Moon to Mars 2011 solution:
We do a 4 burn solution. Start with a prograde burn to raise the Ap very high. At the Ap, do a single burn that does a plane change of 90 degrees aligning with the ecliptic. At the moon gravity well do a prograde lunar ejection burn that sends you to a low Pe at Earth, then as you round the Earth do the final prograde burn. All that’s left are MCCs.
Finding the solution:
The usual low deltav path from the moon to Mars is to retrograde from the moon and fall toward Earth rounding it just above the atmosphere and in the gravity well do a prograde burn. Often just 450 m/s are enough of a burn in the Earth gravity well to transfer to Mars.
To solve for a solution one can start by looking at the transfer stage from Earth to Mars. Setting up as a sling type plan seems to allow an easier progression through the various values for strength and direction of the ejection and while doing it watching the Earth centered stage for the orientation of the hyperbolic eject trajectory. From this, we need to look at where the moon is at the time 3 to 6 days before the date of the Earth eject. Then finally if the moon is in the correct location for the craft to fall to Earth, we then need to look at the orientation of the orbit at the moon. BTW, to create the plan in stage 3 (sun centered), turn Autoplan “Off” then choose “Sling” as the plan, and the trajectory will appear in stage 2 if in stage 2 you turn Advanced “On” and then for Plan Type choose “Initial”.
Craft that are already in orbit around the moon can be tougher to find a solution than if they are landed on the moon. Highly inclined lunar orbits generally only have two windows a month for an efficient eject from moon to Earth. Remember that the eject needs to be retrograde with respect to the moons motion around the Earth. If the orbit at the moon is low inclination then the option to eject toward Earth occurs once every lunar orbit.
When adjusting the Earth to Mars stage, changes in the “outward” of the sling change the direction of the eject trajectory going around the Earth. This means that if a solution is close but the moon’s location is off by a day or two, you can bring the eject trajectory to match the moon’s location instead of changing to a different eject date. Or consider a combination or changing the strength, direction and date. But large outward and inclination angles in the sling plan are not very efficient. But used in moderation they sometimes allow a fairly low deltav solution for the Earth Mars transfer.
The moon to Earth 2011 challenge is specifically set up to make no obvious solutions. The orbit is oriented with a LAN of 315. The best location of the moon going around the Earth for the ejection is when the moon is at either at the 7:30 or 1:30 position (as in looking at a clock face, Orbit MFD, ref earth, target moon, view ecliptic). A variety of plans for Earth to Mars were tried but adding enough outward inclination and velocity made any candidate too costly in deltav to be successful.
A solution was found by trying a different approach. Instead of adding expensive outward and inclination to the sling plan (because several hours trying this method had failed), I tried going through several weeks of possibilities with a zero inclination, zero outward highly efficient Earth to Mars sling plan. An eject date of 52023.7798 and velocity of 2856 m/s with zero outward and inclination was a very efficient Earth Mars transfer. The good news was that the moon was in near perfect position about 6 days before (mid 52017) to do the retrograde eject from the moon to begin the long fall toward Earth. Unfortunately the orbit of the craft around the moon was oriented to eject just 20 degrees from directly toward or away from the earth. This would not work as a direct eject since we must eject retrograde away from the moon to then fall toward Earth.
The solution finale comes by realizing that one can burn to create a high Ap out from the moon and the Ap is positioned directly away from the Earth. Then at the Ap, a low deltav, low velocity, 90 degree plane change allows falling back toward the moon aligned with the ecliptic rounding it on the leading side and a gravity well burn near the moon will send it in the required retrograde eject from the moon. It takes a about 2.5 days to do this high Ap single orbit for the plane change so if we wish to arrive back at the moon on 25017.5 then we need to start our initial high Ap orbit on 25015.
The highly eccentric orbit for the plane change was unfortunately not directly lined up with the Earth Moon line which would cause the fall to Earth to take too long. But doing the moon gravity well burn a bit before arriving at the lunar Pe, though less efficient, does the trick of keeping the Earth Pe date in the window for the Mars transfer..
Moon to mars challenge solution: (4 main burns)
Warp to Date=52015.00000
Raise the Ap. Open Align MFD reference moon and set a custom target orbit of ecliptic Inc=0 LAN=0. Starting 20 seconds before reaching DN, burn prograde to raise the Ap until T=~190,000 seconds as shown in Orbit MFD.
Plane Change. Warp to the AN in Align MFD same target alignment as above. Note the orbital velocity value in Orbit MFD (should be around
132 m/s) Set up a TransX maneuver to change planes to match the surrogate by, Vel=
-132, PlaneChange=
+132, and also mix in some outward of about -20 m/s (the negative makes it inward). As you burn watch Align MFD, and stop the burn as it reaches minimum relative inclination. Bring up Orbit MFD. The Pe value should be anywhere from 0 to +500 Km agl. It’s not critical.
Eject Moon, toward Earth. Warp ahead to about 3000 seconds before Pe. Set up a TransX maneuver to burn prograde ~ 1500 seconds before the Pe. Escape FWD to Earth stage. Raise the prograde value until it has a Closest Approach about 6500 Km radius. Note: Changing the maneuver Date value will change the Earth encounter date. Have the Earth encounter date be something between 25023.8 and 25024.8. Have IMFD up to supply actual Earth Pe in its Map program, burn to make Pe= 145 Km. When PeT is around 100Ks (a bit over 1 day), use IMFD to see the Pe value. Burn inward or outward to have the Pe value anywhere from 140 to 175 Km agl. Lower is a bit more efficient in the next step. Now warp to about 1000 seconds before Earth Pe.
Eject Earth, toward Mars. Set up a TransX maneuver, centered at Earth Pe with prograde value to minimize arrival at Mars. Burn using IMFD, ref=sun, target=Mars for shutoff timing to minimize closest approach to Mars. Warp ahead to half way to Mars. TransX maneuver with mostly plane change and some Outward as your MCC to hit Mars. Do additional MCCs as needed.
