How did a computer scientist use differential equations for Apollo missions?

A computer scientist used differential equations to help astronauts travel smoothly from Earth to the Moon, like a toy car moving along a wiggly path.

Imagine you're pushing your toy car on a bumpy road, sometimes it goes fast, sometimes slow. A differential equation is like a special rule that tells us how the speed of the car changes as it moves over different parts of the road. It connects the position and the speed of the car at each moment.

During the Apollo missions, astronauts were like toy cars, but much bigger! The computer scientist used these rules to predict where the spacecraft would be and how fast it was moving at any time. This helped them plan the journey accurately, just like you might figure out how far your car will go if you push it for a while.

These differential equations were solved by computers, kind of like doing really complicated math problems that help astronauts get from Earth to the Moon safely and on time!