Quakes happen, on the moon too. We know because between 1969 and 1972, Apollo astronauts installed seismometers on the moon. In this photo, you can see Buzz Aldrin installing a seismometer in a region known as “The Sea of Tranquility.”
The instruments sent all sorts of data back to Earth until 1977, but it wasn’t until about 2006 that we were able correctly analyze and understand it. Know more.