# How were we able to navigate from the Earth to the Moon with such precision?

How were we able to navigate from the Earth to the Moon with such precision?
Before the days of GPS, engineers had to rely on good old fashioned computation…

Plotting the path from launch pad on Earth to a landing site on the moon—and back again—was made possible in the 1960s by using what we know of the mechanics of the two bodies. These are not easy calculations. After all, the Moon and Earth are moving along their own trajectories, one of them rotating quite quickly the whole time. Fortunately these movements are quite predictable, and there aren’t many twists and turns along the way. Once you’re on the right trajectory, it’s smooth sailing for several days.

However, that “right trajectory” may require lots of small adjustments, especially when you get to either end of the trip. To ensure the spacecraft doesn’t land on the edge of a crater on the Moon, or burn up or skip off into space upon reentry into the Earth’s atmosphere, it’s critical that the pilots are able to know three things about their spacecraft with great precision:

• Where it is in space and where it is going? (navigation)
• Which way it needs to go to stay on or return to the planned path? (guidance)
• How and when to fire its thrusters to match the planned path? (control)

For the Apollo space missions, engineers at the MIT Instrumentation Lab (now the Charles Stark Draper Laboratory) developed the Primary Guidance, Navigation, and Control System (PGNCS), which consisted of a computer, software, inertial measurement unit (IMU), and optical instruments. The crew used an optical sextant and telescope to measure the angles between stars and the Earth or Moon horizons; the computer would calculate those angles and provide the necessary navigation information. For its time, the Apollo guidance computer was state-of-the art. (Today, your hand-held device is capable of much, much more.)

Navigating to the moon requires data about current position and velocity with respect to some frame of reference. A large antenna on Earth, for example, can determine the distance from itself to the spacecraft by measuring the delay of a signal sent from Earth to the capsule and back. It can also determine radial velocity, or the rate at which the spacecraft is moving along the line between the antenna and spacecraft, using the Doppler effect to calculate the frequency difference of that signal and its returned version. Radio tracking is incredibly precise in the neighborhood of Earth, measuring a distance to less than 30 meters of error.

For guidance and control, the Apollo spacecraft featured a large engine and smaller reaction control system thrusters that, when fired, changed the roll, pitch, and yaw of the spacecraft, as well as providing thrust in what direction was necessary to get back on track. However, in order to fire the engines in a specific direction, the spacecraft had to know what its orientation in space was. That’s where the IMU came in. The IMU was about the size of a soccer ball and contained a platform mounted on three gimbals. Sensors on the gimbals could tell how many degrees the spacecraft was rotated around each axis with respect to the platform and thus report the orientation of the spacecraft to the crew via the computer. With that information, the crew could take the steps necessary to stay on course.—Gwendolyn Vines Gettliffe, a Ph.D. candidate in the Department of Aeronautics and Astronautics.

Thanks to Sanjoy, a 40-year-old from Delhi, for this question.

April 10, 2012