Download Ch. 8 Universal Gravitation

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 10-11 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