Question about Apollo Lunar Module

My friend's friend is one of those people who think that we never landed on moon and his reasoning is that the ascent stage of Apollo Lunar Module did not have enough fuel and/or power to lift-off from moon.

I found these specs on wiki:

http://en.wikipedia.org/wiki/Apollo_...e#Ascent_stage

APS propellant mass: 5,187 lb (2,353 kg)
APS engine: Rocketdyne RS-18
APS thrust: 3,500 lbf (16,000 N)
APS propellants: Aerozine 50 fuel / nitrogen tetroxide oxidizer
APS pressurant: two 6.4 lb (2.9 kg) helium tanks at 3,000 pounds per square inch (21 MPa)
APS specific impulse: 311 s (3,050 N·s/kg)
APS delta-V: 7,280 ft/s (2,220 m/s)
Thrust-to-weight ratio at liftoff: 2.124 (in lunar gravity)

I managed to prove to him that it did have enough power to lift-off based on the 2.124 thrust-to-weight ratio but couldn't do anything about his "not enough fuel" theory.

How can I prove that 2353 kg fuel was enough?

On 07/20/2011 09:38 PM, eddman wrote:
My friend's friend is one of those people who think that we never landed
on moon and his reasoning is that the ascent stage of Apollo Lunar
Module did not have enough fuel and/or power to lift-off from moon.

I found these specs on wiki:

http://en.wikipedia.org/wiki/Apollo_...e#Ascent_stage

APS propellant mass: 5,187 lb (2,353 kg)
APS engine: Rocketdyne RS-18
APS thrust: 3,500 lbf (16,000 N)
APS propellants: Aerozine 50 fuel / nitrogen tetroxide oxidizer
APS pressurant: two 6.4 lb (2.9 kg) helium tanks at 3,000 pounds per
square inch (21 MPa)
APS specific impulse: 311 s (3,050 N·s/kg)
APS delta-V: 7,280 ft/s (2,220 m/s)
Thrust-to-weight ratio at liftoff: 2.124 (in lunar gravity)

I managed to prove to him that it did have enough power to lift-off
based on the 2.124 thrust-to-weight ratio but couldn't do anything about
his "not enough fuel" theory.

How can I prove that 2353 kg fuel was enough?

Compare the APS delta-V against the delta-V required for low lunar
orbit. Even accounting for gravity losses, it's more than enough.