Entering into orbit around a Callisto using the Oberth Effect (revisited)

[RGClark]

...

Because, the calculations I have used assumed the mean circular motion of Jupiter around the Sun whereas Jupiter's motion is elliptical, the approach to the L1 'point' is not perfect - but good enough to show how the basic orbit lifting mechanism works.

I suggest that if you want to view the scenario, you load into Orbiter, make a cup of coffee, and watch the orbit trajectory unfold at 100,000X time acceleration. It will probably take up to 20 minutes or so for the scenario to unfold.

For a neophyte, how do you load into Orbiter?


Bob Clark

 

[Keithth G]

Basically, one just loads the unzipped '.scn' file into the "Scenarios" folder in Orbiter. Then, open up Orbiter and in the main Launchpad window, select the scenario.

---------- Post added 08-17-15 at 05:30 AM ---------- Previous post was 08-16-15 at 02:17 PM ----------

In an earlier post, to illustrate the ability of 3-body dynamics to 'lift' the apoapsis and periapsis of a trajectory, I presented a simple scenario of a flight along the 'stable manifold' of the Sun-Jupiter L1 Lagrange 'point'. Rather than ave others load the scenario and run it in Orbiter, I thought it might be more effective to post some of the plots of those trajectories instead.

The first is the plot below is the trajectory of the Delta Glider on (or, rather, close to) the stable manifold of the Sun-Jupiter L1 Lagrange point. The Delta Glider starts out in in elliptical orbit with a periapsis a little above Mars' orbital radius and with an apoapsis about 1 AU below the orbital radius of Jupiter. The trajectory covers a span of 10 years.

If one were to use normal 2-body calculations for this orbit, one would conclude that the Delta-Glider would never reach Jupiter. And yet, the Delta-Glider manifestly does reach Jupiter and, moreover, is captured by it.




To show that capture does indeed take place, here is s Jupiter-centric (rather than a Sun-centric) view of the DG's trajectory. Distances are measured in Astronomical Units (AU) where 1 AU = 150 million km.




And by adjusting scale, we see the same thing a little closer up showing two complete orbits of Jupiter at an average distance from Jupiter of around 25 million km and with an orbital period of around 2.5 years.




This capture process is not something that is found in standard 2-body Kepler dynamics. It is a process that is specific to 3-body (Sun, Jupiter and Ship) interactions. Strictly speaking, capture by Jupiter is not permanent. In this case, the DG is a bit like a fly trapped inside a bottle with an narrow open neck. It found its way into the bottle and, eventually, it will find its way out again. But not, perhaps for many orbits around Jupiter.

 

[Keithth G]

I had a closer look at Belbruno's paper on ballistic transfers to Mars. Having thought about it, Belbruno's (ballistic) technique is unlikely to result in a lower delta-v cost transport to Jupiter from Earth.

Belbruno's technique relies upon riding the stable manifold of the L1 point and, thereby, arriving at L1 with the 3-body equivalent of zero hyperbolic excess velocity. For Mars, the stable manifold passes nowhere close to Earth, so Belbruno constructs a separate elliptical transfer orbit from Earth to get to it. Upon arrival, Belbruno proposes an energetic 2.0 km/s burn to transfer to the L1 stable manifold.

The same is true for the Sun-Jupiter L1 point. Its stable manifold doesn't pass close to Earth, so a separate (and delta-v expensive) transfer orbit needs to be inserted in order to get on to the stable manifold. The incremental cost of that transfer orbit and the burn needed to enter the stable manifold is likely to greatly outweigh the delta-v savings arising from arrival at the Jovian system with a lower hyperbolic excess velocity.

In short, at the moment, I can see no means - 2-body or 3-body - by which one can save on the minimum 1.8 km/s for Europa orbit insertion and circularisation as discussed earlier in this thread.