Apollo 10 contingency plans

[AtomicDog]

When I was a wee lad (well, a teenager) following the Apollo 10 mission on tv, I remember the newscasters repeatedly emphasizing that if the astronauts landed on the moon for any reason whatsoever, that they were dead ducks.

[Bob B.]

With 1,167 m/s Δv, the LM could definitely get into a suborbital trajectory with a high enough apex, but that's not the problem.  For the CSM to rendezvous with them, it would have to slow down and match the LM's velocity.  This would put the CSM on the same suborbital trajectory.  It seems highly doubtful to me that the CSM could rendezvous with the LM, transfer the astronauts, and then get back up to speed all within the brief window of time.

[ka9q]

With 1,167 m/s Δv, the LM could definitely get into a suborbital trajectory with a high enough apex, but that's not the problem. 

Right. Orbits are all about velocity, not altitude.

[Luther]

The problem is the CSM would have to match (at least approximately) the sub-orbital trajectory of the LM to do the transfer.  So they'd have to slow down, dock with the LM, do the transfer, cut loose, and then get out of the death spiral they're in.  Furthermore, all this would have to be done in a few minutes, because the sub-orbital trajectory is going to last less than 45 minutes (and half of that is on the way up) before the LM makes a new crater.  And if they stuff it up, that's three dead astronauts instead of two.

I guess they could revert to a stable orbit with the LM still attached, assuming the CSM has enough fuel, but still - not a lot of time to work with, and a lot of potential for an even worse outcome.

[Luther]

Speaking of stuffing it up, I didn't notice Bob B.'s post, which already said most of what I said 

[BazBear]

With 1,167 m/s Δv, the LM could definitely get into a suborbital trajectory with a high enough apex, but that's not the problem. 

Right. Orbits are all about velocity, not altitude.

And velocity in the right direction. This needs to be explained to some people. I had to do the whole "common sense" (ETA*) explanation to a good friend and contemporary just the other day...well it was at the same time I got him to watch Saturn V footage (mostly Apollo 4 I'm pretty sure). The pitch over threw him...until I explained why 17,500mph-ish straight up wasn't a good idea.

(*ETA Falling "around" the Earth.)

[Obviousman]

Thanks for the responses - the wealth of information makes this place so valuable.

[darren r]

What if one of the astronauts had stayed on the surface, in a "I'm just going outside, I may be some time" manner? Would the ascent module have been able to make it then or would the reduced mass not make all that much difference?

A bit dark, I know, I'm just curious!

[Bob B.]

What if one of the astronauts had stayed on the surface, in a "I'm just going outside, I may be some time" manner? Would the ascent module have been able to make it then or would the reduced mass not make all that much difference?

Too little to make much of a difference.  Leaving behind an astronaut would gain less than 30 m/s, which is still far short of what would be needed.

[Luke Pemberton]

Too little to make much of a difference.  Leaving behind an astronaut would gain less than 30 m/s, which is still far short of what would be needed.

That might only be a measly 30 m/s, but it brings it home how lots of little weight reductions here and there made a lot of difference. It amazes me how the engineers adapted to changes of design, and the impact this had on the whole space craft. System integration must have been an utter nightmare.

[Allan F]

What if one of the astronauts had stayed on the surface, in a "I'm just going outside, I may be some time" manner? Would the ascent module have been able to make it then or would the reduced mass not make all that much difference?

Too little to make much of a difference.  Leaving behind an astronaut would gain less than 30 m/s, which is still far short of what would be needed.

Did you use the reduced mass of the half-fueled LM as basis for that? Seems like a very small velocity gain for the loss of 80 kg.

[Luke Pemberton]

Did you use the reduced mass of the half-fueled LM as basis for that? Seems like a very small velocity gain for the loss of 80 kg.

I got exactly the same figures as Bob, a little under 30 m/s is gained in dV for a loss of 80 kg, unless we're both doing something daft. Maybe someone can check both our figures and put up the equations.

[Allan F]

How much mass had to be lost before the LM could get to any orbit with half fuel? 1000 kg?

[Bob B.]

Did you use the reduced mass of the half-fueled LM as basis for that? Seems like a very small velocity gain for the loss of 80 kg.

I used the figures in Reply #13, i.e. 8,273 lbm total mass (with 2 astronauts) and 2,631 lbm propellant.  However, I just realized I made a mistake.  I intended to use the mass of an astronaut with his suit and backpack, but I forgot that I was working in pounds-mass instead of kilograms.  An astronauts in his EMU with PLSS backpack had a mass of about 350 lbm.  Therefore the corrected numbers are,

With two astronauts,

Δv = 311 * 9.80665 * LN(8273 / (8273 - 2631)) = 1,167 m/s

With one astronaut,

Δv = 311 * 9.80665 * LN((8273 - 350) / (8273 - 350 - 2631)) = 1,231 m/s

So the difference is 64 m/s instead of 30 m/s.

Now that I think about it, were PLSS backpacks included on Apollo 10?

[Bob B.]

How much mass had to be lost before the LM could get to any orbit with half fuel? 1000 kg?

About half its mass.  Δv is a function of the ratio of the fully fuelled mass to the empty mass.  If you cut the fuel mass in half, then you have to cut the empty mass in half in order the maintain the same ratio.