What must you calculate to reach the Moon?

That time, that place

NASA's Langley center had a division dedicated to computation, and within it a separate room for Black women. Separate restrooms, separate dining.

Katherine Johnson worked there. Told she could not attend the engineers' meetings, she asked why not. No one could answer, and she went.

Why this question

The problem in front of her ran like this.

Launch from a rotating Earth, circle in orbit, and come down at a specified point in the ocean. A few seconds' error in launch time or a small error in angle puts splashdown hundreds of kilometers off.

And there is a person inside.

What was found

In 1962 John Glenn was about to become the first American to orbit the Earth.

By then NASA had begun handing orbital calculations to electronic computers. Glenn did not trust the machine's numbers.

Before launch he made a request: get the girl to check the numbers. If Katherine Johnson recomputed them by hand and said they were good, he would fly.

She did, he flew, and he came home.

Seven years later she worked on Apollo 11's trajectories — including the calculation that brought the lunar module back up to the command module waiting in orbit. Get that wrong and there is no way home.