Solar System, Kepler and Universal Gravitation Physics 12

Ptolemaic System Geocentric Very complicated as sun and moon orbited Earth but other planets both orbited the Earth and completed a Epicycle in their orbital path

Copernican System This system, proposed by Nicholas Copernicus in 1543, simplified the mathematics as the Sun became the centre of the Solar System This was rejected by the clergy and is most famous as a result of the persecution of Galileo Galilei for supporting this system

Tychonic System An intermediate system where the moon and Sun orbit the Earth but other planets orbit the Sun This system never gained widespread acceptance but Tycho Brahe was responsible for contributing a significant amount of detailed information regarding the Solar System

Astronomy as Science Before the advent of modern telescopes, Tycho Brahe was able to develop instruments that were precise to 1/30 of a degree without magnification As a result, he was able to accurately catalogue over 700 stars was well as detailed information about our Solar System Astronomy continued to evolve as a science as the ability to machine high quality lenses was refined

Kepler’s Laws Brahe invited Kepler to be one of his assistants in 1600 which gave Kepler access to Brahe’s detailed records Kepler was able to develop three empirical relationships to describe heavenly bodies Today, these relationships are known as Kepler’s Laws

1st Law – Planets move in elliptical orbits with the Sun at one Focus

2nd Law – A Planet will sweep out an equal area in equal time intervals

3rd Law – The ratio of the radius cubed to the period squared will be the same for any two objects orbiting the same object

Kepler, Halley and Newton When Kepler published his equations, they were not based on an understanding of why the universe behaved in this manner, rather it simply described how it behaved Sir Edmond Halley had described a relationship between gravity and the square of the distance between objects but couldn’t make it predict orbits He approached Newton about how to apply this concept

Newton’s Law of Universal Gravitation Newton immediately answered Halley with the fact that orbits must be elliptical; despite the fact that this answer was purely intuitive, it led to an article called De Motu (on motion) Newton later expanded this into one of the most famous works in scientific literature, Philosophiae Naturalis Principia Mathematica (often just called Principia)

Newton’s Law of Universal Gravitation Fg is the gravitational force G is the Universal Gravitational Constant m1 and m2 are the masses of the objects r is the distance between the objects Note, Newton did not measure G but it is now known to be 6.67x10-11Nm2/kg2

Practice Problems Page 580 Questions 1-8