Apollo docking mechanism.

[nomuse]

Far as I know it was done under manual control, with the computer only in an advisory capability (aka rendezvous radar).

But I'm not sure it is appropriate to rule out the possibility of computer control due to loop speed or inability to handle the calculations. As an extremely rough approximation, the AGC had about the effective refresh rate and bit depth of the first generation Ardupilot (an AVR-micro based hobby board) and the latter was able to fly, navigate, and land a drone with clock cycles to spare.

[Chew]

I should have been clearer. How did they achieve the accuracy of entering the same orbit as the CM so that they were within close proximity?

Here is a lengthy description of how they did it: http://history.nasa.gov/afj/loressay.htm

[Apollo 957]

How did they achieve the accuracy of entering the same orbit as the CM so that they were within close proximity?

They'd had practice on the Gemini missions, and on all the previous manned Apollo missions.

The orbital mechanics and laws of physics don't change between missions.

Strikes me it would be radically easier than negotiating two refuelling planes in a force 9 gale, rain, and thunderstorm .....

[Flookie]

Here is a lengthy description of how they did it: http://history.NASA.gov/afj/loressay.htm

And that's the simple explanation...  I'll try to get my head around it 
 
I'm used to handling misconceptions & conspiracies to do with medical & biological research. This one was beyond my knowledge and left me curious as to the finer details. Thanks for the explanations everybody.

[Flookie]

Strikes me it would be radically easier than negotiating two refuelling planes in a force 9 gale, rain, and thunderstorm .....

I'll stick to pulling into parking spaces 

[raven]

It's not easy or intuitive, but amateurs can do it, with practice, in Kerbal Space Program. Now, that's much more forgiving, plus, unlike reality, there's quicksaves, but the basic mechanics are the same.

[bknight]

Gemini 11 first performed the direct ascent maneuver that Apollo used for rendezvous/docking
https://en.wikipedia.org/wiki/Gemini_11

[Allan F]

It's not easy or intuitive, but amateurs can do it, with practice, in Kerbal Space Program. Now, that's much more forgiving, plus, unlike reality, there's quicksaves, but the basic mechanics are the same.

The real astronauts had much practise, and some very smart people were working the problem for several years, so the chance of success was quite high.

[Kiwi]

"Try using your brain and explaining how the LEM and control module managed to reconnect two 3' ringed-circles in a frictionless environment with only four directional thrusters and a computer that wasn't fast enough to help. They didn't even use a cone-type receiver like a jet would to re-fuel."

Don't ya just love it when someone is rubbishing the accomplishments of Mercury, Gemini and Apollo, and suggests to another party "try using your brain", yet doesn't even know that the original term, "Lunar Excursion Module" was changed to simply "Lunar Module"?

Flookie, you might like to point out to Brainbox that the correct abbreviation is LM not LEM.

Furthermore, what does Brainbox mean by "only four directional thrusters"?  I thought it was 16, but could be wrong. And why does he think the computer was necessary when the final docking step could be done manually and guided by a pair of eyes and a brain?

Not to mention his nonsense about the lack of a "cone-type receiver" which has already been covered by ka9q in reply No. 1...

In terms of "using your brain" it seem a good idea to ask the people who would know 

True -- and keep asking questions if you're not sure of something.  Plenty of people here are willing to help and to be appropriately pedantic when necessary.

Also Flookie, welcome to ApolloHoax.

[smartcooky]

Not to mention lots and lots of practice ahead of time. I would think that docking two spacecraft once rendezvous is complete is objectively easier than aerial refueling.

I agree.

Connecting for in-flight-refuelling is exceedingly difficult to do. It takes many hours of practice to be able to hook up first time/every time. I know this because I was given an opportunity to try it on a tech-check flight  in a TA-4K Skyhawk. You have turbulence, crosswinds and vortices coming off the tanker to contend with. It was even more difficult than you might expect for us because the "tanker" wasn't a nice big stable aircraft like a KC-135, it was another A-4K Skyhawk with a refuelling pipe trailing off a centreline drop tank. I was allowed four goes and failed all four times.

Docking in space must be mere ducksoup by comparison.