Delta G. David J. Crawford

the gigahertz or billions per second common today. They were also difficult to program, but provided a useful test bed for basic computer concepts.

      It seemed that we have now come full circle. ICBM targeting could also no longer be counted on to depend on the simplistic targeting algorithm of the day. The Titan II missile system was designed to destroy enemy strategic targets in a minimum amount of time. To do so, the warhead must be placed on a target with a high degree of accuracy and from a distance of over 5,500 miles. This degree of accuracy is comparable to hitting a golf ball into the cup 150 yards away or making a hole in one from a par three. It is obvious that many variables must be considered in attaining this degree of accuracy. The powered portion of flight lasts less than one sixth of the total flight time or about five minutes. Control of the flight path was not possible after powered flight ends. The missile goes into a ballistic free fall for the remainder of the flight.

      Several parameters must be met before the end of powered flight to permit the warhead to arm itself and free-fall to the target. All missile systems exist solely for this purpose. The targeting of a Titan II ICBM involved an algorithm containing only 13 parameters. These include obvious variables such as launch site and target coordinates, velocity, altitude, and even barometric pressure. However, there are other not so apparent variables that enter the equation.

      Polar motion produces variations in several parameters employed in targeting computations which are traditionally treated as constants. These include the Earth’s angular velocity vector, launch site gravity magnitude and astronomic coordinates, and target and launch site inertial velocities. The resulting targeting error is assessed for each of these quantities. The dominant error is shown to be the Inertial Measurement Unit (IMU) azimuth alignment error. This results in a large cross-range error caused by a shift in the Earth’s poles.

      Why is this important? Because all of the test launches of our ICBM fleet were launched from Vandenberg AFB on the California coast and launched westward towards the Johnson Island Atoll or Kwajaline Atoll about 5,550 miles out into the Pacific Ocean. This westward launch did not adequately simulate an actual launch over the pole to the north. Going over the pole represented a whole slew of challenges and problems not fully understood or anticipated.

      The IMU azimuth alignment relied upon celestial navigation. The azimuth was determined using an optical collimator that consisted of basically a periscope using a mirror and prism system that was piped down through the silo and into the reentry vehicle (RV), the polite and politically correct term for nuclear warhead. This optical system established the missiles exact coordinates on Earth in reference to the pole using the North Star as a bench mark. This was done based upon the position of the North Star timed with the aid of an atomic clock. A small measurement error on the launch end represented a huge error on the target end of the trajectory. Gravitational “anomalies” were also encountered when flying over the poles as was experienced with spacecraft placed in polar orbits.

      Every object in the universe attracts every other object in the universe with a force (F) directed along the centers of the two objects proportional to the product of their masses (M1 and M2) and inversely proportional to the square of the distance between the two objects (R). This is the basis of the famous Newtonian formula below:

      F = G (M1 × M2)/R²

      where G (Gravitational constant) = 6.67300 × 10^-11 m³ kg^-1 s^-2

      Don’t confuse this “big G” with “little g”. Big G is considered a universal constant or the same number throughout the known universe. Little g is the known as the acceleration due to gravity. On Earth, it is normally about 9.82 meters per second squared. That means that when an object is dropped it falls at a rate of 9.82 meters per second for the first second. After the next second it falls at 17.64 meters per second. After the third second it is falling at 26.44 meters per second and so on and on as it picks up speed. It is also conceded that little g is not a true constant but varies from the pole to the equator and due to the pear shape of the Earth. It can also be affected by the relative mass and density of materials such as mineral deposits, mountain ranges, ice packs, and ocean depths. It has to do with the amount of mass beneath your feet.

      These deviations in little g have been fairly well understood and even mapped by geologists, oil companies, and the Colorado School of Mines. Even with all the targeting deviations, precessions and errors known, it was nearly impossible to validate that the algorithm was correct when you had to launch a missile toward the North Pole to prove it. The Russians and Chinese would take a dim view of this. Anything remotely approaching the pole would be considered a threat.

      Thus, the only other alternative was to map out the gravitational anomalies and account for them in the targeting algorithm. This gave birth to a multibillion dollar black program called Delta G in deference to the changing gravitational constant.

      Newly promoted First Lieutenant Sheridan was now about to embark on another career broadening experience. He was summoned to Headquarters at North American Aerospace Defense Command (HQ NORAD) at Cheyenne Mountain near Colorado Springs. One of NORAD’s primary functions was to track space-borne objects in orbit around the Earth. This included all satellites, and space junk down to the size of a tennis ball. As a matter of fact, one of their smallest objects tracked was a glove that floated loose from a spacewalk operation out of a Gemini capsule. NORAD uses a combination of radar and optical sensors to track and catalog over 9,000 space objects.

      Another mission includes a Laser Clearinghouse (LCH) for laser operations and Collision Avoidance (COLA) for NASA; both functions are intended to protect on-orbit assets. COLA and LCH use the computer projections to propagate objects over the laser emitter or launch site to determine if there is a possibility of collision.

      Sheridan was escorted into Cheyenne Mountain by Captain Dennis Murphy. The entry procedures were similar to those for the Titan sites. Once inside the giant drive-thru blast doors, they hopped into an electric golf cart that whisked them the 300 yards into the cavernous operational control center. This place looked like a launch control center on steroids. Again, everything was shock mounted and situated on huge isolation platforms. Murphy led Sheridan into one of the modules and then down a hallway into a conference room. Sheridan had to smile at the cherry wood paneling, table, and furniture. For a place built to last beyond doomsday, no expense was spared on the details and little things in life.

      General Ron Giffen entered the room along with a staff of a half dozen technicians and asked, “Sheridan, do you really know why you are here?” The question took him back a little. He responded sharply, “Sir, I was told to attend a briefing on orbital tracking, space operations, and targeting algorithms.”

      Giffen replied coldly, “Sheridan, this operation is classified TS and just to be clear that you know the ramifications, I’m sending you to the North Pole afterwards to implement the operational plan,” added the General. Dave didn’t see that one coming as his jaw dropped.

      Giffen continued, “You’re now a world class subject matter expert on ICBM targeting and are intimately aware of the fact that launching an ICBM over the pole makes it about as accurate as my tax return. The only saving grace with the Titan is that it carries one hell of a punch. That ten megaton warhead means you only have to be close. However, we have other problems.”

      The General paused for a moment for dramatic effect, “ICBMs aren’t the only thing we launch over the poles. The Space Shuttle is due to be launched out of Vandenberg from SLC-6 in a year or so. We’re going to put it in a polar orbit to augment our reconnaissance satellites that are currently in a polar orbit.”

      General Giffen stood up and walked over to the wall display, “Now with that said, I want to show you something very interesting.” He had one of the technicians call up a program showing a graphical representation of the Earth and several thousand objects apparently in orbit. “Sergeant, delete all objects not in polar orbit at or below eighty degrees north latitude.” The screen now showed only a few dozen objects.

      “Lieutenant, these objects represent the satellites that we and the Russians have in