Wednesday, September 12, 2007

Gravity

Man has always been aware of gravity, even if that conception was as simple as "what goes up, must come down". Before the advent of the scientific revolution, the study of science was merely qualitative: it was a matter of speculation and philosophical debate rather than evidence and testing hypotheses. Aristotle for example, believed that all things moved downwards because it was their natural place.

Although ideas of gravity were pretty well developed outside of Europe (although we always pay our attentions in the history of science to European scientists, we must not forget that scientists in the Middle East, India and China were often much more advanced than Europe at various times, especially during the Dark Ages), it was in Europe that major theoretical advances were made.

In the early 16th century, a Catholic cleric named Nicolaus Copernicus, who was also a highly skilled astronomer wrote a book named De revolutionibus orbium coelestium. Legend has it that on the day Copernicus died, the book was delivered to his hands, and died peacefully after he had seen it. This book was the first of its kind offering an alternative to the geocentric theories (the idea that the Sun revolved around the Earth). Copernicus, being a Catholic cleric was wary enough to state very clearly that his work was merely a fantasy, and not something that he believed was true, because to believe in heliocentricity (the Earth revolving around the Sun) was considered contrary to the Bible.

In his book, he proposed that the planets, including the Earth, revolved around the Sun in perfect circles, and in so doing was able to explain some phenomena that were never very well explained by the geocentric theory, such as the fact that Mars does not move in a continuous motion throughout the sky at times, sometimes going forwards, coming to a halt, and then moving backwards (known as Retrograde motion)

However his theory wasn't able to match up fully with celestial observations at that time. It would take subsequent modification by Kepler (who did away with the perfectly circular motion and replaced it with simply elliptical motion) to become a coherent set of rules that could easily predict the motion of the planets.

Kepler developed his own three laws of planetary motion to explain how the planets revolved around the sun (click here to find out more).



For example, one of Kepler's laws state that if a planet, at two different segments, sweeps out an area (as shown in blue) with equal area, then they must have travelled that segment in the same amount of time.

Notice that his laws are useful in the prediction of the motion of planets, but yet do not tell us fundamentally the reasons for their motion: This is why his laws are considered laws of kinematics: we can describe the motion, but we don't really know why, much like the laws of kinematics that you have studied.

Notice also that his laws do not involve gravity, whereas today we know the reason for their motion is because the Sun's gravity acts on them. It may seem obvious to us today, but before Isaac Newton was knocked on the head by an apple, it was difficult to realise that the same gravitational force that brings apples to the ground also kept the planets in motion!

Our first truly useful theory of gravity was provided by who else but Isaac Newton. He hypothesised that gravitational force could be computed as follows:



The force of gravity between two objects is given by the mass of one object multiplied by the mass of the other, divided by the distance separating them squared, times the universal gravitational constant G.

What this equation says is profound: firstly, it states that any, and truly any two masses exert a gravitational force on one another. Right now, whether you know it or not, even though I am halfway across the world, I am exerting a gravitational pull on you now, although of course it is so small as to not affect you at all. (There is something profound in this as well. Clearly it is very absurd that my movement right now can somehow affect you halfway across the world: how is the force transmitted?)

Also, notice that the denominator of the equation is squared: what this means that for an increase in distance between two objects, the force drops off significantly, which suggests that the force of gravity is very weak.

And finally, one of the most excellent strokes of brilliance by Newton, his universal gravitational constant was a constant that he believed applied everywhere in the universe: an extremely bold conclusion! But yet, a few hundred years later, he was proven right: the value of G was found to be 6.67 x 10-11, as first determined by the Cavendish Experiment.

This equation was put to great effect by Newton in explaining the motion of the celestial bodies, successfully incorporating all three of Kepler's Laws under this simple equation. Today, this equation is no longer regarded as the best way to describe gravity: it has been supplanted by General Relativity. But still, it is extremely useful in the prediction of celestial objects in the Solar System, since the difference between Newton's law of gravitation is not significantly different from General Relativity in our region. When I start my lessons in relativity I may come back here and talk more!