During the Apollo missions, the lunar module (LM) that carried astronauts to the lunar surface did not match the orbit of the command module (CM) directly after launch. Instead, the LM descended from orbit to a landing site on the Moon's surface, and then ascended back into lunar orbit to rendezvous with the CM. Here's a general overview of the process:
Descent to the lunar surface: After separating from the CM in lunar orbit, the LM used its descent engine to initiate a powered descent towards a predetermined landing site on the Moon's surface. The LM's guidance and navigation system, along with inputs from the astronauts, helped control the descent trajectory and ensure a safe landing.
Lunar surface stay: Once the LM landed on the Moon's surface, the astronauts conducted their activities, performed experiments, and collected samples during their surface stay, typically lasting several hours.
Ascent from the lunar surface: To leave the Moon's surface and rejoin the CM in lunar orbit, the LM's ascent stage, with its ascent engine, was used. After ignition, the ascent stage propelled the LM off the lunar surface, leaving behind the descent stage, which was no longer needed.
Rendezvous and docking: The ascent stage of the LM then maneuvered to match the CM's orbit in lunar orbit. To accomplish this, the ascent stage had the ability to alter its trajectory and adjust its velocity to rendezvous with the CM. This was achieved using the LM's guidance and propulsion systems, with assistance from ground-based mission control.
Docking and crew transfer: Once the LM rendezvoused with the CM, the two spacecraft docked together. The astronauts then transferred from the LM to the CM, leaving the ascent stage of the LM behind.
The landing site on the Moon was selected based on various factors, such as scientific objectives, surface conditions, and safety considerations. The LM had limited control over its landing point within a pre-determined area, but adjustments could be made during the descent to avoid hazards and ensure a safe landing. However, the ascent from the lunar surface and subsequent rendezvous with the CM required the LM to have the capability to modify its trajectory and velocity to match that of the CM in lunar orbit.
Overall, the Apollo missions involved a complex series of maneuvers and calculations to ensure the safe return of the astronauts to Earth, with the ascent and rendezvous process playing a crucial role in the success of the mission.