As I mentioned before, I will not be providing a comprehensive rebuttal to Mr Willis’ article. He hasn’t yet convinced me it will be worth my time to produce one. So we’ll start with the introduction to his article, which contains some isolated claims, and see how well he fares. If he impresses me with his handling of my rebuttal, we’ll proceed.
The astronauts who descended onto the lunar surface ─ Charles “Pete” Conrad and Alan Bean ─ had been tasked with making a precision landing. Just four months earlier the Apollo 11 LM Eagle had landed six kilometres off target. Conrad and Bean brought their LM down at a distance of only 155 metres from Surveyor 3.
You don’t provide any line of reasoning. You draw a contrast here, but to what point? The reader is presumably meant to imagine that the Apollo 12’s feat seems suspiciously adept in light of its forerunner. But it’s intellectually dishonest to walk right up to your point and then not say it. Previous Aulis authors did that a lot. They “let the reader draw the conclusion,” and by that sketchy rhetoric they absolve themselves of having to defend the only conclusion the reader was supposed to draw, but which they disclaim ever having made themselves. That’s where an editor would have helped you write honestly. We’ll proceed as if you stated the conclusion you evidently wished the reader to draw.
It’s easy to suggest something seems suspicious if you just leave out the explanation of how it was done, which is what you did. And it’s lazy to make your fact-checkers have to compensate for your disinterest in the whole story, which is what we now have to do. My sources are the flight plans, mission reports, and crew technical debriefings for Apollos 11 and 12, and the supporting documents they reference. These would be considered primary sources in researching what Apollo procedure was and how effective it was determined to be.
Apollo 11 was
not tasked with making a precise landing. It’s a bit misleading to say they landed 6 km “off-target.” They landed that far from the
center of a target ellipse measuring 20 by 5.5 km. Apollo 11’s objective was to make a safe landing -- anywhere on the lunar surface -- and then return to Earth. Everything past that was a secondary objective. A landing anywhere within the target ellipse would satisfy a secondary mission objective: to show that they had reasonable model of what lunar navigation entailed, if not yet all the fine quantitative details.
It’s also important to realize that the different mission objectives informed which of several possible alternatives the flight controllers opted for on the fly in each case, which then affects the outcome. To imply that
Eagle didn’t make a pinpoint landing because it couldn’t omits this important principle.
A well-known feature of the Moon is its lumpy gravitational field. A pure Keplerian approach to orbital mechanics isn’t accurate enough to specify precisely how objects orbit the Moon. A more generalized solution involves harmonic equations. Under contract from NASA, Boeing produced a 13-term spherical-harmonics model to describe the potential energy in lunar orbit. The model having so many degrees of freedom, using it to predict an accurate picture of the spacecraft’s orbit around the Moon was possible only after repeated observation. Ground trackers measured the Doppler shift in the ship’s radio frequency as it moved away from Earth going around to the far side, and toward Earth as it emerged again. The error between the model’s predicted velocity state and the measured velocity state was used to alter the parameters of the model and refine the prediction. That’s a straightforward curve-fitting problem -- straightforward in the sense that no mathematical chicanery is involved. Less straightforward in the realization that it takes a 1960s mainframe an appreciable amount of time to get the fit to converge.
From its circular parking orbit around the Moon, the lunar module went into a pre-descent orbit, with a pericynthion (PC) just a few kilometers above the lunar surface. Since PC had to be on the near side, where the landing site is, the retrograde LM DPS burn to achieve it happened on the far side, at the corresponding apocynthion, where ground observation is impossible. Mission Control couldn’t watch the LM do this burn, or measure its speed and position from Earth. Thus the LM emerged from behind the Moon in a different orbit, not the one painstakingly curve-fit to the Boeing R2 gravity model over several revolutions.
But not to worry. The new orbit can be acceptably derived from the precisely-determined one by integrating the effects of the DOI (descent orbit insertion) burn, as recorded in the LM’s guidance system. Every maneuver produces residuals, and these are also recorded in the guidance system and were trimmed with the LM’s RCS to achieve as near to zero a measured error as possible for the overall maneuver. With that mathematical idea of the LM’s new orbit computed, a landing trajectory can then be fashioned to connect the desired landing site with the orbital model. The result is the point along the computed orbit near PC where the actual powered descent had to start.
But what if the computed orbit is not the actual orbit? As
Eagle appeared from the right side of the Moon, it transmitted its trimmed DOI residuals so that the ground computers could add the appropriate kinetic energy to the orbit. Then as it rounded the face of the Moon to start its descent, ground observers began to note that its Doppler-measured velocity was about 4 meters per second faster than the residual-corrected R2 model predicted. You need several Doppler measurements taken over a few minutes to determine the orbital path that’s producing them. A method for doing this is in Bate’s
Fundamentals of Astrodynamics. This error ultimately meant the spacecraft’s state vector, which was being deduced by the computer from the model orbit, believed it was more than 5,000 meters behind where
Eagle actually was in its orbit. And since the model -- not the actual position -- is what schedules the PDI burn (powered-descent initiation), the burn would come too late and the ship would land long. And the crew confirmed this too, because their expected landmarks were passing under the ship sooner than the orbital model predicted.
Now nominally this can be fixed. The LM’s computer has only a simplified mostly-Keplerian orbital model. It was always part of the plan that the state vector would be updated in lunar orbit periodically from the ground, based on fitting the Doppler data to the R2 gravity model. That’s what happened with the CSM during the many orbits that preceded the landing attempt. The effect of the update is to correct the errors that arose out of the AGC simplification. In general, throughout an Apollo mission, all the simple AGC models would work in the short term, and the more accurate ground-based measurements and more sophisticated mathematical models run on the bigger computers would periodically recalibrate the onboard computer.
And it was certainly part of the mission plan that the orbit extrapolated from the DOI burn and its residuals was likely to be off by a certain amount from the empirical Doppler measurements. The onboard accelerometers are only so accurate. A last-minute update of the state vector was possible between DOI and PDI. But since Apollo 11 had no accuracy constraint on its landing, this was deemed unwarranted for this mission. Landing 5 km long was considered okay, and not worth the invocation of a guidance contingency. Don’t fix it if it ain’t broke.
So what was done differently on Apollo 12?
First, Apollo 12 went into a higher inclination orbit around the Moon. The R2 model is more accurate with inclinations farther away from zero, because there’s more variation in the latitude parameter. You can fit data more confidently to a more sharply inflected curve. Apollo 11’s orbital inclination was constrained by the free-return translunar trajectory. Apollo 12 used the hybrid translunar trajectory.
And the gravity potential model was revised to the so-called L1 model, which extended the R2 model with an added term to improve its accuracy. The motivation to do this was purely an engineering concern.
Intrepid didn’t attempt to trim its residuals from DOI using the RCS. While the guidance system is very accurate in measuring accelerations in three dimensions while under powerful SPS propulsion, The accelerometers are less accurate in the lower range, such as that produced by RCS translations. This is due in part to the mechanical limitations of pendulous accelerometers, but also to the granular error inherent to the measurement.
If your car speedometer reads off speeds in increments of one kilometer per hour, it’s easier to regulate your speed to arrive somewhere on time at speeds of, say, 50 km/h. The difference between 50 and 51 km/h is proportionally small. It won’t result in much error. But if you need to go at exactly 1.5 km/h, the difference between 1 and 2 km/h is dramatic. If your readout is 1, you don’t know if your actual speed is 1.1 km/h or 1.9 km/h. And the error could result in you arriving almost twice as early or twice as late.
With this principle in mind, mission analysts concluded the trim that
Eagle attempted might have actually given them a worse reckoning of the ultimate residuals that were integrated into Apollo 11’s R2. The untrimmed residuals were determined to have a greater precision, even if their magnitude was larger. So second, part of the role played by the new term in L1 was to integrate the untrimmed residuals from DOI directly.
Third, and onward, are the many things Apollo 12 didn’t do that Apollo 11 had done that affected the LM descent orbit in ways the guidance system couldn’t measure, record, or compensate for. Let’s look at this in more detail.
The Apollo guidance computer can operate in accelerated-flight mode, in which burns by the SPS, DPS, APS, or even in some cases the RCS (in translation) are integrated through the accelerometers into the state vector by a computer routine called the Servicer. Or it can operate in orbital mode, in which the state vector is maintained by the Encke method of conic integration, referring to Keplerian orbital mechanics. This relies on orbital elements deduced from previous maneuvers or transmitted from the ground. No attempt was made to integrate these flight modes, as it would have exceeded the capacity of the AGC. Encke-based dead reckoning ignores the accelerometers. Servicer-based dead reckoning ignores the orbital model. Both modes are open-loop control logic. That means the spacecraft has no way of actually knowing whether it’s actually on the deduced path. That information has to come from the ground.
Now fourth -- an uncoupled RCS burn is one in which balanced pairs or sets of jets are not used, and in fact only one jet may be used. I described this to the astonishment of our previous hoax claimant, Jr Knowing. In uncoupled RCS attitude burns, the desired rotation is accompanied by undesired translations. There were plenty of those on the far side before and after DOI. In docked flight, and just after undocking, certain RCS jets have to be inhibited in order to protect the delicate high-gain antennas of the companion spacecraft.
Eagle also performed hot-fire RCS tests, a post-undocking separation maneuver, and lots of stationkeeping activity while Michael Collins in
Columbia checked out the exterior of the ship. What’s important to know is that none of this activity was being integrated into the state vector because the AGC necessarily was in conic-integration mode. Those maneuvers certainly affected the orbit, but they would not have been captured in the only guidance data the LM sent back to the ground -- the DOI residuals.
All these sources of error were known during and after Apollo 11’s flight. They just weren’t important to deal with under the Apollo 11 mission objectives. Apollo 12 adjusted the flight plan to eliminate the sources of error that could be, and deal with those that remained.
The Apollo 12 undocking occurred with the stack oriented along the orbital radius, instead of along the orbital path. Again, this wouldn’t have registered in the computer because the accelerometers were being ignored. This different orientation for the separation minimized the dispersion that the R2/L1 gravity model would be sensitive to. And there was no separation maneuver from the LM. The separation was accomplished entirely using the SM RCS. No LM stationkeeping, no RCS tests.
Apollo 12 also had the advantage of a landing site farther west. This means the LM would be in view of the Doppler measurements for a longer period before PDI. Not only could the ground trackers accumulate more data to measure the descent orbit, but they had more time to formulate and upload a new state vector. When the crew reported their DOI residuals and the L1 model was updated and fit to the Doppler data, a very accurate state vector resulted and was sent back to
Intrepid.
Finally,
Intrepid’s crew had an easier time of it. Armstrong and Aldrin were distracted for long enough dealing with the AGC program alarms that by the time they looked back out of the window, they weren’t sure where they were. Armstrong could have easily pointed
Eagle to the originally designated landing site, if only he could locate it on the ground in time. He couldn’t. Instead he just chose not to land on the pile of rocks he was headed for. The lunar terrain around Surveyor Crater was much more distinctive, and Commander Conrad didn’t have a computer problem to deal with. He could easily recognize the intended landing site and easily point the LPD to it.
This is a very detailed explanation of what was different about the engineering and procedures used in Apollo 12 that allowed it to meet an objective that was not set for Apollo 11. Properly researched and understood, there’s no reason for suspicion. You, the author, are not necessarily responsible for reproducing this detail for your reader. But you are responsible for
knowing it, and for writing whatever summary of it you want to make in terms that accommodate it. Your insinuation that Apollo 12’s landing was suspiciously accurate after Apollo 11 is either unaware of the solution or deliberately ignoring it.
