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EARLY COSMOLOGY TUTORIAL TOPICS Dr. Brian Monson has created this group of pages as a supplement for the unit on early astronomy that is taught in most college astronomy courses and has graciously granted ScienceMaster permission to republish them. It is by no means a complete discussion of this topic. To explore more work by Dr. Monson please visit his Planetary Conjunctions page. |
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Fourth Iteration
Isaac Newton (1643 - 1727)
Kepler's three laws were a significant achievement but there was still work to be done in describing the universe. His laws are the type scientists call "empirical". That is they are discovered through trial and error and demonstrated to be true in all cases, but they are not derived from a more basic principle. Kepler knew that the area swept out by the sun-planet line was constant in equal time intervals but he did not know why.
Sir Isaac Netwon provided these missing basic principles. According to Kepler's 2nd law, planets accelerate and decelerate as they orbit the sun. This means there must be a force acting on the planet. Kepler did not specify what his force was but believed that it might be magnetism. The first clues to the nature of this force came from Robert Hooke. He was studying a device known as the conical pendulum(shown below). To make a conical pendulum, take a weight and suspend it from a string. Then pull the weight away from the vertical and toss it so that it traces out a horizontal circle like the black path in the Figure. The vertical part of the tension in the string exactly balances the weight of the object. The horizontal part of the tension will always point to the center of the circle. This told Hooke that whatever force was causing the planets to orbit, it must always point from the planet directly to the sun. We now call such a force a "central force". He went even further and conjectured that the strength of this force must fall off as the inverse square of the distance in order to reproduce elliptical orbits but he was unable to prove this mathematically. He communicated this conjecture to Newton in 1679.
Newton, however, was able to prove this theory, perhaps because he had just invented calculus and was still the only person who knew how to use it. He was able to show that the only possible form of the force that could create elliptical orbits was an inverse square law of this form:
He also showed that parabolic, hyperbolic, and circular orbits were possible. The deciding factor on orbit shape is the ratio in potential to kinetic energy of the planet. He also proved that Kepler's second law is a natural consequence of this force law. Today we refer to the principle Newton discovered as "the conservation of angular momentum". This is same principle that figure skaters take advantage of to speed up their spin moves by drawing in their arms and legs. And finally, he proved Kepler's third law again by starting with this force law. His version looks like this:
This formula gives the astronomers of today their only tool to measure the masses of celestial objects.
The constant G in these two formulas was not know in Newton's day and was not measured until 1798 when Henry Cavendish suceeded in determining its value.
Newton's physics was extended and improved by many other people. Notable achievements were made by Edmund Halley , Urbain Le Verrier and John Couch Adams. Halley studied the orbit of the comet of 1682 and found it to be elliptical and very similar to comets seen in 1537 and 1607. He deduced that these three comets were really just separate apparitions of the same comet and that it would reappear in 1758. It returned very close to the time predicted by Halley. Adams and Le Verrier independently predicted the coordinates of Neptune in 1846 based on irregularities in the orbit of the newly discovered planet Uranus. Le Verrier convinced a German astronomer named Johann Galle to look at his coordinates and Galle did find Neptune very close to them after a brief search.
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