# Gravity, Still a Mystery

We are so accustomed to the effects of gravity that we fail to remember that although we can predict its effects, we don’t really know how it works. Really, we don’t.

The mysteries of gravity have attracted some of the greatest minds in history. Aristotle grappled with gravity in Ancient Greece and postulated that heavy objects would fall faster than light ones. Galileo proved Aristotle wrong by dropping both solid and hollow cannon balls from the Leaning Tower of Pisa and demonstrating that they landed at the same time.

Next up on the Who’s Who of physicists who studied gravity was Sir Isaac Newton, who did not really conceive of his Universal Theory of Gravitation when he was struck on the head by a falling apple. Newton did successfully predict that the attraction of two bodies, an apple and the earth, or Uranus and Neptune, could be calculated with the following equation,

F = GM_{1}M_{2}/R^{2}

in which M_{1} and M_{2} are the masses of the two objects which are attracting one another, and R is the distance between them. The value G, the Universal Gravitational Constant, requires a bit more explanation. When scientists are trying to evaluate data they often try to find an equation which can successfully correlate the data. Once you find an appropriate equation, you can then use the correlation to predict the outcome of future experiments. (That was the scientific method in a nutshell.)

Consider this simple example. Imagine you are an ancient Babylonian mathematician in 1900 BC and you are trying to determine the relationship between the circumference and diameter of a circle. You take the best measurements that you can from a bunch of circles and you notice that if you divide the circumference by the diameter you get a number which is quite close to 25/8. Now you’ve got yourself a useful equation

(Circumference) = (25/8) X (Diameter)

which can be used for future calculations. For example, say you want a circular arena with a circumference of 100 ft. Circumference is hard to measure in the field but diameter is easy. So you calculate the diameter of a circle with a circumference of 100 ft using the equation above, diameter = (100)/((25/8)) = 32 ft. Then you make a 32 ft diameter circle to get the circumference you want. (By the way, in case you haven’t guessed, this is an actual history of the discovery of Pi.)

In Newton’s Universal Law of Gravitation, G is like Pi. It’s the ratio of two numbers, the force of attraction divided by the value M_{1}M_{2}/R^{2}.

When Newton published his Law of Gravitation in 1687, there were two key problems. On the practical level, he had no way to accurately measure the value of G. This would have to wait another 100 years until 1783 when Henry Cavendish of England designed a very sensitive torsion scale which could measure the attraction between two steel balls allowing G to be calculated as 6.673 X 10^{-11} m^{3}/kg-s^{2}. Now that the value of G was known, the force of gravity between any two objects in the universe could be calculated. This was a pretty big deal. Sadly for Mr. Cavendish, no one really remembers him.

The second issue for Sir Isaac was much more challenging. His formula implies what physicists call “action at a distance.” Newton couldn’t wrap his mind around the fact that objects in space – planets, stars, comets and the like – were all somehow pulling on one another from great distances away. Here is how he expressed his thoughts on the subject:

*“It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent, acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers.”*

I feel the same sense of wonder and confusion as Sir Isaac on this front. The tides in the oceans are the result of the pull of the moon’s gravity. But how does the moon pull on the water? Physics is easy to understand when you hit a ball with a bat, but gravity is a mystery.

Physicists continue to grapple with gravity today. The holy grail of theoretical physics at the moment is to develop what physicists call the Unified Field Theory, or in popular vernacular, “The Theory of Everything,” in which all forces of the universe can be described by single equation. As I have noted in previous columns, I like to be reminded that our search for knowledge in the universe continues. In the mean time, we can still marvel at the same questions as Aristotle.

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