Solar System, Kepler & Universal Gravitation

Physics 12

Clip of the day:

•Minutephysics•http://

www.youtube.com/watch?v=uhS8K4gFu4s

A bit of history about the solar system and orbits……

Ptolemaic System:• \tä-lə-ˈmā-ik\• 2nd century AD• Earth is at the orbital

center of all celestial bodies (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:

• koh-pur-ni-kuhn• 1543• Nicholas Copernicus • 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:• tahy-kon-ik• Late 16th century • Combined what he saw as

the mathematical benefits of the Copernican system with the philosophical and "physical" benefits of the Ptolemaic system.

• 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:

•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, know today as Kelper’s Laws!

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

Vocab Alert:•Aphelion: the point in the orbit of a planet,

asteroid, or comet at which it is furthest from the sun

•Perihelion: the point in the orbit of a planet, asteroid, or comet at which it is closest to the sun

•Apogee: the point in the orbit of the moon or a satellite at which it is furthest from the earth

•Perigee: the point in the orbit of the moon or a satellite at which it is nearest to the earth.

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

2

3

2

3

2

3

B

B

A

A

T

r

T

r

T

rk

Period = time to complete one orbit

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

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

221

r

mGmFg

Try it:•Page 580

▫Question 1-7•Kelper’s Law Graphing Assignment