Getting into Lunar POLAR orbit

[RuBisCO]

I remember hearing talk that the baseline Saturn V-Apollo system lacked the Delta-V to enter Lunar Polar orbit. This gets me wondering, why does it require more Delta-V to enter Lunar polar orbits and by how much compared to a lunar equatorial orbit? I good question for KSP is could this difference be determined in in KSP with the Mun?

[OtherDalfite]

Mostly for the same reason that getting into a polar orbit expends more Delta-V then equatorial. Mostly just for the inclination change, but more so it's a bit more complicated to come back to Earth when you're in a polar orbit, because the extra normal or anti-normal altitude changes your placement. I'm unsure about velocity if leaving from a polar orbit, but what makes sense to me is the inclination changes, as those can be pretty taxing if you don't start immediately from launch.

[Nibb31]

Getting into polar orbit only requires a small change during the LOI burn. However there were other constraints that made a near-equatorial lunar orbit desirable. For example, they wanted to land with the sun behind them, for better visibility. The landing sites also had to be properly lit, and had to face the Earth. The biggest requirement though was that an equatorial orbit is safer, because you have your free-return trajectory if the SPS engine fails to start (or if you do an Apollo 13) and you get one TEI window every orbit whereas things are much more complicated if you are on a polar inclination.

[K^2]

Mostly for the same reason that getting into a polar orbit expends more Delta-V then equatorial. Mostly just for the inclination change, but more so it's a bit more complicated to come back to Earth when you're in a polar orbit, because the extra normal or anti-normal altitude changes your placement. I'm unsure about velocity if leaving from a polar orbit, but what makes sense to me is the inclination changes, as those can be pretty taxing if you don't start immediately from launch.

Nah. Try it in KSP. If you think in terms of SoI, there is almost no difference. Just plot your transfer to touch Mun SoI in direction of one of the poles. Same for the return trip. dV is almost the same.

In the real world, however, you are dealing with 3-body physics. You are never influenced by just the Earth or just the Moon. That makes transfer from Earth to a roughly equatorial Lunar orbit to be significantly easier than a transfer to a polar orbit. I don't think there is a simple way to visualize this. You kind of have to work in a rotating frame, where Earth and Moon are almost static with respect to each other due to effective potential of the rotating frame. Then see how the forces on a transfer trajectory work to note that it's easier to organize a transfer in the plane of Earth-Moon system than out of the plane.

Basically, the simple answer is 3-body physics, and complicated answer is complicated.

[PakledHostage]

There is a good article about the Apollo mission launch constraints on NASA's history website. It supports much of what has been said already:

http://history.nasa.gov/afj/launchwindow/lw1.html

[OtherDalfite]

Nah. Try it in KSP. If you think in terms of SoI, there is almost no difference. Just plot your transfer to touch Mun SoI in direction of one of the poles. Same for the return trip. dV is almost the same.

In the real world, however, you are dealing with 3-body physics. You are never influenced by just the Earth or just the Moon. That makes transfer from Earth to a roughly equatorial Lunar orbit to be significantly easier than a transfer to a polar orbit. I don't think there is a simple way to visualize this. You kind of have to work in a rotating frame, where Earth and Moon are almost static with respect to each other due to effective potential of the rotating frame. Then see how the forces on a transfer trajectory work to note that it's easier to organize a transfer in the plane of Earth-Moon system than out of the plane.

Basically, the simple answer is 3-body physics, and complicated answer is complicated.

I think I get you. I must have been thinking in a simple 2-body system in which you wouldn't have alternative forces working on you. Thanks for clarification.

[RuBisCO]

Ok well there was talk about post Apollo 20+ missions being polar, up to 45 day mission using a Block III service module with up to 14 days on the surface. In KSP it took me about 3-4% more Delta V to do a Polar orbit over an equatorial orbit and all it required was a mid-course correction. I can understand that a window of return only comes every 14 days from polar orbit, but does it cost more Delta V to do?

[RuBisCO]

There is a good article about the Apollo mission launch constraints on NASA's history website. It supports much of what has been said already:

http://history.nasa.gov/afj/launchwindow/lw1.html

Well this provides much more information than that 3-body hand waving BS, clearly they could do polar orbits with this "Hybrid mission" profile that was done from Apollo 12-17, so the cost in Delta-V must have been very small, and it sounds like the same thing we can do in KSP to achieve polar orbit around the mun. First an elliptical orbit that targets the Mun/moon, followed by a mid-course correction to get the inclination around the Mun/moon you want. I understand that Polar orbits would have only 2 return windows per lunar month though, without plane change or much higher delta-v then equatorial return.

[K^2]

3-body hand waving BS

Then I suggest you do rigorous computations of the trajectory in the 3-body case and compare the two scenarios. Have fun with that.

[RuBisCO]

Then I suggest you do rigorous computations of the trajectory in the 3-body case and compare the two scenarios. Have fun with that.

I'm pretty sure they did that back in the Apollo program, sure they used punch cards and such but this is what they calculated: http://history.nasa.gov/afj/launchwindow/figs/Fig%2022.png

and extra note on the subject:

"One of the difficulties in flight planning the hybrid mission was that the initial trajectory was not amendable to conic approximations. So much time was spent milling around out near the moon that conics or patched conics do not provide accurate simulations. It was extremely important that rapid calculation procedures be available (in the Real Time Computer Complex-RTCC) because of the large number of iterations required to "search in" or design a mission trajectory. This was in the early days of high speed computing, so these calculations required resources which are hard to comprehend today. And if all of this must be done with precision integrating trajectory programs, the time required became excessively large."

So in short n-body physic did not add any noticeable Delta-V requirements to go from equatorial to lunar polar orbit, but does add a lot of computing time to get the inclination and altitude you want.

Edited November 16, 2013 by RuBisCO

[K^2]

Right, so I'm not sure why you are calling it B.S. 3-body physics is a big part of why the trajectory is more expensive. And anything you approximate with conics just isn't going to give you that. Your 3/4% increase is just poor planning. With SoI approximation, you can do much better.

[RuBisCO]

Right, so I'm not sure why you are calling it B.S. 3-body physics is a big part of why the trajectory is more expensive. And anything you approximate with conics just isn't going to give you that.

Hey man I'm citing NASA on that, they could have done polar orbits within the specification of the Apollo program, PakledHostage link basically proves it, and that was with the service module providing the mid-course correction, so the delta-v must have been very low. I'm calling BS on the claim n-body physics adds significant Delta-V, unless you can do or present calculations that explain otherwise, just saying it does so with no formal proof or calculations is hand-waving BS.

[PakledHostage]

In the immortal words of Rodney King: "Why can't we all just get along?"

I didn't post that link to fuel an argument... At the very least, please leave me out of it.

[RuBisCO]

In the immortal words of Rodney King: "Why can't we all just get along?"

I didn't post that link to fuel an argument... At the very least, please leave me out of it.

Fine fine, here another paper from the era, its mainly about the advantages of using L1/L2 (which we can't do in KSP because of lack of N-body physics) There some stuff in their about polar orbits as well.

http://www.lpi.usra.edu/lunar/documents/NASA%20TN%20D-6365.pdf

Pg 48: Going from L2 to Polar orbit would cost at most 61 m/s more then going to Equatorial orbit, which by the way is a minimum of ~770 m/s.

Pg 55: Describes a hypothetical Lunar shuttle mission using polar orbits: 3139 m/s from 185 km earth orbit to 108 hr lunar transit, 914 m/s to 111 km lunar (polar) orbit, those times are nearly identical to average Apollo missions (3160+900), except this shuttle coasting time is ~31 hours longer.