
Math & Physics Mathematical and physical problems of space flight and astronomy. 

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01202018, 12:08 PM  #31 
Orbinaut

Heh  I happened to stumble across a treasuretrove (of course I knew in theory of such things, but, well, hands on is always different).
I couldn't resist trying to plan a trajectory to the Moon once it was insim, and stumbled upon the whole zoo of low energy trajectory solutions. If the spacecraft gets just nudged into the L1 Lagrange point region, the future trajectory can be altered with really tiny propellant usage  basically the vessel gets pulled towards the Moon, but by a tiny nudge this or that way, the closest distance can be controlled  which leads to vastly different swingby scenarios  the craft can be deflected out of the orbital plane by 90 degrees, or set onto a retrograde orbit away from the Moon where it leaves its Hill sphere quickly  or deflected along the lunar orbit, where it gets decelerated by the Moon following it and relatively easily ends up in a closed orbit via a small deceleration burn (for comparison, a Hohmann arrival burn at lunar orbit takes 590 m/s, my cheapest capture into an elliptic orbit was around 150 m/s (there's probably even cheaper solutions  I didn't run the simulation for too long, so I wanted to see periodicity soon). At the same time, there's a series of marginal orbits where the craft goes around the Moon a few times, but then the perturbations by Earth grow so much that it leaves lunar orbit again. I'm still struggling to get a good visualization of what is happening  plotting trajectories in 3d space easily leads to a lot of Spaghetti. But this is terribly good fun to explore. (Sorry to those who already know this stuff to sound overexcited...) 
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04112018, 05:31 PM  #32 
Orbinaut

Despite movie making, I've finally managed to bring the next version 0.3 of the software into existence, source code can be found in the usual place.
This allows to specify the gravitational influence of (up to five) other bodies on an orbit around Earth  but you can use it to explore transfer to the Moon if you so desire (an Earthcentered coordinate system is just a bit awkward to specify the state vectors). I've ran some sanity tests, and the resulting perturbations look qualitatively like I'd expect, the orbital dynamics around the Moon seems okay and the one where I found an analytical benchmark (mean drift of the longitude of ascending node of a geosync orbit due to the Moon) seems to come out okay, but I will honestly say that coding the perturbations in Earthcentered coordinates I have managed to confuse myself no less than three times, so there may be bugs left to discover. I'll start adding new pages to the tutorial series tomorrow to explain the new functions  have fun! (Transfers will probably be a bit more userfriendly in the next version...) 
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04122018, 08:31 AM  #33 
Beta Tester

Windows executable of your 0.3 code: https://snoopie.at/face/beta/leo_targeting.exe
I've tested it with the lunar orbit config, resulting in this zoomed plot of the leftmost orbit differences: 
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04122018, 09:14 AM  #34 
Orbinaut

That's the moonrelative, right?
My suspicion is that gets a lot of perturbation from Earth, but I haven't analyzed in detail. 
04122018, 09:31 AM  #35 
Beta Tester

Quote:
No particular interest here, I just wanted to quickcheck the binary. 
04132018, 05:36 AM  #36 
Orbinaut

Thanks for the Windows work  the executable should now be available (and the first tutorial page is also added).

05232018, 05:14 AM  #37 
Orbinaut

Quick note: I just discovered a regression in the latest version of the code that leads to PEG7 targeted burns not being executed when imperial units are chosen (seems my attempts to streamline the unit management were not entirely successful).
I *think* I understand the issue and will publish a fix shortly. 
05252018, 12:48 PM  #38 
Orbinaut

The bugfix version 0.31 is now online.

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05252018, 02:24 PM  #39 
Beta Tester

Windows executable of your 0.31 code: https://snoopie.at/face/beta/leo_targeting.exe
I've only done a quick smoketest by means of running it with the shuttle insertion config. 
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05252018, 06:00 PM  #40 
Orbinaut

Windows executable is also online.
Sorry for the mess... should have done more regressiontesting... 
12222018, 12:09 PM  #41 
Orbinaut

It's been a while, but I'm now adding support for rendezvous calculations into the tool  here's a first test for a relative motion plot  both target and chaser initialized at the same position, but chaser has a lower speed.
The plan is to add a search for the best transfer orbit as well as a simulation of the stationkeeping problem. 
12312018, 06:53 PM  #42 
Orbinaut

Seems I now have a numerical Lambert solver running...
For specified ignition times TIG 1 and TIG 2 , this computes a 2burn transfer solution via a numerical fit (i.e. J3 gravity, nth body perturbations and finite burn duration optionally taken into account). Here's a range of trajectories in targetrelative coordinates for the interceptor starting on a phasing orbit 20 km lower using TIG 1 of 8150 s for different values of TIG 2. The first transfer is really quick and hence quite pathological  it uses large Delta v values to get there so quickly, so the deceleration burn isn't perfect and there's a residual relative motion with the target. The 11000 s solution already goes through a higher apsis and intercepts the target from the front. The tool spits it out all nicely: Code:
Parameters of burn: Lambert_1 TIG : 8150 Lambert 1 Dx (prograde) : 6.93143 Dy (normal) : 0 Dz (radial) : 6.34362 TIG : 12000 Lambert 2 Dx (prograde) : 4.66364 Dy (normal) : 0 Dz (radial) : 11.8419 For too unreasonable transfer problems, the fit refuses to converge. After some more stresstesting of the fit, I'll implement a fit for TIG1 fo get a nearHohmann solution automatically. This is actually fun to play with... 
01052019, 12:19 PM  #43 
Orbinaut

... and I'm happy to present the 0.4 release of the code (source code available from the usual place ).
This version now includes the ability to define a rendezvous target, do relative motion plots and obtain numerical solutions for the Lambert problem (transfer to the target for specified start and end times)  at least where the transfer is 'reasonable' (it won't do multiple orbit phasing solutions or split second transfers with warp acceperations...) What does a numerical tool do which an analytical Lambert solver does not? J3 gravity, finite burn duration and such things. Here's an example of a solution obtained for the analytical situation (spherical gravity field, impulse approximation for burns) in black  with the parameters then inserted into a J3 field and a spacecraft with the acceleration capability of the Shuttle OMS engines (the initial point is a good 350 km away, shown is the magnified arrival region). The analytical solution misses the target by about 2.5 km and does not actually bring the chaser to a good rest relative to the target  so it'd require further corrections. I found this feature of the code really fun to play with and explore when one can forget about orbital mechanics, when this won't work, what solutions rendezvous with emore eccentric orbits etc. Enjoy! 
01062019, 09:13 AM  #44 
Beta Tester

Windows executable of your 0.4 code: https://snoopie.at/face/beta/leo_targeting.exe
A test with the example rendezvous_lambert1.cfg yields this XYplot: 
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01062019, 02:44 PM  #45 
Orbinaut

Thanks...
The plot is the same I get, but unfortunately it shows that I've put a regression into the fit strategy (the last burn doesn't come out as precise as it could...). I'll have to delve into this and decide whether a bugfix is needed or whether this can wait till the next version. Last edited by Thorsten; 01072019 at 09:16 AM. 
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