Download Lec – History4

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
Days of the week:
- named after 7 “Power” (moving) objects
in the sky (Sun, Moon, 5 planets)
English
Spanish
French
Monday
Lunes
Lundi
Luna (Moon)
Moon
Tuesday
Martes
Mardi
Mars
Tyr
Mercury
Wodan
Sunday
Roman/Latin
Origin
Domingo Dimanche
Sun
Wednesday Miercoles Mercredi
Germanic/
Norse Origin
Sun
Thursday
Jueves
Jeudi
Jupiter (Jove)
Thor
Friday
Viernes
Vendredi
Venus
Frigg
Saturday
Sabado
Samedi
Saturn
Saturn
www.universetoday.com
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”
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
http://alpha.lasalle.edu/~smithsc/Astronomy/retrograd.html
Ptolemaic Model
- “orbit” of planet around Earth
- Deferent
- planets are fixed to smaller circles
- Epicycles
Planets revolve on epicycles while
epicycles revolve on deferent
Claudius Ptolemy (137 A.D.)
- most accurate model of planetary
motion at the time
→ based on Geocentric Cosmology
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
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
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
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)
Copernicus
- used simple geometry to find distances
to planets
- close to modern values!
- but, still used circular orbits
- not entirely accurate
- tried to find correct geometrical shape:
- found that orbits are Ellipses!!
Kepler’s First Law:
Eccentricity:
- measure of how round/flat the ellipse is
- ranges from 0 (circle) to 1.0 (flat line)
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
Kepler’s Second Law:
Kepler’s Third Law:
Kepler studied motion of a planet:
the speed of the planet changes
When Kepler studied other planets, found:
- a planet with a larger orbit
- takes longer to orbit the sun and
moves slower!
- 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
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
P2 = 0.058 yrs2
a = 0.387 A.U.
a3 = 0.058 A.U.3
Jupiter:
P = 11.86 yrs
P2 = 140.6 yrs2
a = 5.20 A.U.
a3 = 140.6 A.U.3
Example: An object that orbits 4 A.U. from Sun
a3 = 43 = 64
P = √a3 = √64 = 8 yrs
Object will take 8 years to orbit Sun
a = 4 AU:
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 (FF = 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
(“actionaction-reaction”)
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:
Sun
Jupiter
Mass
Weight
68 kg
4000 lbs
68 kg
400 lbs
Mars
68 kg
60 lbs
Moon
68 kg
25 lbs
Asteroid
68 kg
1/2 oz.