In Their Own Words: Frank Borman on Flying Aboard Saturn V
"The first orbit and a half around the Earth were spent by the people on the ground checking out every individual system. Of course we had our checks to do too, particularly Bill Anders was checking all the instrumentation that he could access and not only with the instruments, but also the guidance. The first orbit and a half was basically a check out before we launched to the moon.
We didn't have much really in the way of preparation for translunar injection. That was done by the third stage of the Saturn 5 and that was controlled by the instrument unit in the third stage. It was really like a third launch. After we've gone around once and a half we're informed by Mike Collins who was the capsule communicator that we would go for TLI. TLI is Trans Lunar Injection. That meant that they would they would ignite the third stage of the Saturn V, the SIVB, and it would accelerate us from 17,000 miles an hour to 25,000 miles an hour and we would be on our way to the moon. In order to escape the Earth's gravity you had to reach an escape speed of around 25,000 miles an hour. We sat there and all of a sudden we started accelerating on up to 25,000 miles an hour and then you could tell that you were going pretty rapidly away from the Earth because you could actually see the earth start to get smaller.
Once the Saturn V shut down, you're going very, very swiftly. But the Earth's gravity is continuing to pull you. So you're slowing up much like throwing a rock. Once it leaves your hand it slows up until you reach the apogee and come back. But before we became completely free of the earth we’re being attracted by the moon and somewhere around the space between the Earth and the Moon, the lunar gravity became more powerful than the Earth's gravity so then we started falling toward the moon.
We're coasting. Once the Saturn V shut down, we were coasting all the way to the Moon. The the third stage of the Saturn 5 put us in such a perfect trajectory that I believe we could have gone all the way to the Moon without any kind of trajectory correction.
It was a great feeling, though, that we're finally on our way to the moon."