A History of Gravity

The Copernican Revolution

It is upon their work his ideas he laid,
and while perched upon their shoulders he saw
a grand new vision that for Newton made
universal gravitation a law.
He stood in awe of those whence his ideas came,
Copernicus, Kepler and Galileo.
In ideas exchanged we remain the same.
From centuries past comes a scenario,
from ink in quill to parchment put, to keys
on a board we write, letters to be read
each from another. If only one sees
that wisdom gained is nothing to dread,
but something to embrace, then in time will come
a rebirth and understanding for some.

Eric Francis Diaz

Copyright © 2010 Eric F. Diaz

It was Aristarchus of Samos (310BC -230 BC), who ironically lived after Aristotle (384 BC – 322 BC), who was the first person in recorded history to come up with the idea of a heliocentric system, centuries before the Polish canon, physician and astronomer Nicolaus Copernicus (1473-1543) wrote and posthumously published his seminal treatise, De Revolutionibus Orbium Coelestium (“On the Revolutions of the Heavenly Spheres”). Aristarchus’ idea of a heliocentric model of the cosmos, unfortunately, just didn’t take with the ancient Greeks.

Illustration of the Copernican heliocentric system from De Revolutionibus Orbium Coelestium.

The reason why the Ptolemaic (geocentric) view of the cosmos, with its epicycles, lasted so long is because it did and still does work! It just happens to be wrong. But today, an armillary sphere or an astrolabe (a two-dimensional version of an armillary sphere) both based on the Ptolemaic system, work just as well now as they did then.

Even Stranger Models of the Cosmos

If you think Claudius Ptolemy’s model was strange, then you haven’t seen anything yet. Even though Tycho Brahe’s data made it possible for Kepler to formulate his three laws and thus helped establish the Copernican (heliocentric) model, Tycho, himself, did not believe in the Copernican system. He instead devised his own peculiar, geo-heliocentric system (below), in which the sun orbits the Earth and the stars and other planets orbit the sun.

The Tychonic System

But, on Tycho’s deathbed, he handed over to Kepler the observational data, which he had so long withheld, and instructed him to make good use of it, which as we know, Kepler did. It is reputed that Tycho while he lay there dying said to Kepler: “Let it not seem that I lived in vain”. It was by this union of labors that the two men were able to revolutionize our view of the cosmos.

Johannes Kepler

Johannes Kepler is perhaps best known for his three laws of planetary motion. The first law, known as the Law of Ellipses was directly derived from the data collected from the meticulous observations made by Tyho Brahe of the planet Mars.

  • The Law of Ellipses

    • The shape of the orbit of each planet is an ellipse, with the sun at one of the foci of the ellipse.

Kepler also derived the Law of Equal Areas and the Law of Harmonies.

  • The Law of Equal Areas

    • The Law of Equal Areas simply stated is as follows: Imagine if a line were drawn from the center of the sun to the center of a planet orbiting the sun. If such a line were to exist, it would sweep out equal areas in equal time intervals as the planet traveled around the sun. What this law entails is that the closer a planet in its orbit is to the sun, the faster it will travel, and the farther in its orbit it is from the sun, the slower it will travel.

  • The Harmonic Law

    • The Law of Harmonies or the Harmonic Law is stated as follows: The square of a planet’s orbital period is directly proportional to the cube of its average distance from the sun. What Kepler’s third law entails is that the larger the orbit of a planet, the slower the planet will travel in its orbit, and conversely, the smaller the orbit of a planet, the faster it will travel.

Galileo Galilei (1564-1642)

Although he is often attributed with its invention, Galileo did not invent the telescope–the telescope actually having been invented by Hans Lippershey (b. c.1570-d. c.1619) in 1608. But, even though he didn’t invent it, Galileo made extensive use of the telescope and built a strong body of evidence in support of the Copernican model with his observations. When he observed the moon with his occiale (i.e., telescope) he saw that, contrary to the Aristotelian view that all celestial objects were smooth and perfect, it was covered with craters and mountains. He observed that the sun had spots, and that it, too, was not perfect. But, perhaps, what was the most devastating blow to the Aristotelian/Ptolemaic (geocentric) system was Galileo’s observations of the phases of Venus and the discovery of four of the moons of Jupiter. Galileo published his observations in his book Sidereus Nuncius (“The Starry Messenger”) on March 12, 1610. In 1611, Johannes Kepler, with whom Galileo had been corresponding for some time, gave his support to Galileo’s observations.

The title page from Sidereus Nuncius ("The Starry Messenger"), Venice, 1610

Galileo’s contribution to our knowledge of the universe is not confined to his astronomical observations. His experiments with falling objects increased our understanding of gravity. It was, in fact, Galileo who first realized that it was an external force which caused objects to fall to Earth and that all objects, in free fall, accelerate at the same rate. These ideas were later developed by Sir Isaac Newton in his law of universal gravitation. Galileo was also the first to gain insight into inertia, an insight which later led to Newton formulating his first law of motion.

Sir Isaac Newton (1642-1727)

Godfrey Kneller's 1689 portrait of Sir Isaac Newton

In 1669, at the age of twenty seven, Sir Isaac Newton became Lucasian Professor of Mathematics at the University of Cambridge–a post held by only sixteen other men–one of whom being the British theoretical physicist, Stephen Hawking. In 1672, Newton was elected to the Royal Society and became its president in 1703. Included among Newton’s many achievements are his pioneering work in the field of optics (his book Opticks was published in 1704), the invention of the Newtonian reflecting telescope and the codiscovery of calculus. But, what Newton is, perhaps, most noted for are his three laws of motion and the law of universal gravitation, which are contained in his seminal work Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), which was published in 1687.

Newton’s Three Laws of Motion

First Law: Newton’s first law of motion states that a body at rest will remain at rest, or a body in motion will move in uniform motion, in a straight line, unless acted upon by a force. Newton’s first law is also known as inertia or in other words a body’s resistance to a change of velocity or direction of motion. It was Galileo who first realized that a force was not necessary in order to keep a moving body traveling at a constant velocity, and that a moving body would continue to move in a straight line, at a constant velocity, unless acted upon by a force such as, for example, friction or air resistance.

Second Law: Newton’s second law deals with the acceleration of a body. Newton’s second law can be stated as follows: The rate of change in a body’s linear momentum is proportional to the force applied to the body, and the acceleration will be in the same direction as the applied force, i.e. F = d(mv)/dt = m(dv/dt) = ma.

Third Law: Newton’s third law is commonly stated as follows: For every action there is an equal and opposite reaction. It is the third law that makes it possible for rockets to be launched into space.

It was by applying these three laws of motion to Kepler’s laws of planetary motion that Newton was able to derive his law of universal gravitation.

Newton’s Law of Universal Gravitation

Kepler’s three laws of planetary motion do a fine job of describing the motion of the planets in our solar system, but they do not offer an explanation as to why the planets behave as they do. Newton’s law of universal gravitation, on the other hand, does. By applying his own laws of motion to Kepler’s laws of planetary motion Newton was able to formulate his law of gravitation, which can be stated as follows: The force of attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of their distance apart, or

where G is the gravitational constant (G = 6.670 × 10^-11 newton-M^2 /kg^2). What this all means in plain English is that the strength of the gravitational force between objects depends upon both the mass of the objects and the distance between them. The more massive an object is, the stronger it’s gravitational field will be. And, the closer objects are to each other, the stronger the gravitational pull will be between them. Conversely, the gravitational force between objects will decrease by the square of the increase in the distance between them, e.g. if the distance between two objects doubles then the force of gravity will decrease to 1/4 of its strength; if the distance is tripled then the force of gravity will become 1/9 as strong and so on. Newton’s law of gravitation is, perhaps, one of the most eloquent expressions of the inverse-square law. Newton maintained also that the gravitational force that a body exerted acted as though all the mass of the body were concentrated at the center of the body.

Newton’s law of gravitation was able to explain things that up until then had remained a mystery, such as why things do not fly off an Earth that is rotating. Newton’s law of universal gravitation still holds up well for most circumstances, and it remained unchallenged until Albert Einstein published his general theory of relativity in 1915, in which gravity is defined as the curvature of space-time.

The Problem of Mercury’s Orbit

Neither Kepler’s laws of planetary motion nor Newton’s law of universal gravitation could accurately account for the precession of Mercury’s orbit. According to Newton, because of the gravitational influence of the other planets in our solar system, Mercury’s perihelion–the perihelion being the point in a planet’s orbit at which the planet is closest to the sun–would precess by 531 seconds of arc per century. But, in reality, the precession of Mercury’s perihelion progresses 574 seconds of arc per century, a discrepancy of 43 seconds of arc.

It wasn’t until Einstein’s general theory of relativity that the discrepancy was finally explained. According to Einstein’s theory, a massive object, like the sun, warps the space around it and thus creates a pocket or gravity well in the surrounding space. Because the space is curved around the sun, the distance that the planets have to travel is greater than it would be if the space were flat–as it would be in the Newtonian model, and therefore, it takes the planets slightly more time to travel from one point in their orbits to another. And, since Mercury is so close to the sun, where the curvature of space is so much greater, the difference between Newton’s prediction and the actual precessional rate is quite apparent.

Let me end by saying that even though we may have a better understanding of the workings of gravity than our spear-throwing “Cro-Magnon” ancestors of the workings of gravity, we still do not have a really good grasp of it yet. And the way things are looking, I’m not sure that we ever will.

When Sir Isaac Newton formulated his law of universal gravitation, he did not even attempt to offer an explanation as to what gravity might be, which surprises many physicists today. Newton did not even concern himself with the dynamic stability of our solar system, fully aware of the problems of tidal perturbations inherent in it. He merely attributed the stability of our solar system to the realm of the Divine.

It wasn’t until Pierre-Simon, marquis de Laplace’s five volume treatise of celestial mechanics, Méchanique céleste was published that resolving the problems of tidal perturbations in our solar system was even addressed in a comprehensive fashion

There is a cute little anecdote about a discussion between Napolean Bonaparte and Laplace. According to an account by Rouse Ball, Napolean had heard that there was no mention of God in Laplace’s work. When Napolean remarked to Laplace, “M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its Creator.” To which Laplace replied, “I had no need of that hypothesis.” Napolean was greatly amused by Laplace’s reply.

Copyright © 2010 Eric F. Diaz

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