Navigating Apollo to the Moon

As NASA first set its sights on landing humans on the Moon by 1969, the intricacies of flying to the Moon were an unknown science.

But the entire success of the Apollo missions depended on navigation engineers that invented the technology and software to guide the Lunar Module to a perfect touchdown.

In this guest blog, British Apollo engineer Pat Norris describes his experience of helping Apollo navigate and land on the Moon.

MASCONS – Distortions in the Moon’s gravity

Like the Earth, the Moon is not an exact sphere, bulging slightly at the equator and being very slightly pear shaped.  Simple mathematical formulas could be used to calculate the pull of gravity caused by these shapes, and we had hoped that any other non-spherical gravity effects would be very small.  Alas, the Lunar Orbiter satellites from the mid-1960s and the Apollo 8 mission in 1968 showed that these other effects caused significant changes to the trajectory.

Two NASA scientists, Paul Muller and Bill Sjogren, at the Jet Propulsion Laboratory in California had shown in 1968 that the problem was caused by the unexpected roughness of the Moon’s gravity field. The strongest effects were over the circular Maria (Serenitatis, Crisium, Humorum, Nectaris, etc.) which had been created by the impact of large asteroids billions of years ago. Those impacts had released heavy material from deep inside the Moon which came close to the surface and generated stronger gravity than the surrounding regions.

The areas of strong gravity were given the nickname mascons. In general the Moon’s gravity field needed a very complex mathematical formula to represent it accurately. And it would require more spacecraft flying over all parts of the Moon at low altitude to provide the data in that complex formula – something that wouldn’t be achieved until the 1990s.

Apollo 10 dress rehearsal

The Lunar Orbiter satellites had shown that the Moon’s gravity field distorted the trajectory of a low flying spacecraft in unpredictable ways. For the Apollo missions, the plan was that the Lunar Module would receive a trajectory update from Mission Control which was intended to be accurate one orbit later at the time of touchdown. The mascons and other unknown features of the Moon’s gravity field meant that this trajectory information was likely to be in error by several kilometres at touchdown. Furthermore the Lunar Module would emerge from behind the Moon just a half hour before the landing so there would no time for the crew to enter complicated updates into the guidance computer. That computer, therefore, had no choice but to use the information sent up by Mission Control before the spacecraft went behind the Moon for the last time an hour and a half earlier.

To help address this problem, Apollo 10 was programmed to fly on exactly the path that Apollo 11 would take two months later. The thinking was that Apollo 11 would experience the same trajectory alterations as Apollo 10 allowing Mission Control to provide an accurate final trajectory update.

Small computers and simple maths

My job at aerospace giant TRW in Houston was in support of Mission Control helping to analyse the trajectory information and the sensor data used to calculate it.  The team I led resolved some of the problems noticed during Apollo 8, such as calculating the correct longitude of NASA’s isolated island tracking stations in Hawaii, Ascension Island and Guam, some off by as much as 300m.

My team also explored a variety of ways to determine an accurate trajectory for an Apollo mission using actual data from the Lunar Orbiter missions and from Apollo 8. Several other groups around the USA were also trying to resolve the problem and we shared our results with them. Eventually we concluded that a single orbit’s worth of tracking data and one particular mathematical formula for the Moon’s gravity field gave the best results. NASA accepted our recommendations as giving the best chance to reduce the error in predicting the trajectory forward one orbit but we and Mission Control realised that the result might still be some kilometres in error.

The small size of the computers in the Lunar Module meant that only a very simple mathematical formula could be used to calculate its descent from orbit down to the surface – calculating the effect of its rocket engine as well as the Moon’s gravity. Today’s computers are several tens of millions of times more powerful than those in 1969. So even though Mission Control had some of the largest computers in the world, these were small in modern terms. Mission Control therefore had to limit its software to fairly simple mathematical formulas in order to keep up with the mission as it unfolded.

Newton’s Third Law – The problem with thrusters

We knew that the Apollo 11 spacecraft, namely Columbia, the Command & Service Module and Eagle, the Lunar Module, would occasionally fire their fine-control thrusters to separate one from the other or to correct their orientation. We also knew that these small impulses were not accurately monitored by Mission Control.

Newton’s third Law of motion dictates that any such impulse causes a similarly small change to the spacecraft trajectory, and we realised that these impulses could be part of the reason for the errors in predicting the trajectory an orbit ahead. NASA had soldered deflector panels underneath Eagle’s small rocket thrusters primarily to protect the Lunar Module from the thruster exhaust plume and a secondary effect was that the impulses were scattered and thus didn’t change the trajectory as much.

Next up - Apollo 11

Following in Apollo 10’s footsteps, with deflectors under Eagle’s thrusters and with the best trajectory information that Mission Control could provide, we were reasonably confident that Apollo 11 would be on target in mid-July 1969. The Saturn V rocket, Columbia, Eagle and the astronauts would have to ensure that the first humans landed on the Moon’s surface – safely.

During the event, Neil Armstrong and Buzz Aldrin in the Apollo 11 Lunar Module overshot their intended landing site by about 6 km. Armstrong had to take over control from the guidance computer which was steering them to the boulder-strewn edge of the 190m wide West Crater. He throttled up Eagle’s engine to stop their descent and allowed its forward momentum to take them another 400m or so to a flat zone before putting down and declaring “Houston, Tranquillity Base here; the Eagle has landed”. The date was 20 July 1969. The landing video captures the drama of these moments.

The landing site was just inside the “landing ellipse” designated by NASA before the flight, so in one sense the landing was a success. But it was in the extreme south-west corner of the ellipse and about 7 km from the ellipse centre (6 km west, 2 km south).

The influence of the Moon’s complicated gravity field on spacecraft navigation was highlighted the next day when the Soviet Union’s uncrewed Luna 15 crashed when attempting to land in Mare Crisium 800 km to the east of Apollo 11. The Soviets had spent nearly an extra day trying to calculate an accurate trajectory for Luna 15 without success. They attempted the landing anyway in the hope that the probe could grab a sample of lunar dust and send it back to Earth before Apollo 11 returned. This was the second Soviet attempt at a robotic sample return mission, and it would take six attempts before they succeeded with Luna 16 in September 1970.

Apollo 12 - Precision Navigation

The overshoot of Apollo 11 was in fact noticed as it came from behind the Moon a few seconds earlier than expected on its last orbit before the landing.

So for Apollo 12, four months later, a fudge was introduced whereby this time measurement was converted into a distance, and this single number radioed up to the crew who entered it into their guidance computer.

The computer adjusted its path accordingly and they landed bang on target a half hour or so afterwards, 200m from the Surveyor III robotic probe as intended.