17 September 2013

Trajectory to the moon

1950s era comic depicting the general expectation for space travel -- a space age which never came to pass because of deadly space radiation and other problems that have not yet been overcome
In getting from the ground to space the boosting rocket must provide the energy for lifting the mass, overcoming gravity and air resistance and getting up to orbital speed.  It's a big job that takes a big rocket. Apollo's rocket was one of the biggest, the Saturn V:

It's a biggy: the Saturn V

Initially the weight of the rocket is very large comprising mainly of the weight of the fuel and oxygen necessary to power it.  It must also over come gravity and air resistance which are also significant in the early stages. 

At 1.78 km/s, lunar orbital speed is much less than that for earth orbital speed, 7.8 km/s.  So the Apollo spaceship had to decelerate about as much as it had to accelerate to get up to earth orbital speed. The rocket fuel for maneuvering from earth to the moon and back was housed in the Service Module.

Even though the Service Module (SM) had to do roughly the same job as the Saturn V in terms of acceleration it makes sense that the SM is smaller than the Saturn in light of the fact that it is a lot lighter and therefore has less mass to move; and it doesn't have gravity or air resistance to deal with. But is the SM too small in comparison to the Saturn?

Slight size discrepancy between Saturn 5 (left) and Apollo S/C/LM (right)
Put it this way: did the SM have enough fuel to perform the necessary acceleration (or deceleration)? To assess this one must consider the the type and amount of fuel onboard.

The SM was propelled by aerozine-50, a 50-50 mixture of hydrazine and UDMH.  According to the US Air Force:
The available chemical energy from reacting one gram mole of aerozine-50 (.6522 mole hydrazine + .3478 mole UDMH) with 1.02 moles of nitrogen tetroxide at 25oC (298 0 K) is approximately 1.54 X 105 calories (6.63 X 103 BTU per pound aerozine-50 reacted).
Hydrazine N2H4 molecular weight = 32.05 g/mol

Nitrogen tetroxide N2O4 = 92 g/mol

UDMH ((CH3)2)H2N-N = 60 g/mol

Combining Hydrazine and UDMH as per the above proportions:

aerozine-50 =  0.6522 x 32.05 + 0.3478 x 60 = 41.8 g/mol

Converting 1.54 X 105 calories to joules, x 4.2 = 

646,800 J/mol

This means that aerozine-50 has a chemical energy density of 15,484,798 J/kg.  (This compares favourably to NOAA's figure for the chemical energy of pure hydrazine of 19,410,000 J/kg.  It also equals 6.63 X 103 BTU per pound as per the above reference. Hydrazine has a higher energy content than UDMH but the latter is more stable, hence there use in combination for rocket fuel.)

Each kilogram of aerozine-50 was burned with about double the weight in nitrogen tetroxide (which acted as the oxidant).  So, the total propellant weight carried on the SM of 18,410 kg would have yielded 15.4M x 18,410 / 3 = 95,025,043,726 J = 95 GJ.

The weight of the Command Module (CM) was 5,809 kg, SM = 24,523, LM = 15,200 kg.  Total = 45,532 kg.  Some of the rocket fuel will be burned on the way to the moon, let's say half for the forward journey, and assume it's gone at the beginning.

Using the kinetic energy equation 1/2mv2  from earth orbital speed of 7.8 km/s to moon orbital speed of 1.78 km/s:

1/2*(36,327)(7,800 - 1,780)2 = 658 GJ.

If only half the fuel was burned it would yield 47.5 GJ. Let's assume that all of the fuel was burned on the way to the moon:

658/95 = 6.9 times.  You would need 6.9 times the total fuel the SM had just for the required velocity change, i.e. not including for course corrections -- not all of the SM's fuel was for brute acceleration.

Now we factor in the fact that rocket fuel is only about 70% efficient at converting chemical energy to thrust. So you would need 6.9/0.7 = 9.89.  About ten times the total fuel the SM had was required just for the forward journey to the moon...it was clearly an unrealistic task.

Also, consider how difficult it would be for the primitive computer and guidance systems of the day to compute and achieve the exact trajectory required to orbit the moon; return to earth; etc. Even with modern equipment such space navigation would be difficult.  It would have been impossible with 1960s technology.


About this series

There's more to come, but that's all for now on the topic of Apollo Moon Hoax. I published 15 posts of mostly original material denying that the moon landing, or various aspects of the manned space race, took place.  

The porous plate sublimator article was based on material I came up with years ago but put on the back burner.  It came to the front burner when I had an argument with the good folks at the Jo Nova website who defend NASA's honour with pride (my pseudonym is Stylo there).  

I was going to leave it but I felt like making a point, resulting in my first three articles about how NASA faked the moon landing (1,2,3).

Then I finished my porous plate article.  Then while I'm researching that article I come across the story of Apollo 13 and was surprised to read that NASA said it was cold when it lost power.  I hadn't watched the movie Apollo 13 because I had read Ralph Rene's NASA Mooned America by that time and knew the moon landing was fake and didn't feel like watching more propaganda.

A quick bit of research and I discovered that we had every reason to expect Apollo 13 should have been really hot, being in the direct sunlight!  NASA got that story wrong and have had to live with the blunder ever since.

Then a couple of months ago I'm sitting there looking at the drawing of the Apollo capsule during reentry and I think: hang on, that's not an airplane.  That's not like a B-2 flying wing.  That's bogus.  It's not aerodynamic, it wouldn't work...resulting in my series Space Reentry Vehicles.

Future posts on this topic include rebutting the paltry three or four points defenders of the moon landing bring up, such as photo-shopped NASA LRO pictures of the moon landing sites; and all the "independent" tracking of Apollo, that was really just the picking up of a radio signal.

Keywords: NASA lied about the bogus hoax fake faked moon landing.

1 comment:

  1. Hello There,

    Your analysis is interesting but it misses the fact that they used moon itself to decelerate using sling shot physics. However I do not think they slowed down all the way to 1.68km/s. They must have preserved the velocity and used it for returned journey.

    I wondered similar things but restricted my analysis only to the ascent and descent stage of LM. Here are my simple calculations.

    The LM was 15 tons while descending and 5 tons dry. So assuming 10 ton of fuel at 15million joules per kg. They only required 3.5billion joules to descend and ascend from 110 km orbit. That could be provided by only 227KG of fuel. So they had ample fuel in the LM itself to get down and come up.

    My calculations were based only on potential energy and assume 100% fuel efficiency. But I was only trying to establish if LM descent and ascent was practical. And it seems it is.

    I am also convinced that slingshot allows travel from earth to moon.

    I am curious about return journey which i think is possible if they somehow preserved their velocity (perhaps in an elliptical orbit or a low moon circular orbit).