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LOPG to Brighton Beach and Back Again
by MontBlanc2012 03072019, 02:45 AM
Here's a challenge that might appeal:
NASA has proposed parking its planned LOPG (Lunar Orbital Platform Gateway) station in a Near Rectilinear Halo Orbit (NRHO) and, from this station, allow lunar landers to target landing at any site on the Moon's surface. This raises interesting questions about the most fuel efficient strategies to depart LOPG and land on the surface; and, equally, to depart the Moon and rendezvous with LOPG. Following on from recent postings in relation to halo orbits (See here), I've constructed a scenario with two DeltaGliders. The first DeltaGlider is parked in a LOPG style NRHO; and the second is at Brighton Beach. One can either try to find the most fuelefficient for the first DeltaGlider to land at Brighton Beach from its LOPG orbit; or one can take the Brighton Bach DeltaGlider and find a fuel efficient rendezvous strategy for rendezvousing with the DeltaGlider. The Near Rectilinear Halo Orbit that the first DeltaGlider is placed in is a fair proximities for the 'real' proposed LOPG orbit: it's a L2 halo orbit with a near 4:1 synodic orbital resonance  so this challenge will do a fair job of simulating the type of problems that one might encounter in landing and rendezvousing. The scenario is as follows: Code:
BEGIN_ENVIRONMENT System Sol Date MJD 52013.754909351 Help CurrentState_img END_ENVIRONMENT BEGIN_FOCUS Ship GL02 END_FOCUS BEGIN_CAMERA TARGET GL02 MODE Cockpit FOV 40.00 END_CAMERA BEGIN_SHIPS GL01:Deltaglider STATUS Landed Moon POS 33.4450800 41.1217030 HEADING 66.59 ALT 2.553 AROT 18.270 16.773 41.004 AFCMODE 7 PRPLEVEL 0:1.000000 1:1.000000 NAVFREQ 0 0 0 0 XPDR 0 HOVERHOLD 0 1 0.0000e+000 0.0000e+000 GEAR 1.0000 0.0000 AAP 0:0 0:0 0:0 END GL02:DeltaGlider STATUS Orbiting Moon RPOS 16083384.788 3158071.948 5516819.356 RVEL 382.8380 536.2102 146.3039 AROT 74.634 34.764 157.159 AFCMODE 7 PRPLEVEL 0:1.000000 1:1.0000000 NAVFREQ 586 466 0 0 XPDR 0 HOVERHOLD 0 1 0.0000e+000 0.0000e+000 AAP 0:0 0:0 0:0 SKIN BLUE END END_SHIPS There are no 'rules' for this scenario other than that for the BrightonBeach to LOPG rendezvous variant, the orbit of the LOPG vessel must not be changed. It's on a carefully calculated ballistic trajectory and it's orbit cannot change. And don't take too long: the orbiting DeltaGlider isn't subject to active stationkeeping and after one orbit will start to deviate significantly from the NRHO track. Last edited by MontBlanc2012; 03072019 at 12:43 PM. 
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Comments 16

Thanked by: 
03072019, 11:27 AM  #2 
Orbinaut

Where is "Date MJD" ?

03072019, 12:44 PM  #3 
Orbinaut

Ajaja  yep, sorry about that: I accidentally omitted the ENVIRONMENT section of the scenario. I've now amended the scenario in the above.
Cheers. 
03112019, 04:12 PM  #4 
Orbinaut

Something odd. GL02 escapes Moon after two revolutions. Is this really NRHO? Can you recheck, please?

03122019, 12:20 AM  #5 
Orbinaut

Quote:
The fact of the matter is that the halo orbit used as a basis in this scenario is a numerically precise for the CR3BP but it does not (and is not intended to) take full account of gravitational perturbations  principally those due to the Moon's orbital eccentricity and solar tidal forces. Moreover, Also, note that the because (in twobody terms), the orbital eccentricity is high. This means that the DeltaGlider is only weakly bound to the Moon. After two revolutions, it seems, perturbations kick the DeltaGlider up to an energy state where it can 'escape' the Moon. This weakly bound state is confirmed by calculating the Jacobi constant for the orbit which is close to 3. This scenario was set up so that readers could get a feel for the kind of orbit that LOPG will be placed  i.e., a high inclination and high elliptical orbit  and was intended to highlight to orbital rendezvous problems that this orbit creates for going to or leaving LOPG. Is it possible to create a high fidelity LOPG orbit for Orbiter? Yes, it is  but it requires a robust framework for performing active stationkeeping over weeks or months; and it requires splicing together a trajectory solution using a full ephemeris gravity model over multiple lunar orbits. 
03122019, 09:52 AM  #6 
Orbinaut

It has to be more than 23 revolutions. For example try this values (for the same Date MJD 52013.754909351):
RPOS 12142686.086 14397704.633 5091606.013 RVEL 176.6108 590.1609 100.3061 I'm not sure if it is exactly a NRHO, I didn't do the math, just did a simple "bruteforce" optimization in GMAT to find a stable LOPGlike orbit, and it's definitely much more stable in Orbiter too. 
03122019, 02:19 PM  #7 
Orbinaut

Ajaja:
it's a case, really, that not all NRHOs are made equal. The scenario I put forward has an initial perilune of around 6,700 km whereas yours appears to have a perilune that is much lower at around 2,500 km. The stability of NRHOs is strongly dependent on this perilune radius. According to Kathleen Howell (Professor of Aeronautics and Astronautics in the College of Engineering at Purdue University and advisor to NASA on all things halo), the stability of orbits in the CR3BP varies according to perilune as shown the following figure: This figure was extracted from her paper: Near rectilinear halo orbits and their application in cislunar space which is a 'good read' if one is interested in the subject. Basically this shows that there are regions of stability of NRHOs (in the CR3BP model) and these occur when the perilune radius is very low; or when it is around 15,000 km. But for NRHOs with perilunes of circa 7,000 km as per my scenario, the number of revolutions before departure is expected to be about one. And that's exactly what we observe. On the other hand, you have selected an orbit with a much lower perilune and, according to the graph, it has a higher stability and may survive a few more orbits before departure. So the fact that your halo orbit survives longer that mine before departure is a bit of a blessing  but not unexpected. But it doesn't say anything else. Congratulations, though, on using GMAT to construct a NRHO. 
03122019, 02:49 PM  #8 
Orbinaut

Yes, the periapsis was redused by GMAT.
BTW, they want to use a low perilune for LOPG too: https://en.wikipedia.org/wiki/Lunar_...atformGateway The LOPG would be placed in a highly elliptical nearrectilinear halo orbit (NRHO) around the Moon which will bring the station within 1,500 km (930 mi) of the lunar surface at closest approach and as far away as 70,000 km (43,000 mi) on a sixday orbit.[15] This orbit would allow lunar expeditions from the Gateway to reach a polar low lunar orbit using 730 m/s of deltav in half a day. Orbital stationkeeping would require less than 10 m/s of deltav per year.[16] 
03122019, 02:57 PM  #9 
Orbinaut

I've seen various figures for LOPG perilune orbital period. As I understand it, the goal is to have a synodic resonance of either 9:2 or 4:1 to avoid occultation of the solar panels. Assuming that the synodic period of the Moon is around 29.5 days, a 4:1 resonance has a period of around 7.35 days; and a 9:2 resonance has a period of 6.5 days. The 4:1 resonance has quite a high perilune; whereas the 9:2 resonance has a substantially lower one.

03122019, 04:37 PM  #10 
Orbinaut

Yes, with your periapsis it is less stable, but still, it should be possible to do more than 23 revolutions:
RPOS 15969338.210 3884420.146 5698604.470 RVEL 368.6800 556.7144 165.8636 
03132019, 03:17 AM  #11 
Orbinaut

Ajaja:
Thanks for recalculating with GMAT with a more comparable perilune. I guess the question is: where and why is there a difference? As a bit of preamble, let's just compare the osculating orbital elements of the two orbits: Code:
MB GMAT  Perilune radius: 6,770 km 6,779 km Eccentricity: 0.8460 0.8751 Inclination: 91.76 deg 93.98 deg LAN: 198.60 deg 198.73 deg Argument of Periapsis: 98.61 deg 94.99 deg Is the GMAT solution 'better'. Yes, in that it takes into account perturbations in a more accurate and more systematic fashion. But it is also a 'black box' solution and generally I prefer to work with tools that I've built. That's just me. Can I build a GMATlike full ephemeris solver? Yes, but not just yet. That's work in progress. Should one use the GMAT solution in this scenario instead? Well that all depends on what you want to do with scenario? The original intention of the scenario was: * to illustrate a LOPGlike NRHO; * to highlight the practical implications of leaving the quasi halo orbit and landing a manned lander at 'an arbitrary point' (Brighton Beach); and * to highlight the difficulties of achieving rendezvous with LOPG where one assumes that one doesn't want to have a crew trapped in a cramped lunar lander for more than perhaps a day or two. 
03132019, 08:42 AM  #12 
Orbinaut

Quote:
Currently for this scenario I see two opposing solutions. The first (timecritical and fuel wasteful) is to catch the ship near the perilune. The second (economical) is to meet our LOPG in the apoapsis. The first one, I think, is possible to do in Orbiter with standard instruments, but the second one is a real challenge especially without using some thirdparty tools like GMAT. Although LTMFD or IMFD could help here. The issues with orbit stability appeared when I tried to apply simple approach to solve the challenge. I waited when the NRHO plane aligns with the longitude of Brighton Beach. Looks like for regular cargo/crew transfers between LOPG and a nonpolar base at Moon it is the best way. The NRHO plane makes whole turn in a month, so we should have 2 windows per month. It doesn't work in our case, but a more stable NRHO would be suitable for simulating such transfer in Orbiter. 
03132019, 01:54 PM  #13 
Orbinaut

Quote:
Rendezvous at apoapsis would have astronauts in the lunar lander for threefour days. Let's hope that whatever design for the lunar lander is used, it is a little bit more than a glorified tin can. Quote:
('my' NRHO doesn't simulate this corotation character of NRHOs very well  although it achieves it to a limited degree and for a limited time. But having looked at the IMFD projection of your GMAT solutions, your solutions should simulate this behaviour much better.) 
03132019, 02:39 PM  #14 
Orbinaut

Quote:

03142019, 09:32 PM  #15 
Orbinaut

GMAT gives an interesting solution:
The green line is the trajectory to the LOPG from a low circular orbit above BrightonBeach and the yellow is the return trajectory. The most interesting fact is that we need less than 200 m/s at the apoapsis to align speed with LOPG, dock, and then to make a burn to return back. dV = 2343 m/s + 86 m/s + 99 m/s + 2344 m/s Last edited by Ajaja; 03142019 at 09:34 PM. 

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