Some numbers:
Lunar surface gravity is ~ 1.6 m/s^2, which is 1/6 of Earth’s surface gravity, not 1/3.
Orbital velocity at the Apollo lunar parking orbit (from where the LM began its descent) of ~110 km is given by sqrt(GM/r), where G is the gravitational constant, M is the mass of the Moon, and r is the distance from the center of the moon (mean lunar radius + 110 km), which gives us roughly 1671.6 m/s if I’ve done the math right (which I think I have, since Wikipedia gives the delta-v from lunar orbit to the surface as ~1.6 km/s).
So the LM had to go from 1671 m/s to 0 m/s relative to the Lunar surface to land safely.
From the Tsiolkovsky rocket equation (dv = ve * ln(m0/m1)), we can get a very rough idea of whether the LM’s Descent Propulsion Stage (DPS) was up to the task.
required delta-v (dv) is 1671 m/s;
DPS specific impulse was rated at 311 sec, meaning an effective exhaust velocity (ve) of around 3000 m/s (again, if I’ve done the math right);
DPS propellant mass: 8200 kg;
LM mass at start of descent (m0): 14696 kg;
LM mass at touchdown (m1): 14696 – 8200 = 6496 kg;
So, 3000 * ln (14696/6496) ~ 2240 m/s.
That’s a 0th-order estimate, not taking into account that the DPS could be throttled during the descent, and assuming that *all* the propellant is used during the descent. But as a first cut, it shows that the LM DPS had the necessary power and propellant to land safely.
As it is, the DPS was rated at 2500 m/s delta-v, which was more than enough to soft-land on the lunar surface.
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The following report has been discussed elsewhere in the thread: http://ston.jsc.nasa.gov/collections/TRS/_techrep/CR188427.pdf
Here was the conclusion:
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