IN MY FECKLESS YOUTH I once made a mathematical mistake, a technical error. Unfortunately, mine became embedded in the public consciousness throughout most of the world, and remains there today. I was reminded of this when reading an on-line European magazine report on a then-recent space launch. The figure they gave for the planned geosynchronous orbit was wrong—and that’s my fault.

It came about this way.

In 1971 I was working for Boeing as a tech writer, supporting NASA’s Unmanned Launch Operations Directorate (ULO) on Cape Canaveral. My title was “Project Writer,” and it meant I did all the technical documentation for the NASA branch responsible for Atlas-Centaur vehicles. I also manned a console during launches. Two other experienced tech writers supported the Delta and Atlas-Agena branches, and we all worked with the branch that managed the spacecraft. The contractors who built and launched the three vehicles had their own tech writing staffs, and produced different, though sometimes overlapping, launch documentation.

I had worked in ULO for two previous years, 1966 and ’67, in the same position, before transferring to Kennedy Space Center to support the Apollo Program. Though operating in the giant shadow of Apollo, and not drawing that much interest from the general public, ULO had continued to grow during my four-year absence.

The primary growth area was communications satellites, with a increasing emphasis on those designed to operate from geosynchronous orbits. (Which would be called “Clarke” orbits, if this was a just world. Arthur C. Clarke published the first article pointing out that three equidistant satellites in geosynchronous orbit could provide communications to most of the inhabited world; see Wireless World, Oct. 1945).

“Geosynchronous” means positioned over the equator and moving in line with it, at the exact altitude and orbital velocity that completes one orbit in 24 hours. Since the equator also rotates once during those 24 hours, the net effect is that the satellite appears to remain motionless in the sky. This is very desirable for people sending up data to be retransmitted over a large area, such as television and radio signals.

One of my more rewarding duties as Project Writer was to prepare a little sheet of basic facts on each planned launch of the Atlas-Centaur. Written in layman’s language, it provided a fairly complete overview. This fact sheet had begun as a one-page basic list, but when I took over I expanded it to provide a comprehensive overview of the entire mission. It grew very popular, and I was asked to prepare one for Delta launches as well — though another writer handled all the purely technical documentation. (The Atlas-Agena program had been killed.)

Shortly after I arrived back at ULO, the Atlas-Centaur was scheduled to launch an INTELSAT communications satellite into geosynchronous orbit. When I did my usual study of the voluminous technical documentation in preparation for writing the mission fact sheet, I had my first encounter with geosync orbit parameters. I knew the general operating concepts, of course, but here were the exact figures for this particular mission. The INTELSAT was to be injected into an orbit with an apogee (high point) of about 22,400 statute miles above the Earth’s surface, and a perigee (low point) of under 22,200 miles. That was the acceptable range. The spacecraft’s own small thrusters would refine whatever orbit was actually achieved to reach the satellite’s final height, which was not given.

The general public didn’t care that much about preliminary orbital altitudes. I knew they would want the planned final one, which would be somewhere between the apogee and perigee. And I needed to round off the actual figure to the nearest hundred miles. That was as close as most people, and in particular the news media (who had started asking for my fact sheets after they became popular) would ever remember. So, within the range of 22,400 and 22,200, I selected 22,300 miles as the figure for the planned final altitude, and used that.

My fact sheet sailed through the routine checks by NASA engineering managers without a problem, and was published. The idea of a satellite that could sit apparently motionless in the sky was still very new. INTELSATs, the first satellite system designed to provide communications over the entire world, were receiving a lot of attention. Story after story appeared in the media about the advantages of geosynchronous orbit. And all of them used the figure I had supplied as the correct altitude, 22,300 miles. Within a year or two, it had become the established figure. Everyone, from knowledgeable newsmen to devoted space program fans, used it. Even NASA people doing briefings for the press and public adopted it.

ULO continued to launch vehicles, the only U.S. action around after the last manned flight for Apollo, the Soyuz Test Project in 1975. Among these were several in the swiftly growing area of spacecraft designed to operate from geosynchronous orbit.  And going over the orbital parameters for another one, a year or so after my first, I discovered something.

There is such a physical dimension as a perfect geosynchronous orbit altitude. Few spacecraft attain it or rigorously hold to it, because it isn’t that important. A satellite can move slowly up or down in orbit (the only visible effect of not being in a perfect circle) fifty miles or so, without seriously affecting the antennas transmitting to it from the ground, or the coverage area of its broadcast signal. Spacecraft operators don’t waste precious fuel trying to keep a satellite at an exact altitude; here, close is good enough.

But the perfect altitude for a Clarke orbit, it turns out, is 22,237 statute miles above mean sea level. (And it is of interest to note that the master visionary, in his Wireless World article, called for an orbit with an estimated radius of 42,000 kilometers from the center of the earth. That works out to about 22,100 miles above mean sea level; very close.) That meant I should have rounded off geosynchronous altitude as 22,200 miles above the Earth, the closest hundred. Using 22,300 miles had been a mistake.

By the time I recognized my error, the 22,300 figure had become thoroughly established. Everyone was using it, even engineers and others who were experts in orbital mechanics and knew better. I tried to correct the mistake by using the exact planned apogee and perigee figures on ensuing factsheets, but it was too late. The news media ignored the exact figures, sticking with the incorrect final planned altitude of 22,300 miles.

When I saw the European magazine using the 23,300 mile figure, decades later, I realized it has obviously become a world-wide standard.  It should be 22,200, but tell that to anyone except someone with expertise in orbital mechanics, and you will start an argument.

It’s wrong. And it’s all my fault.

It’s probably also my only real claim to lasting infamy—except that no one but a few people to whom I’ve spoken, and the readers of the fanzine Challenger, which published an earlier version of this article in Issue 20, know the facts

Ah, well.

Image credit: NASA