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Slide 21

In symbols, Newton’s Law of Universal Gravitation is:

Fgrav = G

Where G is a constant of proportionality.

G = 6.67 x 10-11 N m2/kg2

Mm

r 2

Slide 22

Newton’s Law of Universal Gravitation is often called an inverse square law, since the force is inversely proportional to the square of the distance.

Slide 23

An Inverse-Square Force

Slide 24

Experimental Evidence

The Law of Universal Gravitation allowed extremely accurate predictions of planetary orbits.

Cavendish measured gravitational forces between human-scale objects before 1800. His experiments were later simplified and improved by von Jolly.

Slide 25

In Newton’s time, there was much discussion about HOW gravity worked - how does the Sun, for instance, reach across empty space, with no actual contact at all, to exert a force on the Earth?

This spooky notion was called “action at a distance.”

Slide 26

During the 19th century, the notion of the “field” entered physics (via Michael Faraday).

Objects with mass create an invisible disturbance in the space around them that is felt by other massive objects - this is a gravitational field.

Slide 27

The Gravitational Field

So, since the Sun is very massive, it creates an intense gravitational field around it, and the Earth responds to the field. No more “action at a distance.”

Slide 28

To measure the strength of the gravitational field at any point, measure the gravitational force, F, exerted on any “test mass”, m.

Gravitational Field Strength, g = F/m

Slide 29

Gravitational Field Strength

Near the surface of the Earth, g = F/m = 9.8 N/kg = 9.8 m/s2.

In general, g = GM/r2, where M is the mass of the object creating the field, r is the distance from the object’s center, and G = 6.67 x10-11 Nm2/kg2.

Slide 30

If g is the strength of the gravitational field at some point, then the gravitational force on an object of mass m at that point is Fgrav = mg.

- Early Astronomy
- The Earth-Centered Universe
- Ptolemy’s Solar System
- Copernicus’ Solar System
- Objections to Copernicus
- Galileo & Copernicus
- Tycho and Kepler
- Tycho and Kepler
- Kepler’s Laws
- Kepler’s Second Law
- The Apple & the Moon
- Universal Gravitation
- At the Earth’s Surface
- Weight of the Moon
- Weight of the Moon
- Weight of the Moon
- Universal Gravitation
- Law of Universal Gravitation
- Inverse Square Law
- Action at a Distance
- The Gravitational Field
- Gravitational Field Strength
- Gravitational Force
- Gravitational Field Inside a Planet
- Black Holes
- Earth’s Tides

- Friction
- Understanding Heat Transfer, Conduction, Convection and Radiation
- History of Modern Astronomy
- Newton’s Law of Gravity
- Radiation Safety and Operations
- Practical Applications of Solar Energy
- Direct heat utilization of geothermal energy

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