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I'm new to spaceflight, is it possible to explain in a clear way the following?

When returning from the Moon's surface with the astronauts to the 'mother' ship for return to earth, how can lunar landing craft match its speed in order to meet it, dock with it, and allow transfer of the crew?

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The upper stage of the Apollo lunar landing module ("LM") is itself a complete rocket ship, with an engine, propellant tanks, small thrusters to steer with, a guidance computer, and all the other requirements.

With the moon's low gravity, it's possible to reach orbit with such a small (~4.5 metric ton) ship, especially as it only needs to operate independently for a few hours. The bulk of the batteries, oxygen, water, and other consumables in the Apollo LM were kept in the descent stage, as detailed here.

The command/service module (CSM) would be in orbit around the moon traveling at a speed of about 1600 m/s. The LM ascent stage would lift off vertically, then tilt over to gain horizontal speed. The liftoff would be timed to reach orbital speed at a point in space reasonably close to the CSM. Once in orbit around the moon, the LM would use its radar and its small thrusters to meet the command module, as detailed in this answer.

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  • $\begingroup$ This is a nice introductory answer. I would also add that if you can make a lander safely and accurately go down, then going back up is (somewhat) the reverse of that. Less fuel is needed going back up, but aiming against the moving target is harder, as explained in the linked answer. $\endgroup$ – DrSheldon Jul 17 '19 at 22:37
  • $\begingroup$ I believe you miss understand my question..and the comment likewise. the point. If the mother rocket is doing a speed of ( I assume) 24,000 miles an hour whilst orbiting the moon, how can the lunar landing craft match that to rendezvous with it? $\endgroup$ – rodd Jul 19 '19 at 19:59
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    $\begingroup$ CSM is doing about 3600mph In lunar orbit, not 24,000. The landing craft has a rocket engine. It lifts off initially vertically then tilts over to gain horizontal speed. The liftoff is timed so that it reaches orbit speed at a point in space reasonably close to the CSM. What else do you want to know? $\endgroup$ – Russell Borogove Jul 19 '19 at 20:08
  • $\begingroup$ last comment from @RussellBorogove is the ansewer... not the answer itself, which t alks about gravity rather than about speed! $\endgroup$ – jumpjack Feb 29 at 8:34
  • $\begingroup$ I have incorporated that comment into my answer. $\endgroup$ – Russell Borogove Feb 29 at 15:30
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The "landing craft" is made of two parts: Descent Stage and Ascent Stage.

Descent stage remains on Moon surface after takeoff; Ascent Stage uses its engine to raise its altitude up to CSM orbit, then it turns thanks to its thrusters, so the engine has also an horizontal component of thrust and can increase Ascent Stage horizontal speed until it matches to Command Service Module speed already in orbit.

Final fine tuning of speed and position are made by thrusters.

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    $\begingroup$ Reaching altitude of the CSM was combined with acquiring orbital speed, it was not done in two distinct steps. The trajectory for rendezvous was guided by the computer of the LM using the distance to the CSM measured by the rendezvous radar. $\endgroup$ – Uwe Feb 29 at 10:12

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