I was trying to get a lower roundtrip delta-V for lunar missions by flying directly to the lunar surface rather than going first into lunar orbit then descending, the "direct descent" mode. Here's a list of delta-V's of the Earth/Moon system:

Delta-V budget.Earth–Moon space.

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Delta-v budget - Wikipedia, the free encyclopedia

If you add up the delta-V's from LEO to LLO, 4,040 m/s, then to the lunarsurface, 1,870 m/s, then back to LEO, 2,740 m/s, you get 8,650 m/s, withaerobraking on the return. I wanted to reduce the 4,040 m/s + 1,870 m/s = 5,910 m/s for the trip to theMoon. The idea was to do a trans lunar injection at 3,150 m/s towards the Moonthen cancel out the speed the vehicle picks up by the Moons gravity. Thiswould be the escape velocity for the Moon at 2,400 m/s. Then the total wouldbe 5,550 m/s. This is a saving of 360 m/s. This brings the roundtrip delta-V down to 8,290 m/s. I had a question though if the relative velocity of the Moon around the Earth might add to this amount. But the bookThe Rocket Company, a fictional account of the private development of a reusable launch vehicle written by actual rocket engineers, gives the same amount for the "direct descent"delta-V to the Moon 18,200 feet/sec, 5,550 m/s:

The Rocket Company - Patrick J. G. Stiennon, David M. Hoerr - Google Books

Another approach would be to find the Hohmann transfer burn to take it from LEO to the distance of the Moon's orbit but don't add on the burn to circularize the orbit. Then add on the value of the Moon's escape velocity. I'm looking at that now. Here's another clue. This NASA report from 1970 gives the delta-V for direct descent but it gives it dependent on the specific orbital energy, called the vis viva energy, of the craft when it begins the descent burn:

SITE ACCESSIBILITY AND CHARACTERISTIC VELOCITY REQUIREMENTS FOR DIRECT-DESCENT LUNAR LANDINGS.

http://ntrs.nasa.gov/archive/nasa/ca...1970023906.pdf

The problem is I couldn't connect the specific orbital energy it was citing to a delta-V you would apply at LEO to get to that point. How do you get that?

With the lower delta-V number, I can carry more payload with low cost proposals for manned lunar missions:

Polymath: SpaceX Dragon spacecraft for low cost trips to the Moon.

The Coming SSTO's: Applications to interplanetary flight.

http://exoscientist.blogspot.com/2012/08/the-coming-sstos-applications-to.html

Bob Clark