1. Solar System, Kepler and Universal Gravitation
Physics 12

2. 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

3. 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

4. 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

5. 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

6. 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

7. 1st Law – Planets move in elliptical orbits with the Sun at one Focus

8. 2nd Law – A Planet will sweep out an equal area in equal time intervals

9. 3rd Law – The ratio of the radius cubed to the period squared will be the same for any two objects orbiting the same object

10. 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

11. 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)

12. 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

13. Practice Problems
Page 580
Questions 1-8