During the Apollo missions, the astronauts were able to determine that they were in orbit around the Moon through a combination of visual observations, radio communication, and data from onboard instruments.
Firstly, the astronauts could visually observe the Moon's surface from their spacecraft as they approached it. They could see the Moon becoming larger and more detailed as they got closer, indicating that they were in proximity to the lunar surface.
Secondly, they had a communication link with mission control on Earth. By receiving signals from tracking stations on Earth and comparing their own observations with the predicted trajectory, they could confirm that their spacecraft was indeed in orbit around the Moon.
Additionally, the Apollo spacecraft carried onboard instruments such as radar altimeters and inertial navigation systems. These instruments provided precise measurements of the spacecraft's altitude, velocity, and position relative to the Moon. By analyzing this data, the astronauts and ground control could determine whether the spacecraft was in a stable orbit around the Moon.
The Apollo missions had specific orbital insertion maneuvers designed to place the spacecraft in lunar orbit. These maneuvers were carefully planned and executed to achieve the desired orbit around the Moon. By monitoring the spacecraft's trajectory and velocity changes during these maneuvers, the astronauts and mission control could confirm that the spacecraft had successfully entered lunar orbit.
Overall, a combination of visual observations, radio communication with mission control, and data from onboard instruments allowed the Apollo astronauts to determine that they were in orbit around the Moon.