motions of the planets...geocentric cosmology - earth is at center, stationary - sun, moon, 5 known...

Motions of the Planets (“Wanderers”)

Planets move on celestial sphere - change RA, Dec each night - five are visible to naked eye

Mercury, Venus, Mars, Jupiter, Saturn

www.universetoday.com

Days of the week:

- named after 7 “Power” (moving) objects in the sky (Sun, Moon, 5 planets)

English Spanish French Roman/Latin Origin

Germanic/ Norse Origin

Sunday

Domingo Dimanche Sun Sun

Monday

Lunes Lundi Luna (Moon) Moon

Tuesday

Martes Mardi Mars Tyr

Wednesday

Miercoles Mercredi Mercury Wodan

Thursday Jueves Jeudi Jupiter (Jove) Thor

Friday

Viernes Vendredi Venus Frigg

Saturday

Sabado Samedi Saturn Saturn

Motion of the planets: - move near ecliptic (through zodiac)

- most of the time, move eastward

“Prograde Motion”

- occasionally: change direction and move westward

“Retrograde Motion”

http://alpha.lasalle.edu/~smithsc/Astronomy/retrograd.html

Models of the Universe: Aristotle: philosophy of “Idealism”

( 2000 years ago)

- circles and spheres are ideal shapes

structure of universe based on circles and spheres

Geocentric Cosmology

- Earth is at center, stationary

- Sun, Moon, 5 known planets

revolve around Earth on concentric circles

- Earth at center of rotating Celestial Sphere

Claudius Ptolemy (137 A.D.)

- most accurate model of planetary motion at the time

based on Geocentric Cosmology

Ptolemaic Model

- “orbit” of planet around Earth - Deferent

- planets are fixed to smaller circles - Epicycles

Planets revolve on epicycles while epicycles revolve on deferent

Link:

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

http://www.polaris.iastate.edu/EveningStar/Unit2/unit2_sub1.htm

Ptolemaic System

- used for over 1300 years - over time, needed adjustments

Eventually, model had 234 epicycles to describe the motion of 5 planets!! Orbit of Mercury

Nicholas Copernicus (1473 - 1543)

- developed an accurate Sun centered (“Heliocentric”) model

Heliocentric Cosmology - Earth is a planet, orbiting around the sun - other planets on larger or smaller orbits

explains retrograde motion in simple way: - Earth passes by outer planets - gives appearance that other planets

change direction

http://mars.jpl.nasa.gov/allaboutmars/nightsky/nightsky04/ http://astro.unl.edu/naap/ssm/animations/configurationsSimulator.html

Copernicus

- used simple geometry to find distances to planets

- close to modern values!

- but, still used circular orbits - not entirely accurate

Tycho Brahe (1546 - 1601) “Greatest Observational Genius of the Age”

- very accurate & precise observations before telescope

- accuracy of 0.1o (or 6')

- near limit of human eye

- measured positions of planets

Johannes Kepler (1571 - 1630) “Greatest Theoretician of the Age”

- assistant to Tycho Brahe

- used data to describe planetary orbits (after Tycho’s death)

- tried to find correct geometrical shape: - found that orbits are Ellipses!!

Kepler’s First Law:

Orbits of planets: - are ellipses - with the sun at one focus

Properties of an Ellipse:

b

a

focus focus

a - semimajor axis b - semiminor axis

Eccentricity: - measure of how round/flat the ellipse is - ranges from 0 (circle) to 1.0 (flat line)

Kepler’s Second Law:

Kepler studied motion of a planet: the speed of the planet changes

- planets move faster when closer to sun (closest point: Perihelion)

- planets move slower when farther from sun (furthest point: Aphelion)

A line joining a planet and the sun: - sweeps out equal areas in equal times

Kepler’s Third Law:

When Kepler studied other planets, found: - a planet with a larger orbit

- takes longer to orbit the sun and moves slower!

The squares of the periods are proportional to the cubes of the semimajor axes

Definition: For Earth’s orbit Semimajor axis = 1 Astronomical Unit

For any planet, P2 = a3

Mercury: P = 0.241 yrs a = 0.387 A.U. P2 = 0.058 yrs2 a3 = 0.058 A.U.3

Jupiter: P = 11.86 yrs a = 5.20 A.U. P2 = 140.6 yrs2 a3 = 140.6 A.U.3

Example: An object that orbits 4 A.U. from Sun

a = 4 AU: a3 = 43 = 64

P = √a3 = √64 = 8 yrs Object will take 8 years to orbit Sun

Galileo Galilei (1564 - 1642) - first person to use telescope to study sky

Astronomical Observations: Surface of the Moon - normal geological features like mountains, craters, valleys

similar to Earth

Surface of the Sun - saw spots on surface (“blemishes!”)

could measure rotation

Moons of Jupiter - four moons in orbit around Jupiter - obeyed Kepler’s Laws - Earth not only “center of revolution”

Venus - goes through same phases as Moon - becomes larger when dimmer,

smaller when brighter

Previous Observations -Mercury, Venus always close to sun

Geocentric (Earth-centered) Model:

- their orbits around the Earth must be linked to sun

Heliocentric Model: - their orbits are smaller than Earth,

cannot move far away from sun

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

If Venus has all the phases of Moon:

Venus must orbit sun!

Observations cannot be explained by Geocentric Cosmology!

Isaac Newton (1642 - 1727) - described what causes motion

FORCE - a “force” is a push or a pull

Newton’s Three Laws of Motion:

First Law (Law of Inertia)

if no net force, an object: - will be at rest - or moves at a constant speed, in straight line, forever Second Law (F = ma)

If a net force acts on an object: - it changes its motion (accelerates)

- speeds up, slows down, or turns - depends on mass of object - more mass, harder to accelerate

Third Law (“action-reaction”) If two objects apply forces on each other:

- the forces are exactly the same strength, but opposite in direction

Planets move on elliptical orbits - change direction, speed due to force on planets!

Newton: Universal Law of Gravity

FG = G m1 m2

r2

G - gravitational constant = 6.67 x 10-11 m3/kg s2

- proportional to masses (m1, m2) - inversely proportional to square of distance (r)

Mass versus Weight Mass - amount of matter Weight - force of gravity on matter If you weighed 150 lbs on Earth: Mass Weight Sun 68 kg 4000 lbs Jupiter 68 kg 400 lbs Mars 68 kg 60 lbs Moon 68 kg 25 lbs Asteroid 68 kg 1/2 oz.