In this week’s Â鶹´«Ã½, we recall the dramatic moment when the Apollo 11 astronauts realised they were landing in the wrong place, and reveal how the problems that dogged their landing could still plague future missions. We talk to the elite club of astronauts who made it to the Moon in the heady days of space exploration, and discover what we could gain – and lose – by returning there.
Guiding astronauts to a safe touchdown was never going to be easy, writes Pat Norris. But NASA thought it had solved the major problems – until the day of landing
Neil Armstrong’s first glimpse of the landing site told him things were not going to plan. A few minutes later, he could see boulders directly beneath the descending lunar module, and he knew something was definitely wrong.
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NASA had promised a smooth spot for the landing, yet from the pilot’s seat of the lunar module, Eagle, Armstrong could see that he and Buzz Aldrin were fast approaching a lunar landscape pocked with craters. The landing site was also supposed to be free of obstacles, but with the surface still 100 metres below he could almost count the boulders strewn across it. The first visitors to the Moon were coming down in the wrong place.
More than a quarter of a million miles away, TV viewers on Earth had joined the engineers and scientists at NASA in witnessing the crisis live. They watched Armstrong steer Eagle round the field of boulders and, with barely a minute’s worth of fuel left before the descent would have to be abandoned, begin searching for a safe spot to land.
NASA knew there were problems in guiding the Apollo 11 astronauts to the selected landing site on the Moon, but thought it had solved them. As Eagle’s unexpected last-minute manoeuvres drained Eagle’s fuel, the chilling prospect of failure began to take hold of officials at Mission Control in Houston as they were forced to consider ordering Eagle to switch to the ascent engine, which had its own fuel tanks, and return to the safety of the orbiting command module piloted by Michael Collins. That they did not have to is history, of course. Armstrong finally found an adequate landing spot, and went on to claim the Moon for humanity.
Weeks later, having studied pictures taken by the astronauts, scientists in Houston calculated the margin by which Eagle had missed the intended landing site. Travelling westward over the surface, the lunar module overshot the target by about six kilometres, and it was at least two kilometres off track to the south. Instead of landing comfortably on a smooth patch in the Sea of Tranquillity, Eagle finished up in one of the sea’s less hospitable spots, which was even outside the region that had been catered for in ground simulations of the landing.
At the time I was working for TRW, a Houston-based aerospace contractor, where I managed a team of analysts and programmers who were helping NASA to develop software to guide the Apollo missions. During the preceding two years we had improved the accuracy of the Apollo navigation systems – but evidently not enough. And even now, 25 years later, space engineers still do not have the technology to avoid similar problems on future missions to the Moon and beyond.
The main cause of the navigation error was our poor knowledge of the way the Moon’s gravity varies over its surface. Evidence of this problem emerged during the five Lunar Orbiter missions to map the Moon’s surface, launched in 1966 and 1967. Classical physics should enable scientists to calculate to within a fraction of a second when a spacecraft reappears from behind the Moon. But the Lunar Orbiters were often several seconds early or late. Irregularities in the lunar gravitational field were influencing the speed of the orbiting spacecraft, making them go faster or slower depending on whether the gravitational pull was greater or smaller than expected.
Then there were unexplained variations in the tracking signals from the orbiters. We could monitor the position of the craft only by exploiting the Doppler effect, the way in which an object’s speed affects the frequency of signals from it. We expected to be able to predict the change in the tracking signal’s frequency of several kilohertz to within a few hundredths of a hertz, or about 1 millimetre per second in the speed of the craft. We found that our forecasts were out by up to 0.5 hertz, equivalent to speeds of 10 or 20 millimetres per second. As the phenomenon appeared time and time again, and when the spacecraft were close to the Moon, engineers dubbed it ‘perilune wiggle’.
Research teams around the US analysed the problem throughout 1967 and into 1968. Many suspected the cause to be differences between the Moon’s real gravitational field and the smooth, near spherical field on which predictions of the spacecrafts’ paths had been based. The Earth was known to have a highly complex gravitational field because of the nonuniformity of its shape and local variations in density, so why not the Moon too?
A mathematical description of the Earth’s gravitational field typically requires hundreds of terms, but a similarly large mathematical description of the Moon’s gravitational field, derived from the trajectories of the Lunar Orbiters, failed to remove the effects of perilune wiggle from the Doppler data.
All this spelt trouble for the Apollo missions, and especially for those spacecraft that would be making low lunar orbits, during which perilune wiggle is most noticeable. Furthermore, NASA wanted Apollo 11 to circle the Moon at least a dozen times before releasing the lunar module carrying Armstrong and Aldrin.
THE WIGGLE FACTOR
For those of us in Houston charged with keeping Apollo on course, NASA’s decision presented a tremendous challenge. We had to devise a mathematical model of how each orbit would evolve from its predecessor, and then work backwards to calculate an initial orbit for the craft to adopt that would take it over the selected landing site during the orbit in which the module would be launched. Perilune wiggle was the constantly recurring phenomenon that scuppered every model we drafted.
The alternative to modelling the spacecraft’s complete path might have been to leave the corrections until the final orbit, but there simply wouldn’t have been enough time for such corrections to be made. The plan was for the lunar module to separate from the command module on the far side of the Moon, and to land within half an hour of its reappearance. This didn’t give Houston long enough to record the Doppler measurements from the spacecraft, compute a new flight path, and radio that information to Armstrong and Aldrin for them to key it into The Eagle’s navigation system. And though corrections for preceding orbits could be computed and radioed to the astronauts before they disappeared behind the Moon, they would be immediately compromised by subsequent perilune wiggle.
A breakthrough came in 1968, when Bill Sjogren and Paul Muller of the Jet Propulsion Laboratory in California proved that the Moon’s gravitational field was responsible for perilune wiggle. They calculated the accelerations that must have caused each wiggle in the Doppler data, which would be directly related to the unknown forces, and then plotted them on a map of the Moon. They found that areas of high acceleration coincided with the circular maria or seas that are surrounded by one or more rings of mountains – unlike other maria with large amorphous shapes, such as the Sea of Tranquillity.
The scientists concluded that the ringed maria must be the densest regions of the Moon, and hence the zones where gravitational effects are greatest. They speculated that these mass concentrations, or ‘mascons’, are either the remnants of asteroids that had hit the Moon, or dense material from the lunar interior that had been released by such impacts. Mascons were found in all but the smallest of the maria, and matched the pattern of accelerations that Sjogren and Muller had plotted.
PROBLEMS IN ORBIT
But though the cause of the orbital oscillations of spacecraft near the lunar surface was now confirmed, a practical way of modelling perilune wiggle remained out of reach. In practice, the spacecraft deviated significantly even from predicted orbits that took into account the gravitational forces of the mascons. A mathematical model to describe features on the scale detected by Sjogren and Muller would have required a thousand or more terms. Also, Sjogren and Muller’s results were so rough and ready that it was difficult to express them in the forms required.
Though researchers used the JPL data to create more representative models for navigating spacecraft to the Moon, they were not much of an improvement on the simple model known as R2 that had been developed by the Boeing Aircraft Company during the orbiter missions. Furthermore, the computers on board Apollo 11 were primitive by today’s standards, and could deal with only the simplest of expressions.
At TRW we were anxious to gauge the accuracy of the navigational information we were supplying to spacecraft, and to test how well various mathematical models dealt with the Moon’s troublesome gravitational field. To do this, we compared sightings of specific features on the Moon’s surface, typically the rim of a crater, taken during various orbits on the same or different missions. The uncrewed orbiters photographed craters and radioed the information to Earth; astronauts aboard Apollo 8 and 10 used a sextant to take sightings of surface features.
We found that the apparent location of certain surface features, based on the calculated position of the spacecraft from which they were observed, varied by several kilometres from mission to mission, and from orbit to orbit on the same mission. Equally importantly, from our point of view, it depended on which gravity model was used to determine the position of the spacecraft. A typical example is provided by the four sightings of a crater taken from Apollo 10 in May 1969 on its 24th, 25th, 26th and 27th orbits of the Moon. This crater was particularly interesting as it was located in the Sea of Tranquillity, close to the point where Apollo 11 was due to land two months later. Estimates of its latitude and longitude varied by up to 6 kilometres, and its altitude by up to 1 kilometre.
We had hoped that crater sightings could give reliable information about the position of Apollo 11 relative to the lunar surface, but we didn’t find a way of using them successfully in time for the first landing. In the end, Houston had to supply the command module with corrections as it completed each orbit, but this was not an ideal solution because repositioning manoeuvres used up valuable fuel.
For the second crewed flight to the Moon, in November 1969, we did a little better. We incorporated one extra term in the mathematical model of the Moon’s gravitational field, and as the spacecraft appeared from behind the Moon on the orbit in which the landing was due to take place, Houston relayed a navigation correction verbally, which the crew entered into the Lunar Module computer. The correction was based only on the difference between the time the spacecraft reappeared and the time it was expected to do so. But crude and inelegant as this approach was, it proved successful, and Apollo 12 landed within walking distance of its target.
Knowledge of the Moon’s gravitational field remains sketchy. Because the Lunar Orbiter and Apollo missions could be tracked only when they crossed the near side of the Moon, they did not provide complete coverage of the lunar surface. Even today, any spacecraft flying in low lunar orbits is likely to be out of position by several kilometres, and similar gravitational anomalies will affect the navigation of missions to Mars, Mercury, Venus and other planets of the Solar System
Pat Norris is business development manager for the space division of Logica, a computer software company based in London.
