kepler’s laws of planetary motion. debate on planet motions geocentric or heliocentric universe
TRANSCRIPT
Claudius Ptolemy
• Ptolemy developed a geocentric model of the solar system that was so successful in predicting the positions of the planets that it endured for more than 1300 years.
Retrograde Motion
• If you watch the planets carefully, you will see that they move through the sky from night to night.
• However, a given planet will appear to stop, move backward for a while, stop again, and then continue its forward motion.
Heliocentric Theory
• Nicolaus Copernicus (1473-1543) argued that the motion of the Sun and planets could be equally described by a Sun centered (heliocentric) system.
• Galileo (1564-1642) was the first scientitst to use a telescope to observe the sky. He observed the phases of Venus and the moons of Jupiter. Both observations supported the heliocentric model.
Kepler’s Laws of Planetary MotionKepler’s Laws of Planetary Motion
–Law 1 - Law of Ellipses–Law 2 - Law of Equal Areas–Law 3 - Harmonic Law (P2=ka3)
•Kepler’s laws provide a concise and simple description of the motions of the planets. Discovered in 1609.
Kepler’s First Law: Each planet moves about the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse.
Kepler’s First Law
• The major axis is the widest diameter of the ellipse.
• The semimajor axis is ½ this distance.– This is the average distance of the planet from
the Sun.
• The eccentricity is a measure of the roundness of the ellipse:– An eccentricity of 0 is a perfect circle.– An eccentricity near 1 is a very elongated
ellipse.
Major
Axis
Minor
Axis
Focus PointsCente
r
90°
Semi-major Axis = ½ Major Axis
axismajor oflength
points focusbetween distance
tyeccentrici
e=0 perfect circle
e=1 flat line
The Ellipse
Kepler’s Second Law: The straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time.
Kepler’s Third Law: The sqaures of the planets’ periods of revolution are in direct proportion to the cubes of the semimajor axes of their orbits.
Kepler’s Third Law
• Kepler’s Third Law can be expressed as: (distance)3=(period)2
D3 = P2
if distance is measured in AU and the period in years.– Examples:
• The semimajor axis of the Earth’s orbit is 1 AU and its period is 1 year. Therefore, we can easily see that: 13=12.
Kepler’s Third Law
• Halley’s Comet takes 76 years to orbit the Sun. What is its average distance from the Sun?
AU 17.9D
5776D
5776D
)76(D
PD
3
3
23
23