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Gravitation and the Waltz of the Planets Chapter 4.

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Presentation on theme: "Gravitation and the Waltz of the Planets Chapter 4."— Presentation transcript:

1 Gravitation and the Waltz of the Planets Chapter 4

2 Kepler’s Laws First Law: Planets orbit in ellipses with the Sun at one focus First Law: Planets orbit in ellipses with the Sun at one focus Second Law: Planet – Sun line sweeps out equal areas in equal time Second Law: Planet – Sun line sweeps out equal areas in equal time Third Law: There is a relationship between a planets orbital period (P) and its average distance from the Sun (a), P 2 = a 3 Third Law: There is a relationship between a planets orbital period (P) and its average distance from the Sun (a), P 2 = a 3

3 First Law Meaning An ellipse is like an elongated circle. Instead of one point in the center, an ellipse has two points called foci. An ellipse is like an elongated circle. Instead of one point in the center, an ellipse has two points called foci. For planetary motion then, each planet does not orbit the Sun in a circle and thus the distance from the planet to the Sun varies. For planetary motion then, each planet does not orbit the Sun in a circle and thus the distance from the planet to the Sun varies.

4 Second Law Meaning A planet’s orbital velocity varies. A planet’s orbital velocity varies. The planet orbits the Sun faster at perihelion and slower at aphelion. The planet orbits the Sun faster at perihelion and slower at aphelion.

5 Third Law Meaning ‘P’ is the period of a planets orbit ‘P’ is the period of a planets orbit ‘a’ is the average distance from the Sun, or the semimajor axis ‘a’ is the average distance from the Sun, or the semimajor axis A planet that is farther away from the Sun has a slower orbital velocity and thus it takes longer to go around once. A planet that is farther away from the Sun has a slower orbital velocity and thus it takes longer to go around once.

6 Newton’s Laws First Law: “Inertia” – A body remains at rest, or moves in a straight line at constant speed, unless acted upon by a net external force. First Law: “Inertia” – A body remains at rest, or moves in a straight line at constant speed, unless acted upon by a net external force. Second Law: If there exists a net external force, there is an acceleration produced that is proportional to the force. F = ma Second Law: If there exists a net external force, there is an acceleration produced that is proportional to the force. F = ma Third Law: For every force, there is an equal and oppositely directed reaction force. Third Law: For every force, there is an equal and oppositely directed reaction force.

7 Examples

8 Newton Newton’s Law of Universal Gravitation: Masses attract each other with a force that is directly proportional to their masses and inversely proportional to their separation distance. Newton’s Law of Universal Gravitation: Masses attract each other with a force that is directly proportional to their masses and inversely proportional to their separation distance.

9 Newton and Kepler Newton’s form of Kepler’s Third Law: Is more general than K3, and applies in any situation where two masses orbit each other. Newton’s form of Kepler’s Third Law: Is more general than K3, and applies in any situation where two masses orbit each other. Ex. Two stars, two galaxies, a star and its galactic center, a star and planet, a planet and a moon, etc…. Ex. Two stars, two galaxies, a star and its galactic center, a star and planet, a planet and a moon, etc….


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