The claim you mentioned about NASA achieving approximately 24,791 mph (miles per hour) during the flight to the Moon is correct. The Apollo missions, which included the iconic Apollo 11 mission that landed humans on the Moon, did indeed reach such speeds. However, the reason it took several days to travel from Earth to the Moon despite the high speed is primarily due to the vast distances involved and the orbital mechanics of the mission.
The distance between the Earth and the Moon is about 238,900 miles on average. Even at the impressive speeds achieved by the Apollo spacecraft, it still takes time to cover such a considerable distance. The spacecraft needed to follow a specific trajectory that allowed it to intercept the Moon's orbit while accounting for the gravitational forces and orbital mechanics involved. This trajectory was designed to optimize fuel consumption and ensure a safe and accurate landing.
In addition, the Apollo spacecraft used a technique known as Trans Lunar Injection (TLI) to leave Earth's orbit and head towards the Moon. This involved firing the spacecraft's engines at a precise time and angle to provide the necessary velocity to break free from Earth's gravitational pull and enter a trajectory towards the Moon. The spacecraft then coasted for most of the journey, using minimal course corrections to refine the trajectory.
Furthermore, the Apollo missions aimed for a lunar landing with a specific approach angle and timing to ensure a successful touchdown. This required careful planning and alignment with the Moon's orbit. The spacecraft had to adjust its trajectory and slow down significantly to enter lunar orbit and prepare for the landing.
Overall, the time it took for the Apollo missions to reach the Moon despite the high speeds achieved during the journey can be attributed to factors such as the vast distance, orbital mechanics, the need to follow precise trajectories, and the requirements for a safe and accurate landing.