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Kepler’s laws Kepler’s laws. Ancient Astronomy Ancient civilizations observed the skies Many built structures to mark astronomical events for religious.

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Presentation on theme: "Kepler’s laws Kepler’s laws. Ancient Astronomy Ancient civilizations observed the skies Many built structures to mark astronomical events for religious."— Presentation transcript:

1 Kepler’s laws Kepler’s laws

2 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)

3 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.

4 Caracol temple in Mexico This temple at Caracol, in Mexico, has many windows that are aligned with astronomical events: Keeping track of the seasons

5 The Geocentric Universe Aristotle ( B.C.) Ancient astronomers observed: Sun Moon Stars Five planets: Mercury, Venus, Mars, Jupiter, Saturn

6 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

7 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

8 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 launcher:3.15 Ptolemy’s model

9 The scientific method New observations (retrograde motion, phases of Venus) lead to new model: New observations (retrograde motion, phases of Venus) lead to new model: Heliocentric universe Heliocentric universe Heliocentric universe allows for new predictions: Phases and retrograde motion of other planets Heliocentric universe allows for new predictions: Phases and retrograde motion of other planets

10 The Foundations of the Copernican Revolution ( ) 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.

11 Kepler’s Laws of Planetary Motion Kepler’s laws were derived using observations made by Tycho Brahe( ) Kepler: AC

12 Kepler’s 1’st law First Law: Planetary orbits are ellipses (not circular), Sun at one focus Cosmic lecture launcher: Drawing an ellipse.

13 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/a Circle: c=0, e=0

14 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

15 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.

16 Kepler’s 2’nd law Second Law: Imaginary line connecting Sun and planet sweeps out equal areas in equal times Areas: Area A= Area B = Area C Times: t 2 -t 1 =t 4 -t 3 =t 6 -t 1 Distance traveled: d 12 > d 34 >d 56

17 Question Earth is closer to the Sun in January. From this fact, Kepler’s 2 nd law tells us 1)Earth orbits slower in January. 2)Earth orbits faster in January. 3)Earth’s orbital speed doesn’t change.

18 Earth is closer to the Sun in January. From this fact, Kepler’s 2 nd 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 2 nd law means that a planet moves faster when closer to the star. Faster Slower Question

19 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!

20 Question Kepler’s 3 rd law relates a planet’s distance from the Sun and its orbital 1)speed. 2)period. 3)shape. 4)velocity.

21 Kepler’s 3 rd law relates a planet’s distance from the Sun and its orbital 1)speed. 2)period. 3)shape. 4)velocity. Kepler’s 3 rd law P 2 = a 3 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

22 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


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