Lunar mascons can bring a satellite in LLO down. I guess, in theory, there will be orbits in which they could be used to pump satellites into higher orbits.
Could such an effect be useful in terms of saving fuel when arriving at or departing Lunar orbit?
Not strictly cis-lunar orbital mechanics but related. On the Apollo missions PTC (barbecue roll) was established when in cis-lunar space. I believe that the CSM X-axis was near perpendicular to the line of sight to the sun. Does anyone know the attitude more precisely and why it was chosen? Was the X-axis aligned approximately pointing Earth North or South?
Was the X-axis aligned approximately pointing Earth North or South?
the difference is a matter of a few degrees
Program Constellation selected a 3 burn LOI maneuver with highly elliptical intermediate Lunar orbit (with 24 hours orbital period).
If somebody need an electronic version of BMW book you are welcome to ask.
Was the X-axis aligned approximately pointing Earth North or South?
the difference is a matter of a few degrees
Thanks Jim, that's what I suspected. Do you know if that was North or South or did it vary? Was the choice purely arbitrary?
The usual way to get a spacecraft from the earth to the moon on a fast (few days) trajectory is to first put the spacecraft into a highly-elliptical earth orbit, with an apogee somewhat beyond the moon. Departure from earth (or from low earth orbit) is timed so that the spacecraft will pass not far in front of the moon as the spacecraft nears apogee.
At apogee, the spacecraft is moving slowly with respect to earth -- maybe a couple of hundred meters per second. The moon, however, is orbiting at about 1 km/s. With respect to the earth, then the spacecraft is just kind of hanging there and the moon comes by and sweeps it up. From the moon's point of view, the spacecraft is zooming roughly toward it at about 1 km/s. That's at a distance where escape velocity is below 1 km/s, so the spacecraft must slow down with respect to the moon if it is to go into lunar orbit.
If the spacecraft is in the plane of the moon's orbit when it reaches the lunar vicinity, it will go roughly into an equatorial orbit about the moon. If left earth on an ellipse sightly inclined to the moon's orbit, then on reaching the moon it may be a few lunar radii above or below the plane of the moon's orbit. In this case, when it's swept up by the moon, it may pass over one of the lunar poles and go into a polar orbit. If it goes into a polar orbit, it won't pass behind the moon as seen from earth for the first few orbits. As the moon revolves about earth while the orientation of the spacecraft's orbit remains pretty much fixed, the spacecraft will eventually pass behind the moon as seen from earth. A quarter of a lunar month after arriving at the moon, it will be spending about half of each orbit behind the moon, if it's in a low orbit. This means, of course, that a polar orbit in general lines up for easy return to earth only twice a month, whereas in an equatorial orbit there's a departure opportunity on every orbit.
The other key point is that reaching the lunar poles does not require departing from a polar orbit around earth.
I recently described
a path to the lunar poles. Still a work in progress. I believe what you've described is very similar to what I envision.
I am wondering if there are more formal descriptions of this route.
For reaching the lunar poles some people seem to imagine parking in a low inclination low lunar orbit and doing a 90 degree plane change from LLO. I believe this is what John DeLaughter envisions when
he claims reaching the lunar poles takes 8 km/s. It bothers me when people want to do plane changes deep in a gravity well.
The usual way to get a spacecraft from the earth to the moon on a fast (few days) trajectory is to first put the spacecraft into a highly-elliptical earth orbit, with an apogee somewhat beyond the moon. Departure from earth (or from low earth orbit) is timed so that the spacecraft will pass not far in front of the moon as the spacecraft nears apogee.
At apogee, the spacecraft is moving slowly with respect to earth -- maybe a couple of hundred meters per second. The moon, however, is orbiting at about 1 km/s. With respect to the earth, then the spacecraft is just kind of hanging there and the moon comes by and sweeps it up. From the moon's point of view, the spacecraft is zooming roughly toward it at about 1 km/s. That's at a distance where escape velocity is below 1 km/s, so the spacecraft must slow down with respect to the moon if it is to go into lunar orbit.
If the spacecraft is in the plane of the moon's orbit when it reaches the lunar vicinity, it will go roughly into an equatorial orbit about the moon. If left earth on an ellipse sightly inclined to the moon's orbit, then on reaching the moon it may be a few lunar radii above or below the plane of the moon's orbit. In this case, when it's swept up by the moon, it may pass over one of the lunar poles and go into a polar orbit. If it goes into a polar orbit, it won't pass behind the moon as seen from earth for the first few orbits. As the moon revolves about earth while the orientation of the spacecraft's orbit remains pretty much fixed, the spacecraft will eventually pass behind the moon as seen from earth. A quarter of a lunar month after arriving at the moon, it will be spending about half of each orbit behind the moon, if it's in a low orbit. This means, of course, that a polar orbit in general lines up for easy return to earth only twice a month, whereas in an equatorial orbit there's a departure opportunity on every orbit.
The other key point is that reaching the lunar poles does not require departing from a polar orbit around earth.
I am wondering if there are more formal descriptions of this route.
Still Googling....
A You Tube video of LRO's path. It seems to have a an apogee a little in front of and below the moon as Proponent and I imagine. Looks like it's hyperbolic orbit wrt moon is near polar and I'm guessing they did a burn nearly parallel to it's velocity vector for LOI.
I'm guessing they did a burn nearly parallel to it's velocity vector for LOI.
That makes sense, since a parallel burn is much more efficient in changing velocity.
Of course, as
Jorge pointed out previously, CxP envisioned a different approach, first entering a highly-elliptical lunar orbit of low inclination, then executing a cheap plane-change maneuver at apolune, and finally circularlizing at low altitude. I presume the point of this was to allow a fast free-return trajectory. Free returns exist for lunar polar orbit, but they are slow.
Page 15 has a refuel in free-return-trajectory mission mode.
For some reason, I'm just reading this whole thread now. This is a great idea, a completely different mission mode. Very clever.
Okay, here's a question:
Are there orbits which are shorter than the ~44 transit times from LEO to EML2 that Weak Stability Boundary-type trajectories typically have? I'm looking for something intermediate between WSB (at least 44 days, smallest I've seen?) and Hohmann transfers (which take just a few days? 3-6 days?).
At the one end, the delta-v required is about 3.2km/s, at the other it's 3.73-3.9km/s. Are there solutions in the middle between those two that only take, say, 10-20 days? I'm going to try to answer this question somehow, make a graph of delta-v versus delta-t for LEO to EML2 (or EML1) transfer.
I'm guessing they did a burn nearly parallel to it's velocity vector for LOI.
That makes sense, since a parallel burn is much more efficient in changing velocity.
Of course, as Jorge pointed out previously, CxP envisioned a different approach, first entering a highly-elliptical lunar orbit of low inclination, then executing a cheap plane-change maneuver at apolune, and finally circularlizing at low altitude. I presume the point of this was to allow a fast free-return trajectory. Free returns exist for lunar polar orbit, but they are slow.
One of the requirements of CxP was that intermediate burns don't put crew in an orbit where periselene is below the Lunar crust, in case the subsequent burn fails. This was guaranteed by three burn manoeuvre.
IIRC, the relevant L2 document suggested that a two-burn was slightly lower dV.
Cheers, Martin
I'm looking for something intermediate between WSB [...] and Hohmann transfers [...]. Are there solutions in the middle between those two that only take, say, 10-20 days?
FWIW I believe these transfers exist but finding them is computationally expensive. The general approach is to choose your destination orbit around the Lagrange point and then calculate trajectories (by running time backwards) that are on that orbit's stable manifold. Some locations on the manifold are "close" (in x,y,z,vx,vy,vz space) to the apogees of highly elliptical Earth orbits (or just plain high-Earth orbits), and by maneuvering where the trajectories are close you can patch them together.
Belbruno (January 4, 2012 FISO) suggested doing the patching with electric propulsion. I tried to think about this in a posting here:
I think the more delta-v you are willing to put into making the patch point work, the quicker you can arrive onto the manifold of the destination orbit.
Are there orbits which are shorter than the ~44 transit times from LEO to EML2 that Weak Stability Boundary-type trajectories typically have?
Sure, the ones with a lunar flyby as advocated by Kirk Sorensen for example.