Hi,

I'm reading W. David Woods' superb "How Apollo Flew to the Moon" - what an excellent book.

But, very uncharacteristically, the author mentions something regarding the rendezvous and docking of the LM with the CSM on its return from the lunar surface which he does not explain.

He says

"studies and Gemini experience demonstrated that the best approach was to fly this [terminal rendezvous] phase over the time that the CSM had travelled 130 degrees of its orbit"...."planners could choose where in the CSM's orbit they wanted the rendezvous to occur, taking lighting into account, then work back 130 degrees to define the point....where the LM crew would execute the terminal phase initiation [TPI] burn".

And then

"One huge advantage of this 130 degree approach was that as the LM rose to meet the CSM, the latter appeared to be stationary against the background stars".

(The TPI burn turned a 17 X 84km orbit into an orbit with an apolune of ~113Km.)

And then

"As the LM rose to meet the CSM during the terminal phase, the crew...searched for any hint they might be deviating from their preferred trajectory - which was a straight line in terms of inertial space (this being indicated by the fact that they held the target fixed against the stars)."

Eh? The CSM was in a 110 Km orbit around the moon. The LM was rising up to meet it, increasing its orbit. It did this over a 130 degree arc.

How did the CSM appear to be fixed against the stars as they travelled 130 degrees around the moon? How is an arc of the orbit "a straight line in inertial space"? I just do not get any of this. I cannot see how the target seemed to be fixed against the stellar background. And I doubly cannot see how it appeared to stay fixed even as the two craft drew closer.

Can anyone explain this to me in a way my poor frazzled brain can understand?

This is one of the very few points where the book fails to explain what it describes!

After a look at their diagram, it doesn't seem so hard. I don't know the actual positions of 2 craft, or if their diagram accurately portrays paths, but if I assume the craft were close at the end (and that was pretty much the point: rendezvous), I can visualize a direction for the alignment of the LM and CSM. From the much earlier TPI burn I can envision a line parallel to that final line, passing through the two paths -- with the LM trailing the CSM.

At all points in between those times, I can envision additional parallel lines passing through both CSM path points and the LM path. If the LM was in the right places at the right time, as the book passage implies, it could always see the CSM against the same stars. I don't see anything that rules it out.

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Thanks.

Hmm. OK....(sound of cogs whirring) I sort of begin to see. Maybe. I shall draw some diagrams and see if I can get it fixed in my mind.

Presumably then, the 130 degrees only works in this way for these two specific orbits?

I still don't get what he means by the LM's trajectory being "a straight line in inertial space".

Hi. I wrote the book you are discussing. Hope I can help.

Of course both the LM and the CSM are travelling in arcs with respect to the Moon. But visualise the situation of someone in the LM looking at the CSM. To take an easy starting point, imagine the situation before TPI - two concentric orbits, the LM's is faster than the CSM's because it is lower. The CSM will appear to be going backwards when viewed against the stars. The 130-degree terminal phase maneuver just happens to cancel out that apparent backwards motion. This was worked out during Gemini and was used because it gave the crews a backup means of checking their approach. If a longer arc was used, the CSM would still appear to be going backwards wrt the stars. Take away the Moon from your visualisation and think only of the LM and CSM wrt the stars and you see that one is following a straight line to the other. 'With respect to the stars' can be thought of as another way of saying inertial space.

Since you brought up this problem in your understanding, I'll take a note of your comments and if I'm lucky enough to get a second edition, I'll try to make the situation plainer.

Best wishes

David Woods

Well, that's an honor.. Welcome to BAUT forums, David.

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An honour indeed! Great book David, so many scales have fallen from eyes I'm in danger of tripping over them.

OK, the fog is lifting. Is it the case then that :

-I guess the LM and CSM were only in sight of each other for the final ~35 degrees of arc anyway, the moon being "in the way" for the first 90 degrees.

-if you were to take snapshots at various points in time as the two converging craft travelled along their orbits over that final 35 degree portion, then drew lines between each pair of CSM/LM positions, these lines would all be parallel - i.e. if you looked along these lines, you would see the same star patterns.

-this is just a mathematical consequence of the shape of the orbits and the speed at which the two craft travel along them

-presumably, for Gemini, the magic 130 degree figure did not pop out - just the idea that you could have such a trajectory

Am I getting it now, or should I stick to colouring in the pictures?

Once again, a fantastic book. It's right up there with the best of them, and I would have said the same even if I had not known you were liable to view these comments!

Folks; first, thanks so much for the good words. I really have been very pleasantly surprised and humbled at the book's success. It's like being a proud father for the third time, watching it go off on its own life.

To your points. The LM and CSM would have been in line of sight throughout, otherwise the Rendezvous Radar, upon which the solution for the TPI burn depends, would not have been able to do its job of working with the CSM transponder. I guess your 35-degrees comes from a flaw in the visualisation. Need to find a good graphic to show this.

Your second statement is correct, apart from the 35-degree bit.

For your third and fourth points, the choice of rendezvous orbits for the CSM and the whole choreography of rendezvous was evolved through Gemini and applied to Apollo. I'd bet one day in the mid 1960s some smart guy said, "Hey, if we do this, we can get such-and-such benefit," and they'd have kept with that procedure. If you really want to get into this, do a Google search for "APOLLO EXPERIENCE REPORT - EVOLUTION OF THE RENDEZVOUS-MANEUVER PLAN FOR LUNAR-LANDING MISSIONS" It makes for great reading.

One last thing. I'm not a rocket scientist (or a rocket engineer, to be more accurate). I'm an enthusiast, like most of the folk around here. I just read up a but more than was good for me. There are far, far greater experts out there than I. Thanks again for your good words on the book. There's a list of Points Arising on its website - hafttm dot com to address any problems folk find in it.

What a great forum this is!

So now I understand the way in which the CSM appeared fixed w.r.t the stars from the LM's view.

The reason I didn't previously understand how the two craft could be in sight of each other for the full period of TPI burn to rendezvous (hence my rubbish talk of only being in sight for the final 35 degrees) is that I misinterpreted something David wrote.

When he said:

"planners could choose where in the CSM's orbit they wanted the rendezvous to occur, taking lighting into account, then work back 130 degrees to define the point....where the LM crew would execute the terminal phase initiation [TPI] burn".

I incorrectly thought that the CSM was 130 degrees around from the LM at TPI.
But that's not what was meant, or said. The *rendezvous point* was 130 degrees around from the TPI point. But the CSM was much nearer to the LM when the TPI was executed. Their angular separation would never have been anywhere near 130 degrees. During the time it took for the two craft to converge, the CSM moved 130 degrees from the point when TPI was done.

Just out of interest, what was the separation of the two craft when the manoeuvre was started? Or, in other words, how long did it take from TPI from final encounter?

Maybe the diagram in the book could show where the CSM and LM were at the point of TPI and then at a few points between then and rendezvous. That would help explain both areas of confusion. I may be thick, but I'm probably not uniquely so!

Hope these meanderings encourage others to buy the book. I can't praise it highly enough. Fancy having a crack at Soyuz next, David?

My plan is to concentrate on the Apollo Flight Journal for now. Myself and a bunch of other enthusiasts are trying to get as much out on that site for the 40th anniversaries that are coming along, especially Apollo 11. Maybe one day I'll have another crack at writing.