The Birth of Physics
The following notes are excerpted from Journey to the Cosmic Frontier by John D. Fix, Archives of the Universe by Marcia Bartusiak, and Coming of Age in the Milky Way by Timothy Ferris.
In the geocentric cosmology of Aristotle and Ptolemy, the planets, Sun,
Moon, and stars were located on crystalline spheres and the rotation of
the one shell drove the rotation of the next innermost shell. Copernicus's
heliocentric model did away with this quaint explanation of celestial motion
but offered no theory to replace it. Perpetual circular motion was natural
although
Descartes theorized that circular motion could only result from the presence
of unbalanced forces. Kepler's empirical discovery that planets vary their
orbital speeds while traveling along ellipses implied that forces are continually
acting to modify the direction and speed of planets. As stated in the supplemental
notes on Renaissance astronomy, Kepler believed two forces were responsible
for planetary motion: one (the anima motrix) that emanated from
the Sun and rotated with it and a second magnetic force of attraction. These
two forces were believed to change the direction and speed of a planet's
motion.
The next crucial step in the understanding of planetary motion came from Robert Hooke—a brilliant English scientist who had the misfortune of being a contemporary of an even greater natural philosopher: Isaac Newton. Hooke also believed, as did Descartes, that objects would move in a straight line unless acted upon by forces. That planets move did not require explanation; what caused them to continually change direction required a solution. In a demonstration before the Royal Society in 1666, Hooke used a weight suspended from a string to demonstrate that motion along a path (or orbit) required the presence of a centripetal, or center-seeking, force. This centripetal force was theorized to emanate from the Sun and be the same the force that caused objects to fall to the ground: gravity. Hooke tried to measure the variation of gravity over distance but was never able to determine its nature.
Isaac Newton was born prematurely on Christmas Day in 1642, the year of Galileo's death. As a child young Isaac was moody, quick to anger, and brilliant. He made sundials and learned to tell time by the Sun, but often forgot to come home for meals. His absentmindedness made him little help around the farm; once asked to go round up the cattle, he was found much later staring at the swirling water in a nearby stream.
He came into his own while a student at Trinity College, Cambridge, where he studied the works of Copernicus, Kepler, Galileo, and Descartes as well as many other prominent mathematicians and natural philosophers. After earning his bachelor of arts degree in 1665 at the age of 22, an outbreak of the plague forced Cambridge to close and Newton returned home to his family farm Woolsthorpe Manor. Over the next two years, he made fundamental discoveries about the nature of light, formulated the law of universal gravitation, and invented both differential and integral calculus. Usually reluctant to draw attention to himself, Newton was content to investigate the natural world and solve its riddles, but rarely bothered to share discoveries with others. Only when prodded would he reveal the fruits of his labors.
Hooke and Edmund Halley believed the force of gravitation could be explained by an inverse square law but could not prove it. When asked by Halley about the shape of a planet's orbit when a centripetal force such as gravity decreases with the square of the distance, Newton casually said the orbit would be an ellipse. Astounded that Newton was so certain of a result that combined Kepler's laws of planetary motion and Hooke's description of gravity, Halley asked how he knew this. Newton said he had solved the problem years before! He was unable to locate his calculations, however, and had to spend several months recreating them so Halley could see the proof. It's thought that a small error existed in Newton's derivation of universal gravitation that was the cause of his reluctance to immediately share his proof. Only after being put on the spot by Halley did he return to the problem and finally use his corrected theory to derive all three of Kepler's laws.
With a great deal of urging, Newton set out writing a book detailing his discoveries about motion, gravitation, and the orbits of planet. The Mathematical Principles of Natural Philosophy was entirely funded by Halley. The fundamental description of terrestrial and celestial motion is contained in three laws:
- Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
- The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
- To every action there is always opposed and equal reaction: or the mutual
actions of two bodies upon each other are always equal, and directed to
contrary parts.
The mathematical statement of the second law F = ma came later.