•Ch. 2: How do the planets move? •Next Chapter 3

•Ch. 2: How do the planets move?

•Next Chapter 3

Today

Get out your calculator!

Two Theories of the Solar System! Ptolemy (1st century AD ) proposed a geocentric theory ! His theory could explain the retrograde motion of planets, and was

not challenged for over 1000 years.

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Geocentric model

Of Ptolemy

! Copernicus (1500s) proposed a heliocentric theory

! Planets orbited the Sun, not the Earth, in circles.

! His theory also explained retrograde motion--in a much simpler way.

! planets appear to go retrograde when Earth “catches up” to them.

! Galileo’s observations disproved the geocentric theory.

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Tycho Brahe

! Tycho Brahe (1546-1601) was a Danish nobleman

! As a child, he had witnessed a Solar Eclipse

! He was so impressed that eclipses could be predicted, that he dedicated his life to astronomy.

! He built his own observatory on an island.

! He observed a nova or “new star”, and found it was outside the solar system.

Tycho Brahe

! Tycho made the most precise observations of the planets to date …without using a telescope.

! During his life, Tycho was reluctant to share his precise data.

! He also had a wild lifestyle, and lost his nose in a duel. ! He attended many royal parties

! Perhaps one too many…. He died after eating and drinking too much at a party…

Johannes Kepler! After Tycho died, his assistant,

Johannes Kepler, took his place.

! Unlike others, Kepler saw planets as physical real objects.

! (He even wrote the first Sci-Fi novel, Somnium, about space travel)

Kepler studied Tycho’s precise observations of the planets

! He saw patterns in their motion never seen before.

Initially, Kepler thought the orbits of the planets had the same proportions as the “5 Perfect Solids” of geometry.

He studied this for years, but could not support it with observations.

Platonic Solids

Kepler! However, Kepler did not give up.

! His next model matched 10 of Tycho’s observations of Mars perfectly.

! ...But it mis-matched 2 observations.... by only 0.1 degree.

! Kepler’s Laws of Planetary Motion

! So, he rejected that idea also. ! Eventually, found that the planets’ motions could be explained if he

gave up the idea of circular orbits.

! In time he discovered that all planets follow the same three rules…..

Ellipse Shapes

Circle

How to draw an Ellipse

https://www.youtube.com/watch?v=7UD8hOs-vaI

https://www.youtube.com/watch?v=Et3OdzEGX_w

Size of an Ellipse ! An ellipse is a “flattened” circle. ! We measure the size of a circle using: Diameter or Radius ! But how would you measure the size of an ellipse? ! It has two “diameters”:

! The major axis of an ellipse is its “long diameter” ! It passes through the two foci.

© Douglas Flynt

(The minor axis is perpendicular to the major axis.)

http://astro.unl.edu/classaction/animations/renaissance/kepler.html

http://astro.unl.edu/classaction/animations/renaissance/kepler.html

Kepler’s Second Law! When a planet is at its greatest distance from the Sun it moves

the slowest ! When a planet is at its smallest distance from the Sun it moves

the fastest.

! The point of closest approach to the Sun is called perihelion ! The point of farthest distance from the Sun is called aphelion

Kepler’s 3rd Law

Orbital Period (P) = time it takes to orbit the Sun once (in years) Semi-major axis (a) = distance from the planet to the Sun (in AU)

... relates a planet’s Orbit Period to its Semimajor axis

a

The Astronomical Unit (AU) is a unit of distance

It is used to measure distances to planets.

1 AU = Earth’s distance from the Sun

= 93,000,000 miles

Planetary Data

Planet a (AU) P (years) a2 P2 a3 P3

Mercury 0.387 0.24

Venus 0.723 0.62

Earth 1 1

Mars 1.523 1.88

Ceres 2.77

Jupiter 5.203 11.86

Saturn 9.537 29.45

Quaoar 288

PART 1Imagine that you are Johannes Kepler. Your boss, Tycho, just died, and left you with precise data on the planets. In the table above, you find the semi-major axis (a) and period (P) for all 5 planets known to Kepler. Your job is to figure out how these are related. Now, team up into a group of 4 people, and fill out the table above, which involves the squares and cubes of a and P. Do you notice any pattern? Write down a relationship between a and P. This relationship is called Keplerʼs Third Law.

________________ = ________________

PART 2Fast forward to 1801: You are G. Piazzi and have just discovered the first asteroid in the solar system, called “Ceres”. Its distance from the Sun, a = 2.77AU. Since it orbits the Sun, it obeys Keplerʼs Third Law. Ceres was actually “lost” for many months after its discovery. Astronomers didnʼt know where it went. Can you predict how long it will be before Ceres comes back to its original location (ie. determine its orbital period, P) ?

PCeres = __________________ years

PART 3 (Optional)

Imagine that you are Mike Brown, the hip young astronomer from CalTech who discovered a new “dwarf planet” in 2002. Youʼve given the planet the name Quaoar (from Tong-va Native American mythology). Its orbital period is a whopping 288 years! Can you determine its average distance from the Sun (a) ?

Name:

by Chris McCarthy

Hin

t: J

ust use 2

decim

al pla

ces!!

Download this table from: http://www.physics.sfsu.edu/~chris/astro115/lectures/

Planetary Data

Planet a (AU) P (years) a2 P2 a3 P3

Mercury 0.387 0.24

Venus 0.723 0.62

Earth 1 1

Mars 1.523 1.88

Ceres 2.77

Jupiter 5.203 11.86

Saturn 9.537 29.45

Quaoar 288

PART 1Imagine that you are Johannes Kepler. Your boss, Tycho, just died, and left you with precise data on the planets. In the table above, you find the semi-major axis (a) and period (P) for all 5 planets known to Kepler. Your job is to figure out how these are related. Now, team up into a group of 4 people, and fill out the table above, which involves the squares and cubes of a and P. Do you notice any pattern? Write down a relationship between a and P. This relationship is called Keplerʼs Third Law.

________________ = ________________

PART 2Fast forward to 1801: You are G. Piazzi and have just discovered the first asteroid in the solar system, called “Ceres”. Its distance from the Sun, a = 2.77AU. Since it orbits the Sun, it obeys Keplerʼs Third Law. Ceres was actually “lost” for many months after its discovery. Astronomers didnʼt know where it went. Can you predict how long it will be before Ceres comes back to its original location (ie. determine its orbital period, P) ?

PCeres = __________________ years

PART 3 (Optional)

Imagine that you are Mike Brown, the hip young astronomer from CalTech who discovered a new “dwarf planet” in 2002. Youʼve given the planet the name Quaoar (from Tong-va Native American mythology). Its orbital period is a whopping 288 years! Can you determine its average distance from the Sun (a) ?

Name:

by Chris McCarthy

Hin

t: J

ust

use

2 d

ecim

al p

lace

s!!

Kepler’s 3rd Law P2 = a3

P P2A A3

P = orbital period in years a = semi-major axis in A.U.

Kepler was the first to realize that P is related to a ...in the same way for every planet.

Start Sec. 3 & do worksheet

Kepler’s Third Law An Example

P2=a3

The Planet Uranus orbits the Sun at a distance of 19 AU.

So its semimajor axis is: a= 19 AU Question: How long does it take Uranus to Orbit the Sun?

a3 = a x a x a = 19 x 19 x 19 = 6859

P2 = a3 = 6859, so P = the square root of 6859 = 83 years

Kepler’s Third Law An Example

P2=a3

The Planet Saturn orbits the Sun in 29 years

Question: How far is Saturn from Sun?

P2 = 29 x 29 = 841. So a3 = 841

What is a? a3= a x a x a

Take a guess: a=10. Then a x a x a = 1000 …too high

Guess: a=9. Then a x a x a = 729 …too lowAnswer: a= 9.5

Summary