Last night I programmed a simulation of the LM landing on the Moon. The following is a printout of the results:
http://www.braeunig.us/misc/LMdescent.txtColumn 1:Â Elapsed time in seconds from PDI (powered descent initiation)
Column 2:Â Mass of LM less DPS (descent propulsion system) propellant, in kg
Column 3:Â Remaining DPS propellant mass, in kilograms
Column 4:Â Total mass of LM in kilograms, columns 2 + 3
Column 5:Â DPS thrust setting in percent of maximum thrust
Column 6:Â DPS thrust in Newtons
Column 7: LM pitch angle in degrees; 90-degrees is “windows upâ€
Column 8:Â Altitude above mean lunar surface, in meters
Column 9:Â Acceleration of gravity, in m/s^2
Column 10:Â Vertical acceleration of LM, in m/s^2
Column 11:Â Horizontal acceleration of LM, in m/s^2
Column 12:Â Vertical velocity of LM, in m/sec
Column 13:Â Horizontal velocity of LM, in m/sec
The initial conditions shown at T=0 are from the Apollo 17 mission reports. The values for thrust setting and pitch angle were determined and entered by me. All other data is calculated from the initial conditions, the changing thrust and pitch, and the known lunar parameters.
I had only scant information regarding thrust and pitch settings. I had to fill in the missing data by estimating thrust and pitch based on my experience. Altitude and velocity information for six data points were known from NASA reports – the starting and ending points and four intermediate points. I adjusted the thrust and pitch as necessary to make the simulated results match as closely as possible the known data points. For example, occurring at T+440s was an event called “DPS Throttle Recoveryâ€. Below are the planned altitude and velocity for Apollo 17 from NASA and my simulated data:
            NASA   Bob B.
Altitude:       7,847 m  7,845 m
Horizontal velocity   366 m/s  375 m/s
Vertical velocity    -27 m/s  -26 m/sThe closeness of these numbers show that the simulation is working. I probably could have gotten even closer by tweaking the spacecraft attitude a bit more, but this is close enough for my purposes. The intent of the simulation is not to make a perfect match, but rather to show that the LM had sufficient thrust and propellant to soft-land on the Moon.Â
As you can see, after 720 seconds the simulation shows the LM on the ground (altitude=0) with zero vertical and horizontal velocities. The amount of propellant remaining is 913 kg. The actual Apollo 17 landing lasted 721 seconds and had 596 kg of propellant remaining. The simulated numbers verify the real numbers as reported by NASA within a small margin of error.
I performed a similar simulation of the LM's ascent to orbit last year. The results of that simulation again showed the information reported by NASA as accurate.Â