highly eccentric capture orbit can be shaped as desired by an apoapsis burn and/or gravity assists - that's what Cassini did.

 

[Decimator]

Thanks! Let's see if I understand the problem with using reverse-slingshots for this. Above a certain velocity, my hyperbolic orbit is too wide to actually swing my craft around the moon, which means I can't use it to slow down. So I first need to slow down my craft in some other manner, such as an Oberth maneuver. Is this correct? Does my terminology make you cringe?

 

[qraal]

Thanks! Let's see if I understand the problem with using reverse-slingshots for this. Above a certain velocity, my hyperbolic orbit is too wide to actually swing my craft around the moon, which means I can't use it to slow down. So I first need to slow down my craft in some other manner, such as an Oberth maneuver. Is this correct? Does my terminology make you cringe?

Your terminology is fine :-)

Simple answer: Oberth first to brake into a capture orbit, like Cassini and Galileo did. After that, the highly eccentric high orbit can be shaped and modified by gravity assists from the moons. Interestingly the moons of Uranus allow an orbiter to make multiple assists just like Galileo - what matters is the mass ratios of the moons and the Primary, which are practically the same for Jupiter and Uranus. Four largish moons makes for many gravity assist opportunities.

 

[D H]

As far as I can tell the term 'Oberth maneuver' isn't used much at NASA. The preferred term is 'gravity assist'. It is a much more generic term than Oberth maneuver. It would be a bit of a stretch to use the term 'Oberth maneuver' to describe the lunar gravity assists used to put STEREO A and STEREO B in their orbits.

Here is a primer on gravity assists: http://www2.jpl.nasa.gov/basics/grav/primer.php.

 

[qraal]

As far as I can tell the term 'Oberth maneuver' isn't used much at NASA. The preferred term is 'gravity assist'. It is a much more generic term than Oberth maneuver. It would be a bit of a stretch to use the term 'Oberth maneuver' to describe the lunar gravity assists used to put STEREO A and STEREO B in their orbits. Here is a primer on gravity assists: http://www2.jpl.nasa.gov/basics/grav/primer.php.

Hi DH

The Oberth Maneuver is distinct from gravity assists. Gravity assists are essentially orbit shaping, allowing a vehicle to maneuver around (i.e.raise and lower its periapsis/apoapsis and inclination) the gravity field of a larger body by close flybys of smaller orbitting bodies. The Oberth Maneuver is best seen in a periapsis burn when in an eccentric orbit, to make best use of the balance between kinetic and potential energy of the vehicle and its propellant. This is best used when escaping or ensuring capture into orbit. A combination of both is what both Galileo and Cassini used to maneuver amongst the moons of their target planets.

Other kinds of maneuvers are possible - for example, a Jupiter orbiter can be put into weakly bound orbits around multiple Galilean moons without use of engines, if timed correctly. This is somewhat more difficult than the relatively high-speed flybys used by both Galileo and Cassini.

Robert Zubrin describes a scenario which combines the two and is like the questioner's scenario. A cargo vehicle leaves Callisto orbit for an orbit which is exactly half the period of Callisto. Two orbits later it should encounter Callisto, but before doing so its orbit is shaped through a close encounter with either Europa or Ganymede. This sets it up for a Callisto gravity assist which drops the perijove from 489,000 km to just 78,640 km (7,150 km altitude) and the speed at that low point is 55.7 km/s. A perijove burn of just 1.5 km/s gives the vehicle a hyperbolic excess of 6.8 km/s. A burn between 2-3 km/s would drop the vehicle into the Sun and/or throw it out of the System. This shows the dramatic propellant savings an Oberth Maneuver can produce.