Delta G. David J. Crawford

office. “Good afternoon, gentlemen. Have a seat.” Dave sat down at the end of a huge black leather couch. “Captain, I know you haven’t had much time to get acquainted with our two distinguished professors here. So I’d like to take this opportunity to bring you up to speed.” Dave relaxed a bit and listened intently.

      “Quite frankly, General Giffen at NORAD called me VFR direct and wants me to provide you all with any support, facilities, and resources you need to accomplish your mission here. This includes C-130 support to the icecap. I only know the basics of what you’re doing out there: some kind of ice-core drilling for gravitational mapping up here, and something about improving targeting for ICBMs and orbital station keeping for our spy satellites. I don’t need to know the details. I’ll just follow my orders to support you anyway I can.” Colonel Snyder called in the sergeant, “Andy, bring us a pot of coffee and have the club run over some sandwiches.”

      Colonel Snyder continued, “Captain, we have an office set up for you. You will be acting as Quality Assurance Engineer up here watching over the contractors running the DYE sites here in Greenland. Also, the transition from Tactical Air Command to Space Command is going to take some time up here. We’ve got quite a few projects underway to support the Space Shuttle polar orbit operations when they start launching off of SLC-6 at Vandenberg. This cover will give you access to all the facilities and communications capabilities up here. Before you ask, this room has been cleared for TS discussions, no Russian bugs in here. We also have a secure conference room here for your use. Dr. Rapp and Dr. Timken have their lab and facilities located at DYE-3. Their cover, as I understand, is ice-core drilling for researching weather patterns and airborne pollutions. The ice out there is over a hundred thousand years old and over two miles thick. That should keep them busy for a while.”

      Dr. Timken acknowledged this, but also made an interesting point. “Thank you, you are correct Colonel Snyder. Hopefully, we are going to kill about four birds with the same stone out here. We have funding and grants from several different organizations, so we will be doing other science as well as our gravitational experiments. As a matter of fact, gravitational experiments are not new. There is nothing super-secret about what we are investigating out here. We will be trying to delve into the universal gravitational constant. Scientists have attempted to do this all over the world. The trick is you need vast areas of constant density materials to conduct the experiments, such as salt mines. We’ve elected to come up here to the icecap because ice has predictable qualities and near constant density for over the twenty-five square miles that we require.”

      Colonel Snyder interrupted, “Excuse me Dr. Timken, I’m a simple soldier that has a degree in Military History. What’s so special about this constant you are trying to figure out? I took enough science and physics to make me knowledgeable but dangerous. From what I understand g is not a constant. It varies with where you are on Earth. Isn’t it something like 9.8 meters per second²? It’s only about a sixth of this value on the Moon, so how can it be considered a constant?”

      Rapp answered, “Forgive me, Colonel, but you are confusing the acceleration due to gravity known as little g with the Universal Gravitational constant big G.”

      Snyder laughed and said, “That’s nothing new, my wife’s always telling me I can never find the correct G spot.” Everyone had to chuckle at this one.

      “What we are doing up here is trying to prove that the big G is not a constant throughout the known universe. I’d like to take a few minutes to refresh your Physics 101, if I may?” Timken continued.

      Snyder leaned back in his chair and threw his feet up on his desk. “Go right ahead. Continue with your explanation. It’s not like I have a tee time to make or anything. We’ve got all day…which up here can be six months long.” Dave had the sickening feeling that this fact would be stressed time after time.

      Timken laughed and assured everyone that they would not be there anywhere near that long. He continued on with his history lesson. “A few flashes of inspiration and genius occur about every half century that fundamentally change the human race. One of these was the falling apple that inspired Sir Isaac Newton to formulate his findings on gravity.”

      He stood up and walked over to the dry erase board. “Colonel, may I use this to humor my academic nature?” Snyder replied, “Sure, I’m left brained and you’ll need to draw me a picture anyway.”

      “Thank you, sir,” Timken continued, “as you all know, Newton once saw an apple falling from a tree and had an inspirational thought. He observed that as the apple fell, it accelerated since its velocity changed from zero as it was hanging on the tree and then sped up as it moved toward the ground. Thus, Newton concluded that there must be a force that acted on the apple to cause this acceleration. He called this force, gravity, and the resulting acceleration, the acceleration due to gravity. This is the little g as we discussed earlier. He then wondered what would happen if the apple tree was twice as high. Here he again expected the apple to be accelerated toward the ground and pick up even more speed. Thus, he concluded that the force gravity would reach to the top of the tallest apple tree.” Timken paused for a minute and grabbed a cup of coffee that had been poured for him.

      He continued enthusiastically, “I realize this might not sound like one of those eureka moments, but you must understand, it’s what Newton did with this knowledge that counts. His brilliant conclusion was that if the force of gravity reached to the top of the highest tree, should it not reach even further; in fact, might it not reach all the way to the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit around the Earth.”

      Timken drew a picture of the Earth-Moon system on the board and exclaimed, “Eureka!” and continued with his presentation.

      “Newton figured out that every object in the universe attracts every other object in the universe with a force directed along the centers of the two objects that is proportional to the product of their masses and is inversely proportional to the square of the distance between the two objects.”

      With this said, he labeled the Moon, M1 and the Earth, M2, then drew a line between them and labeled it r.

      Timken continued, “Thus, one of the most famous and universally accepted formulas was born.” He again picked up the marker and wrote down the famous Newtonian Equation.

      F=G (M1 x M2) / R²

      By pointing to big G, he concluded his lecture stating, “Where big G equals the Universal Gravitational Constant.” He continued to write out the value for G on the board.

      6.67300 × 10^-11 m³ kg^-1 s^-2.

      Timken put the marker down and pointed to the formula, “This strange looking number followed by these weird series of units is termed a "universal constant" because it is thought to be the same at all places and all times, and, thus, universally characterizes the intrinsic strength of the gravitational force.”

      Everyone just stared at the board for a minute or two. Dr. Timken sat back down.

      Colonel Snyder spoke up, “Wow, how’d you remember the value for big G. I can’t even remember my own Social Security number half the damn time.”

      Dr. Timken continued his lecture by pointing out that, “Just like the value for Pi is a known constant that is used in countless formulas and calculations. And just like Einstein’s famous and inspirational equation E=MC2 equating mass and the speed of light, to energy; Newton’s Gravitational Formula is the glue that holds the heavens together.”

      Dr. Rapp spoke up this time, “However, there is a caveat. Notice that big G only has three significant places past the decimal point. For a very universal constant it is one of the least known numbers in terms of accuracy. In contrast, Pi is a known constant out past a million decimal places. The natural log e is another magic number and constant in science and mathematics. It is also known out to millions of decimal places. I can recall 22 decimal places for the natural log e. It is 2.718281828459045235.”

      Everyone