Was the CM big enough to get back to Earth?

[lenbrazil]

For those of you who missed it Margamatix dregged this up in the BS's money back guarantee thread starting with reply 12

apollohoax.proboards21.com/index.cgi?board=theories&action=display&thread=1125673459&page=1

[rocketdad]

At least the Command Module looked all rockety and stuff. That has to be worth something!

[Count Zero]

You don't even have to work out the distance to the L1 point (where the Earth & Moon's gravitational influence is ~equal). All that's needed is to see if the CSM can achieve lunar escape velocity from low lunar orbit. Once you work work out the mass-ratio based on the fuel left after the LOI burn (to put the CSM & LM in orbit) and the exhaust velocity of the SPS rocket (~3km/sec), it's a straightforward application of the "rocket equation" to find the answer: "Hell Yeah!"

What's interesting is that the total amount of SPS propellant assuming no prior burns is just about enough to lift the CSM off the surface of the Moon on an Earth return trajectory. I think this is a leftover from before they decided to go with the LM & Lunar Orbit Rendezvous. Originally (using either Direct Ascent or Earth Orbit Rendezvous), the Apollo CSM was supposed to land on the Moon using some sort of large descent stage, then the SM would act as an ascent stage to lift-off and send them home.

If this is a holdover, then the difference in propellant mass expended on lunar orbit return versus direct return would have dictated the maximum mass of the LM, since that excess would be burned on LOI w/LM.

And so an engineering requirement was born...

[rocketdad]

Has anybody ever done the numbers for how much fuel the Shuttle would need for a moon mission?

I know docking in orbit with a fuel tank and reconnecting would be pretty gonzo spacework, I'm just curious what it would take to kluge up a moon trip in the ol' space pickup.

[PhantomWolf]

There's quite a long thread on the very soon to be defunk BABB about the shuttle's ability to get to the Moon. The basic conclusions were that without a major redesign it'd be pretty tough due to cyogenic fuel, fuel tank rettatchment and engine reusablitity constrains.

[PhantomWolf]

By the way, I think it's a bad idea spawning cross threads from M's discussions, it allows him to dodge the questions more.

[Bob B.]

I think the name of this thread should be, Was the SM big enough to get back to Earth? It was the service module (SM) that contained the service propulsion system (SPS), thus the SM should be the focus of attention, not the CM. The answer to this question is, of course, yes. Let’s look at Apollo 17 for an example. The Apollo 17 SPS performed six burns as follows (figures are from the NASA mission reports):

Midcourse correction #2: 9.9 ft/s
Lunar orbit insertion: 2,988 ft/s
Descent orbit insertion #1: 197 ft/s
CSM circularization: 70.5 ft/s
CSM lunar orbit plane change: 366 ft/s
Trans-Earth injection: 3,046.3 ft/s

The first three burns were performed with the LM docked and fully fueled. The last three burns were performed with the LM undocked or jettisoned. The total mass of the CM, SM, and LM were as follows:

Command module, CM: 12,874 lbm
Service Module, SM: 54,044 lbm
Lunar module, LM: 36,262 lbm

The mass of SPS propellant was 40,594 lbm, which is included in the SM mass given above.

To determine the amount of propellant used to perform the six SPS burns we will use the following equation,

Mf = Mo*e^-(dV/Ve)

Where Mf = final mass, Mo=initial mass, e=mathematical constant (2.71828), dV=change in velocity, and Ve=exhaust gas velocity. Exhaust gas velocity can be determined from the specific impulse (Isp) of the SPS, which was 314 s, therefore

Ve = g*Isp = 32.174*314 = 10,103 ft/s

We can determine the amount of propellant needed for the first three burns with a single calculation, where the total velocity change is,

dV = 9.9+2,988+197 = 3,194.9 ft/s

The initial mass is simply the combined mass of the CM, SM and LM,

Mo = 12,874+54,044+36,262 = 103,180 lbm

Therefore, the final mass is

Mf = 103,180*e^-(3,194.9/10,103) = 75,207 lbm

The amount of propellant burned is Mo-Mf,

Mp1 = 103,180-75,207 = 27,973 lbm

Now we must determine the amount of propellant burned for the final three burns, where

dV = 70.5+366+3,046.3 = 3,482.8 ft/s

The initial mass is the final mass from the previous calculation, less the LM, which is either undocked or jettisoned,

Mo = 75,207-36,262 = 38,945 lbm

Alternatively, the initial mass is the CM, plus SM, less SPS propellant already used,

Mo = 12,874+54,044-27,973 = 38,945 lbm

The final mass after the last three burns is,

Mf = 38,945*e^-(3,482.8/10,103) = 27,589 lbm

And the amount of propellant used is,

Mp2 = 38,945-27,589 = 11,356 lbm

Thus, the total SPS propellant used is,

Mp_total = 27,973+11,356 = 39,329 lbm

Since our initial propellant load was 40,594 lbm, we have remaining,

Mp_remaining = 40,594-39,329 = 1,265 lbm

According to the mission reports, the actual propellant remaining was 1,630 lbm. This is because I simplified the calculations by ignoring that the mass of the SM was further reduced by consumables used during the flight. 624.7 lbm of SM RCS propellant, 60.9 lbm of hydrogen, and 606.8 lbm of oxygen was consumed during the Apollo 17 mission. These figures are partially offset by the 243.1 lbm of lunar samples collected. There is really no need to get any more precise than my calculations above because even my somewhat conservative computations show that the SM carried enough propellant to perform the maneuvers required of it. And one more thing, the amount of volume needed to storage 40,594 lbm of aerozine 50 and nitrogen tetroxide is about 560 ft^3, which is consistent with the size of the propellant tanks housed within the SM.

countzero said:

All that's needed is to see if the CSM can achieve lunar escape velocity from low lunar orbit.

So why don’t we perform that calculation. Sticking with Apollo 17 as our example, the CSM was in a 61.2 X 63.9 nautical mile orbit following LM jettison and CSM separation. If we take the average and convert to kilometers, we have an orbital altitude of 116 km. The Moon’s radius is 1,738 km, thus the semi-major axis of the orbit was 1,854 km. The orbital velocity of a spacecraft is given by the equation,

V = (GM/R)^0.5

Where V is the velocity, R is the orbital radius (semi-major axis), and the value of GM for the Moon is 4.902794E+12 m^3/s^2. Therefore,

V = (4.902794E+12/1,854,000)^0.5 = 1,626 m/s

The equation for escape velocity is,

Vesc = (2*GM/R)^0.5

Thus,

Vesc = (2*4.902794E+12/1,854,000)^0.5 = 2,300 m/s

Therefore, the amount of delta-V needed to go from orbital velocity to escape velocity is,

dV = 2,300-1,626 = 674 m/s (2,211 ft/s)

On Apollo 17 TEI added 3,046.3 ft/s, which was well beyond lunar escape velocity. This was done to reduce the amount of time needed to get back home. Thus, I have shown the SPS not only had enough propellant to get Apollo 17 back to Earth, but it could get it back quickly and with propellant to spare. Similar calculations for the other Apollo missions will show similar results, that is, the SM was big enough.


edit spelling

[Count Zero]

In other words, "Hell yeah!"

rocketdad said:

Has anybody ever done the numbers for how much fuel the Shuttle would need for a moon mission?

I know docking in orbit with a fuel tank and reconnecting would be pretty gonzo spacework, I'm just curious what it would take to kluge up a moon trip in the ol' space pickup.

To do TLI on a shuttle (in low Earth orbit) for a lunar fly-by with free return trajectory, the mass of the propellant & tanks would be ~200 tonnes (the orbiter itself is ~100 tonnes). That's just to fly you to the Moon & back without going into lunar orbit.

Oh, btw, on the way back you'll hit the atmosphere at 7 miles per second, but the shuttle is only built for 5 miles/sec. Hope you enjoyed the trip!

"Don't you know that you are a shooting star..."

What? You want to slow down before your spectacular finale? Wuss. Oh all right. Whether your adding 2miles/sec at the beginning of the trip, or taking it off at the end, you still need that ~200 tonne tank. The catch is that, at TLI you are now adding 2 miles/sec to the orbiter and the braking tank. For that, you will need an additional ~600 tonne tank of propellant to leave low Earth orbit and get you up to translunar velocity.

The shuttle's payload is ~25 tonnes to low Earth orbit. I will leave it to the imaginative reader to figure out how to get all of this to LEO.

[Bob B.]

Oh yeah, one more thing. Over in this thread (reply #28) I showed that the Saturn V was capable of injecting the combined CSM/LM into a trans-lunar trajectory. In my post above I show that the SPS was capable of performing the subsequent maneuvers. And in this thread I showed that the LM could ascend from the lunar surface to the required altitude and velocity. Therefore, I’m pretty sure the HB claims on this particular issue have been soundly debunked.

I give you real numbers, equations, and calculations, while conmen like Bart Sibrel give you crap like, “The top portion of the lunar module which landed on the moon supposedly popped up off the moon with two astronauts aboard, entered lunar orbit 60 miles up, and docked with the command module in lunar orbit. To look at its design and think such could have actually occurred is absolutely ludicrous.” This is the full extent of his argument, a whole 15 words … “To look at its design and think such could have actually occurred is absolutely ludicrous.” It is Bart Sibrel who is ludicrous.

[PhantomWolf]

I look forward to 'm' totally ignoring you Bob.

[Bob B.]

phantomwolf said:

I look forward to 'm' totally ignoring you Bob.

I'm sure he will. I don't think I've seen margamatix respond to anyone's refutations yet, that is, unless he can find an insult hidden in it somewhere. Then he responds only to the insult while ignoring the meat of the argument. Personally, I think margamatix is a complete waste of all our time. I only responded to the delta-v/propellant claim because I've seen it before and I thought a mathematical treatise was in order. I don't know how many people really pay much attention to all that math, but at least it is on record for those who can understand it.

[Kiwi]

bob said:

Personally, I think margamatix is a complete waste of all our time.

I agree. I don't believe that he actually wants to learn anything because if he did he would have at least tried a little harder to do so.

People here have bent over backwards to help him but he just peed on their carpet in return. He has implied that he has a good moral sense but I have had good grounds to twice suggest that he has lied to us. He didn't deny it on either occasion.

His fingers are firmly jammed into his ears, he loudly sings "La la-la la-la-la" when anyone refutes his ignorant claims, and his mind is made up and firmly slammed shut. I.e.: He is wilfully ignorant.

I observed that sort of dogmatic, narrow-minded behaviour in quite a few stupid old Victorians in the late 1950s when I was about eight years old, and firmly made up my mind then that I would do everything in my power to ensure I would not end up like them. Let's hope that Margamatix's kids have the good sense to make the same decision about their dad if he is indeed like he appears to us.

[PhantomWolf]

Well I know for a fact that he's lied to us at least twice because I called him on them. His opening post contained one of them. Though I still don't agree with him, I respect Turbonium more because I have seen him try and deal with the responses, and also admit when he is wrong, on occasion.

'm' told use that he 'believed in the Apollo missions until recently' however that's a statement I'm starting to question too. Take this example.

Say I had always believed that a whale ws a mammal until I read smething that stated it is a fish. The Author claimed to be a Marine Enthusiast and his claims seemed to make sense, sort of if you didn't think too hard. Now say I jpin a forum for marnie Biologista dnd they destruct the arguments for a Whale being a fish bit by bit. What do I do. Do I a) Cling desperately to the disproven arguments claiming that even if they have been shown wrong, no-one has truely proved that a whale isn't fish. or b) Figure that if the arguments that made me think that a whale was a fish are indeed wrong, that I wasn't so foolish for thinking it was a mammal afterall and return to the original conclusion.

m's entire argument seems to be based on what he has read on pro-Hoax sites and so instead of being able to show how he came to a specific conculsion all he can do is parrot the conclusion without any support, and when faced with a response he can't refute, he simply ignores it.

[nomuse]

phantomwolf said:

...'m' told use that he 'believed in the Apollo missions until recently' however that's a statement I'm starting to question too.
....

I've seen this enough times I wonder if it is a standard part of the hoax literature...somewhere before waving flags but after lack of stars.

Has anyone run into an HB who prefaces discussion with "I always thought it was a hoax, since the first moment I heard of the Apollo program?"

[PhantomWolf]

Very true nomuse. Almost makes me wonder if there is a HB handbook out there somewhere we've all missed.