Description
Calculating trajectories for spacecraft to the Moon is not easy.
Without the required velocity the Moon is not reached, and the return to Earth is a disaster.
Even with the right velocity, making it back to Earth safely is not a given.
The launch point rotates once every 24 hours and the Moon moves around the Earth in 27 days. We need to shoot from a rotating launch point to a rapidly moving target.
Luckily, Nasa does it better than me.