### Author Topic: Lunar Landing Module and how it landed on the moon: a few questions...  (Read 2198 times)

#### aceshigh

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##### Lunar Landing Module and how it landed on the moon: a few questions...
« on: 07/13/2010 08:43 PM »
Hello, I do participate in a few conspiracionist websites, by exposing the Incorrect of the conspiracionists and their stupid theories.

Not being a specialist though, I cant answer all questions. Thus, I would like the help of some members here, who can do the calculations to prove to some of these morons that YES, the Lunar Landing Module COULD land on the moon. (I always do parallels to current missions, but its not easy to convince them).

ANyway, here is the conspiracist post, translated into english. You can laugh at the idiocy. But anyway, more detailed help would be welcome

Quote
A lunar landing is, in reality, a complete freefall. Considering the gravity strenght and the height of the Moon´s gravitational field (err, does this moron realizes that the moon´s gravitational field is quite strong at 300 thousand kilometers height, since it creates tides on Earth???), the impact at soil should occur in a speed near 2,38 km/s (Moon´s gravitational field escape speed), which is about 8,500 km/h. This final fall speed would need to be compensated by the constant and high power jet generated by the module´s rocket. In analogous way, the Lunar Module should take off from the moon and surpass all the moon´s gravitational field thanks to the thrust of its rocket. We should note however that the Landing Modules weight on Earth, according to NASA, 14,515 Kg in the first 3 landings and 16,330 Kg in the 3 last. To reinforce the understanding of the dynamics involved in the moon landings: if there was no constant and powerful thrust to control the fall, the lunar module would be a solid object with weight above 2.5 metric tons hitting the lunar surface at over 8 thousand km/h (HOW WAS IT POSSIBLE TO DEVELOP TECHNOLOGY TO COUNTERWEIGHT THIS IN THE LUNAR MODULE???)

About the "company hired" by NASA to develop the Lunar Module, "Grumman Aircraft Corporation", it informed that all the original drawings and blueprints used in the construction, real historical documents, were simply lost as years passed by."

the only part I wrote is the one in italics.

any possible help with calculations of the thrust needed to break the lunar module and land it on the moon? At what speed, relative to the moon surface, the landing module separated from the Command Module?

#### aph5

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##### Re: Lunar Landing Module and how it landed on the moon: a few questions...
« Reply #1 on: 07/13/2010 09:05 PM »
I've been a lurker here and am far from an expert.   However, it would seem like a little high school physics would solve the problem easily.

Sum of Forces = ma
Thrust -Weight = ma
Thrust - mg = ma

You would need to plug in the values you know and solve for what you want.  Note that g is the acceleration due to gravity on the moon and not 9.8 m/s^2.
« Last Edit: 07/13/2010 09:08 PM by aph5 »

#### Jorge

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##### Re: Lunar Landing Module and how it landed on the moon: a few questions...
« Reply #2 on: 07/14/2010 04:55 AM »
Moon parameters:
mu=4902.7779 km^3/s^2
re=1738.14 km

Apollo LM pre-PDI orbit:
ha=60 nmi
hp=8 nmi (PDI was at perilune)

Using 1 nmi=1.852 km,

ra=re+ha*nmi=1849.26 km
rp=re+hp*nmi=1752.96 km
a=(ra+rp)/2=1801.1 km

and vis-viva equation gives:

vp=sqrt(mu*(2/rp-1/a)=1.694 km/s

which was the speed of the LM with respect to a non-rotating moon at PDI (moon rotates very slowly so can be neglected).

Note that the 2.38 km/s given by the site is not applicable in this situation because that's essentially the escape velocity of the moon, while for Apollo the LM did not begin descent from an escape trajectory, but rather from a low elliptical orbit (for which the CSM did the heavy lift of LOI and, for the later missions, DOI).

Apollo LM parameters:
m0=14696 kg
mp=8165 kg
Isp=311 s

so:
mf=m0-mp=6531 kg

and using 9.80665 m/s^2 for g0 gives:
ve=3.05 km/s

so the rocket equation gives:

dv=ve*ln(m0/mf)=2.47 km/s

as the theoretical delta-v of the LM descent stage.

There will be some gravity losses during descent, especially after throttle-down and during hover, but it's clear that the LM had the muscle for the job with a bit of hover margin to spare.
JRF

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