Universal Gravitation

Sir Isaac Newton: The Universal Law of Gravitation

The Falling Apple

Newton reasoned the moon is falling for the same reason the apple falls – they are both pulled by the Earth’s gravity.

Newton’s Excellent Idea

Now came Newton's truly brilliant insight: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit around the earth.

Source: http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

The Falling Moon

Newton’s First law:– An object (the moon)

will remain in motion in a straight line unless acted on by an outside unbalanced force (gravitational attraction)

The force that pulls an apple to the ground also keeps the moon in orbit.

The Falling Earth

Newton’s theory of gravitation confirmed the Copernican theory of the solar system.

A planets tangential speed allows the planets to orbit the sun without being pulled into it.

Newton’s law of Universal Gravitation

The Gravitational Constant Henry Cavendish 1798

He used a device with two objects on a rod that was hung on a wire. These masses were attracted to two larger objects, twisting the rod slightly. The measurement of the masses, distance between them and the torque on the wire allowed G to be determined.

The Universal Gravitational Constant – A G-thing

G is a constant of proportionality. The magnitude is the force exerted by two

1-kg masses 1 meter apart. G = 6.67 x 10-11 Nm2/kg2

Weight and Mass

Gravity and Distance: The Inverse Square Law

A quantity varies as the inverse square of its distance from its source

A localized source spreads evenly throughout the surrounding space.

The Weight of an Apple?

Gravity and Orbits

Centripetal acceleration– ac= v2/r

Centripetal Force– Fc= mac

The force in circular motion is directed towards the center - centripetal

Why is the Earth round?

Because of gravitation – earth attracted itself together.

The deviation of a planet from its normal orbit is called a perturbation. It is caused by other planets.

Reviewing

Objects orbiting around the Earth are actually falling toward Earth but have great enough tangential velocity to avoid hitting the earth.

Everything pulls on everything else with a force that depends on the mass of the objects and distances between them.

Gravitation decreases according to the inverse square law.

Geosynchronous Orbits

GPS