Gravitational slingshot

[marsbug]

Hi everyone, i've set myself the project of using fortran to program a simple spaceflight simulator. Yes I know fortrans old and clunky but it's what i know and it makes things interesting.
I've got as far as earth to LEO and caculating launch windows for simple Hoffman transfer orbits, but I've come up with a blank on how more complex manouvres, such as gravity 'slingshots', are set up and how opportunities for them are found. I was wondering if anyone knew of any online resources, or better yet examples, for older programming languages were used for problems like this back in their day?
I'm mainly interested in the mathematics used, and my calculus is fairly rusty so if anyone wants to recommend a tutorial that would be very welcome to!

[NEOWatcher]

Cool; I'll be watching this thread closely.

I always wanted to take the time and get a deeper understanding of orbital trajectories, but I've never had the time and the resources at the same time to do it.

I have a math degree that has been long rusted away. And; my early career was primarily in Fortran. But; what really piqued my interest was this statement.

I've come up with a blank on how more complex manouvres, such as gravity 'slingshots', are set up and how opportunities for them are found

I know it's complex, and takes some "zeroing in" on a solution. But; I think it's more a matter of having the right starting data.

[marsbug]

Thanks NEOwatcher, when I've made some progress I'll post it here, any feedback would be very welcome!

[cjameshuff]

Hi everyone, i've set myself the project of using fortran to program a simple spaceflight simulator. Yes I know fortrans old and clunky but it's what i know and it makes things interesting.

Fortran? Yick...
Beware of numeric errors in computing the trajectories. You won't get a stable long term orbit with a simple Euler's method. I've done simulations with both Verlet integration and Beeman's method with good results...and then there's good old standards like Runge-Kutta, just a bit more complex to code.

http://en.wikipedia.org/wiki/Numeric...tial_equations

I've been meaning to do something similar, except using genetic algorithms to search out optimal maneuvers...

[frankuitaalst]

I know that some integrators are programmed in VisualBasic (Gravity Simulator by Tony Dunn fi ) which can rely on the function sets of Windows WinApi32 , making the work "easy" .
I don't know this language but I have myself good experience with PowerBasic for doing this job .
In annex a screenshot in 3D ( red/cyan) of the slingshot the Comet Oterma got in 1963 when it came close to the L1 point of Jupiter .
Callisto's orbit is depicted at the center .
The application was programmed in PowerBasic and is very well performing .

[George]

Fortran? Be sure to check whether or not your spacecraft ends-up doing loops.

[Tim Thompson]

See Binary collisions and the slingshot effect; Rica da Silva & Lemos; Celestial Mechanics and Dynamical Astronomy 100(3): 191-208, March 2008 for a derivation of the slingshot effect equations. There is some relevant material in the American Journal of Physics (the journal of the American Association of Physics Teachers), but they are unfortunately not available online. Still, the journal is not that hard to find in any college or university library, so you can always look them up the old fashioned way: Gravitational Slingshot; Dykla, Cacioppo & Gangopadhyaya; AJP 72(5): 619-621, May 2004 and Gravitational assist in celestial mechanics-a tutorial; James A. van Allen; AJP 71(5): 448-451, May 2003. There is also a Comment on "Gravitational slingshot" along with Reply to "Comment on `Gravitational slingshot,' ''.

There is a Gravity Assist module in the NASA Basics of Spaceflight tutorial. And of course the ubiquitous Wikipedia has a Gravity Assist page. But neither develops the higher level math, though there are several external links from the Wikipedia page that might, I haven't looked.

[mugaliens]

Hohmann transfer orbit

Gravity assist

Orbital mechanics

Tsiolkovsky rocket equation

n-body problem

Have fun!

[marsbug]

Thank you very much everybody, it's always a big heart warmer to see how willing people are to help and get enthusiastic about things here! I think I've got plenty to read on here but if anyone has further suggestions or ideas please post them, the more the merrier! I will keep you all posted on how it goes, and show you the results when things start to come together.
Thank you all again!

[JohnD]

Side thread on slingshots - item in today's New Scientist. The effect of slingshots is not what is expected. There is extra speed to be gained if the probe passes at an angle to the equator.

http://space.newscientist.com/articl...s-at-work.html

John

[NEOWatcher]

Side thread on slingshots - item in today's New Scientist...

Subscription needed to see the details. I don't...

In January, it was thought to be an Unruh electromagnetic radiation effect. I'm sure the angle to the equator has something to do with how those forces react.

Any difference?

The part I could read sounded funny...

To their bafflement, the probe was travelling 3.9 millimetres per second faster than it had any right to be travelling.

It has no "right" to travel faster? But; what if it earns it's privelege to travel faster? If it behaves badly, we can always take that privelege away, can't we?

[slang]

In January, it was thought to be an Unruh electromagnetic radiation effect. I'm sure the angle to the equator has something to do with how those forces react.

See this Universe Today story. It looks like one effect of SR was not properly accounted for in the calculations, so the anomaly was not in what was measured, but in what the measurements were expected to be.

[NEOWatcher]

...so the anomaly was not in what was measured, but in what was expected.

That sounds a bit misleading to me, like I read it wrong... Or maybe I read the article wrong.
But; what I'm getting from it is that the calculation of the measurement of the speed was missing the SR component (or a part of the SR component).

[slang]

That sounds a bit misleading to me, like I read it wrong... Or maybe I read the article wrong.

I think I was not being clear, and changed it a bit. I can't speak to the correctness of either the paper or your statement, it's beyond my understanding of GR (and SR).

[NEOWatcher]

I think I was not being clear, and changed it a bit.

Yes; that is a bit better. thanks. But; I think your statement should be SR, not GR

When a well known but overlooked effect of Special Relativity is taken into account, where the transverse Doppler effect of the Earth’s spin and the velocity of the craft are factored in, there is no flyby anomaly

... it's beyond my understanding of GR (and SR).

Me too, but I don't think I need to understand it to know "what" was not used correctly. If I were to try to understand "how" it were used incorrectly, then I'd be completely lost.

[slang]

You are 100% correct, and I agree with your second statement. Fixed.

[JohnD]

I subscribe to NS on paper, sorry to link to an inadequate reference.
The NS article is a bit long to precis, it features one John Anderson, late of NASA, who announced the Pioneer anomalies and has been studying near-Earth flybys, where the accuracy of the velocity and delta measurements are much greater than with more distant probes. They have studied Galileo (two passes), Rosetta (two and due for a third), NEAR, Cassini and Messenger, and have an empirical formula to calculate the anomaly, that uses merely the entry and exit trajectories relative to the equator. This has held up well with data from previous passes and has been used to predict the anomaly for Rosetta's second pass, but the velocities from that are not yet available. Anderson proposes no mechanism for the anomaly, but hopes that his formula and further study will reveal it. He discounts atmospheric drag, as increase as well as decrease has been observed, or general relativity in the earth's gravity well, as that effect is far too small, as would be any magnetic effect.

Others have invoked MOND or dark matter as the mechanism.
McCulloch seems to have assumed that all the anomalies were positive, which throws the Unruh theory in the bin, as the anomalies are of the order of millimeters/second, and range from Galileo +3.9 and -4.6, NEAR +13.5, Cassini -2, Rosetta +1.8 (first time). (My interpretation, not the MS article)
Anderson predicts +1 for the next two passes of Rosetta.

JOhn

[mugaliens]

Side thread on slingshots - item in today's New Scientist. The effect of slingshots is not what is expected. There is extra speed to be gained if the probe passes at an angle to the equator.

http://space.newscientist.com/articl...s-at-work.html

John

The teaser was there, but I'm not about to subscribe.

Can you be so kind as to paraphrase why this is so?

[mugaliens]

Others have invoked MOND or dark matter as the mechanism.
McCulloch seems to have assumed that all the anomalies were positive, which throws the Unruh theory in the bin, as the anomalies are of the order of millimeters/second, and range from Galileo +3.9 and -4.6, NEAR +13.5, Cassini -2, Rosetta +1.8 (first time). (My interpretation, not the MS article)
Anderson predicts +1 for the next two passes of Rosetta.

JOhn

Since I've yet to see a good explanation, here's mine:

The rotations of all these planets is in the same direction as their orbits around the sun. In all cases where the velocity was increased, it was a slingshot maneuver. Since in all cases it was positive, it's reasonable to assume it has something to do with spacetime in the local vicinity of the planet which is not noticed at a reasonable distance from the planet where the planet can be treated as a point source.

Known:

1. Using the "thumbs up" rule, the rotations and orbits are all positive.

2. All manuevers were done using the slingshot (gravity assist) maneuver, that is, passing behind the planet with a velocity and direct that's also positive relative to the plane of the ecliptic.

3. The spacecraft's transition through the planet's strongest gravitational influence coincided with it's transition through the planet's positive frame-dragging area.

A logical conclusion would be that frame-dragging is the cause. A logical test would be to use a planet with a rotation that's retrograde to the positive motion of the solar system. Since none are available, use Uranus, but make sure that the slingshot maneuver is done in a manner in which the object experiences as much positive frame-dragging time-effect as it does negative.

[frankuitaalst]

The explanation can be found here ...
http://arxiv.org/ftp/arxiv/papers/0809/0809.1888.pdf

[mugaliens]

Ok, GR's Lense-Thirring effect (frame dragging) is negligable. But all that was considered was rotational frame dragging. How about translational (linear) frame dragging (the Earth simply moving through space, the slingshot spacecraft moving behind it, in it's frame-dragged wake, so to speak)?

And what about static mass increase? (an increase in inertia of a body when other masses are placed nearby)

Could the author's SR transverse doppler shift also account for the pioneer/voyager anomalies?