Landing the LM Aug 29, 2011 10:45:48 GMT -4
Post by Bob B. on Aug 29, 2011 10:45:48 GMT -4
That’s correct. The LM was given enough delta-v to land on the moon, not to land on the moon and make a plane change. Had the LM squandered its propellant making a plane change, there wouldn't be enough left over to land. Therefore it wasn’t possible for the LM to land at a position that was far out of plane.
The CSM typically made a plane change prior to LM ascent to bring the landing site back into the orbital plane. Over time the landing site would move out of plane, partly due to the Moon’s rotation and partly due to the CSM's orbital precession. For example, the Apollo 17 CSM performed a 366 ft/s lunar orbit plane change maneuver about 5½ hours before the LM lifted off. This is enough delta-v to make about a 4 degree plane change.
We know the CSM had at least this much capacity to make a plane change. How much more it could do depends on how much unused propellant it had at the end of the mission. Each additional degree of plane change would require about 93 ft/s delta-v. On average, the CSM mass just prior to SM jettison was about 26,500 lbm. So, in rough numbers, it would take about 240 lbm propellant for each additional 93 ft/s delta-v.
I don’t have the SPS propellant numbers available to me right now, but it would be pretty easy to look up how much propellant was remaining at the end of each mission. For each 240 pounds remaining, the CSM could have performed roughly one additional degree of lunar orbit plane change. Of course we have to consider that some of the remaining propellant could be unusable, i.e. it might not be possible to drain every drop from the tanks and get it into the combustion chamber.
Please note that to determine how much propellant was required to provide the additional delta-v, I used the mass of the CSM at the end of the mission rather than the mass at the time the plane change was performed. At the time of the actual maneuver, the CSM would be heavier and the plane change would require more propellant. However, this unscheduled maneuver would lighten the CSM so that subsequent maneuvers, such as TEI and MCC, would require less propellant. The effect of the additional plane change on propellant usage would be as if the extra delta-v were tacked on at the end of the mission.