Kepler’s lawsKepler’s laws
Ancient Astronomy
• Ancient civilizations observed the skies
• Many built structures to mark astronomical events for religious and practical reasons: Seasons, day light gain and loss etc
Summer solstice sunrise at Stonehenge
(2800B.C. till 1100B.C)
Big Horn Medicine in Wyoming
Spokes of the Big Horn Medicine Wheel are aligned with rising and setting of Sun and other stars
Features that align with rising and setting of the sun and other stars.
Caracol temple in Mexico
This temple at Caracol, in Mexico, has many windows that are aligned with astronomical events:
Keeping track of the seasons
The Geocentric Universe
Aristotle (384-322 B.C.)Ancient astronomers observed:
Sun
Moon
Stars
Five planets: Mercury, Venus, Mars, Jupiter, Saturn
Sun, Moon, and stars all have simple movements in the sky
Planets motion are more complicated:
• Move with respect to fixed stars
• Change in brightness
• Change speed
• Undergo retrograde motion
• Inferior planets: Mercury, Venus
• Superior planets: Mars, Jupiter, Saturn
Now know:
Inferior planets have orbits closer to Sun than Earth’s
Superior planets’ orbits are farther away
The Geocentric Universe
Earliest models had Earth at center of solar system
Needed lots of complications to accurately track planetary motions
Cosmic lecture launcher:3.15 Ptolemy’s model
The scientific methodThe scientific method
• New observations (retrograde New observations (retrograde motion, phases of Venus) lead to new motion, phases of Venus) lead to new model:model:
Heliocentric universeHeliocentric universe
• Heliocentric universe allows for new Heliocentric universe allows for new predictions: Phases and retrograde predictions: Phases and retrograde motion of other planets motion of other planets
The Foundations of the Copernican Revolution (1473-1543)
1. Earth is not at the center of everything.
2. Center of earth is the center of moon’s orbit.
3. All planets revolve around the Sun.
4. The stars are very much farther away than the Sun.
5. The apparent movement of the stars around the Earth is due to the Earth’s rotation.
6. The apparent movement of the Sun around the Earth is due to the Earth’s rotation.
7. Retrograde motion of planets is due to Earth’s motion around the Sun.
Kepler’s Laws of Planetary Motion
Kepler’s laws were derived using observations made by Tycho Brahe(1546-1601)
Kepler: 1571-1630 AC
Kepler’s 1’st law
First Law: Planetary orbits are ellipses (not circular), Sun at one focus
Cosmic lecture launcher:
Drawing an ellipse.
Some Properties of Planetary Orbits
Semimajor axis and eccentricity of orbit completely describe it
Perihelion: closest approach to Sun
Aphelion: farthest distance from Sun
x
a
c
e=c/aCircle: c=0, e=0
1) planets orbit the Sun.
2) orbits are noncircular.
3) orbits are elliptical in shape.
4) all of the above
Question
Kepler’s 1st law of planetary orbits states that
1) planets orbit the Sun.
2) orbits are noncircular.
3) orbits are elliptical in shape.
4) all of the above
Question
Kepler’s 1st law of planetary orbits states that
Kepler’s Laws apply to all orbiting objects. The Moon orbits Earth in an ellipse, and the Space Shuttle orbits Earth in an ellipse, too.
Kepler’s 2’nd law
Second Law: Imaginary line connecting Sun and planet sweeps out equal areas in equal times
1
234
5
6
Areas:
Area A= Area B
= Area C
Times:
t2-t1=t4-t3=t6-t1
Distance traveled:
d12 > d34>d56
Question
Earth is closer to the Sun in January. From this fact, Kepler’s 2nd law tells us
1) Earth orbits slower in January.
2) Earth orbits faster in January.
3) Earth’s orbital speed doesn’t change.
Earth is closer to the Sun in January. From this fact, Kepler’s 2nd law tells us
1) Earth orbits slower in January.
2) Earth orbits faster in January.
3) Earth’s orbital speed doesn’t change.
Kepler’s 2nd law means that a planet moves faster when closer to the star.
Faster
Slower
Question
Kepler’s 3’rd law
Third Law: Square of period of planet’s orbital motion is proportional to cube of semimajor axis:
Orbits must be given in AU
and periods in
Earth years!
13
232
a
PaP
Question
Kepler’s 3rd law relates a planet’s distance from the Sun and its orbital
1) speed.
2) period.
3) shape.
4) velocity.
Kepler’s 3rd law relates a planet’s distance from the Sun and its orbital
1) speed.
2) period.
3) shape.
4) velocity.
Kepler’s 3rd law P2 = a3
means more distant planets orbit more slowly.
Question 13
Venus’ Period = 225 days
Venus’ axis = 0.7 AU
Earth’s Period = 365 days
Earth’s axis = 1.0 AU
The Dimensions of the Solar System
Now measured using radar:
Ratio of mean radius of Venus’s orbit to that of Earth very well known