Solar System, Kepler and Solar System, Kepler and Universal GravitationUniversal Gravitation

Physics 12Physics 12

Ptolemaic SystemPtolemaic 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 SystemCopernican 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 SystemTychonic 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 ScienceAstronomy 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 LawsKepler’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

11stst Law – Planets move in elliptical Law – Planets move in elliptical orbits with the Sun at one Focusorbits with the Sun at one Focus

22ndnd Law – A Planet will sweep out Law – A Planet will sweep out an equal area in equal time an equal area in equal time

intervalsintervals

33rdrd Law – The ratio of the radius Law – The ratio of the radius cubed to the period squared will be cubed to the period squared will be

the same for any two objects the same for any two objects orbiting the same objectorbiting the same object

2

3

2

3

2

3

B

B

A

A

T

r

T

r

T

rk

Kepler, Halley and NewtonKepler, 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 Newton’s Law of Universal GravitationGravitation

• 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 Newton’s Law of Universal GravitationGravitation

• 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

221

r

mGmFg

Practice ProblemsPractice Problems

• Page 580– Questions 1-8