Universal Gravitation Sir Isaac Newton: The Universal Law of Gravitation

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.

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