1. Unit 3 Lesson 2 Kepler’s Laws of Planetary Motion

2. Geocentric model fails to account for phases of the inner planets

3. Heliocentric model easily accounts for phases of the inner planets

4. Kepler’s Laws What are the shapes and important properties of the planetary orbits? How does the speed of a planet vary as it orbits the sun? How does the period of a planet's orbit depend on its distance from the Sun?

5. Tycho Brahe (1546-1601) Collected vast amounts of astronomical data (positions of different bodies at certain times)‏

6. Johannes Kepler (1571-1630) Used Tycho Brahe's precise data on apparent planet motions and relative distances. Deduced three laws of planetary motion. Took him the last 30 years of his life.

7. Kepler’s First Law The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse. There is one point called aphelion, where the object is farthest from the sun. The other point is called perihelion, where the object is closest to sun

8. Kepler's Second Law A line connecting the Sun and a planet sweeps out equal areas in equal times. Translation: planets move faster when closer to the Sun. slower faster

9. Kepler's Third Law The square of a planet's orbital period is proportional to the cube of the planet’s average distance from the sun. P 2 years is proportional to a 3 AU or P 2 (orbital period in years) = a 3 (average distance from the sun in A.U.)‏ 1 A.U. = 1.5 x 10 8 km Translation: The further the planet is from the sun, the longer the period.

10. Sir Isaac Newton (1642-1727)‏ Newton’s laws are fundamental principles that govern the motions of all astronomical bodies! He was the first scientist to explain Kepler’s laws mathematically how the force of gravity behaved using

11. Newton's First Law of Motion ● Every object continues in a state of rest or a state of uniform motion in a straight line unless acted on by a force. ● Inertia - resistance to change in motion of object - is related to its mass. (Demo- air track)‏

12. Newton's Second Law of Motion When a force, F, acts on an object with a mass, m, it produces an acceleration (a) equal to the force divided by the mass. a = FmFm or F = ma Acceleration is a change in velocity or a change in direction of velocity. Newton’s laws classify objects as accelerating or non- accelerating, not as moving or stationary.

13. Newton's Third Law of Motion To every action there is an equal and opposite reaction. Or, when one object exerts a force on a second object, the second exerts an equal and opposite force on first. (DEMO – Air Track, Jet Cart)‏ What force governs the motions of astronomical objects, and what factors determine how strong the force is?

14. Newton's Law of Universal Gravitation All objects in the universe attract each other through gravitational force. This force depends upon the masses of these objects. Gravity between objects increase as the masses of the objects increase Gravity decreases when distance is increased between two objects Your "weight" is just the gravitational force between the Earth and you. On the moon your “weight” would be about 1/7 what it is on Earth.

15. Gravitational Force The gravitational force is always attractive The strength of the attraction decreases with increasing distance

16. How does gravity affect planetary motion?

17. How does gravity affect planetary motion? ‏ The inward force that causes an object to move in a circular path is called Centripetal force Gravity is what is keeping the planets in orbit around the sun.