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Ch. 8 Universal Gravitation
Milbank High School

Sec. 8.1 Motion in the Heavens and on Earth
Objectives Relate Kepler’s laws of planetary motion to Newton’s law of universal gravitation. Calculate the periods and speeds of orbiting objects. Describe the method Cavendish used to measure G and the results of knowing G.

Kepler Johannes Kepler (1571-1630)
Was convinced that geometry and mathematics could be used to explain the motion of the planets.

Kepler’s laws 1. The orbits of the planets are ellipses, with the sun at one focus. (Law of Ellipses) The closer the planets are to one another, the more circular the orbit.

Kepler’s Laws 2. An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (Law of Equal Areas) Deals with speed… faster when closer to the sun.

Kepler’s Laws 3. The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (Law of Harmonies) (TA/TB)2 = (rA/rB)3

Universal Gravitation
Isaac Newton 24yrs old… Watching an apple fall to the ground made him wonder if gravity extended beyond Earth Came up with universal gravitation Attractive force between two objects The apple was also attracting the Earth Proposed Law of Universal Gravitation

Law of Universal Gravitation
The force of attraction between any two masses is constant throughout the universe F = G(mAmB/d2) G is a universal gravitational constant between two masses 6.67 x N·m2/kg2

Sec. 8.2 Using the Law of Universal Gravitation
Objectives Solve problems involving orbital speed and period Relate weightlessness to objects in free fall Distinguish between inertia mass and gravitational mass Contrast Newton’s and Einstein’s views about gravitation

Satellite Motion If a projectile moves fast enough, it falls at the same rate that the Earth curves

How fast are satellites moving?
F = ma or F = mv2/r (ac = v2/r) F = G(mAmB/d2) Solve for velocity? Set them equal to each other G(mAmB/d2) = mv2/r which gives you….

Period of a Satellite Circling Earth
T = 2π√r3/GmE or if we know the velocity… T = 2πr/v

Weightlessness What is gravity in outer space?
Where space shuttle orbits…g = 8.7m/s2 How come astronauts are “floating” then? g = F/m

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