Early Astronomy

• As far as we know, humans have always been interested in the motions of objects in the sky.
• Not only did early humans navigate by means of the sky, but the motions of objects in the sky predicted the changing of the seasons, etc.
• There were many early attempts both to describe and explain the motions of stars and planets in the sky.

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The Earth-Centered Universe

• A geocentric (Earth-centered) solar system is often credited to Ptolemy, an Alexandrian Greek, although the idea is very old.

Image from: http://abyss.uoregon.edu/~js/ast123/lectures/lec02.html

Kepler’s Laws

• Kepler determined that the orbits of the planets were not perfect circles, but ellipses, with the Sun at one focus.

Kepler’s Second Law

• Kepler determined that a planet moves faster when near the Sun, and slower when far from the Sun.

Faster

Slower

Why?

• Kepler’s Laws provided a complete kinematical description of planetary motion (including the motion of planetary satellites, like the Moon) - but why did the planets move like that?

The Apple & the Moon

• Isaac Newton realized that the motion of a falling apple and the motion of the Moon were both actually the same motion, caused by the same force - the gravitational force.

Universal Gravitation

• Newton’s idea was that gravity was a universal force acting between any two objects.

At the Earth’s Surface

• Newton knew that the gravitational force on the apple equals the apple’s weight, mg, where g = 9.8 m/s².

W = mg

Weight of the Moon

• Newton reasoned that the centripetal force on the moon was also supplied by the Earth’s gravitational force.

F_c = mg

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Weight of the Moon

• Newton’s calculations showed that the centripetal force needed for the Moon’s motion was about 1/3600^th of Mg, however, where M is the mass of the Moon.

Weight of the Moon

• Newton knew, though, that the Moon was about 60 times farther from the center of the Earth than the apple.
• And 60² = 3600

Universal Gravitation

• From this, Newton reasoned that the strength of the gravitational force is not constant, in fact, the magnitude of the force is inversely proportional to the square of the distance between the objects.

Universal Gravitation

• Newton concluded that the gravitational force is:
• Directly proportional to the masses of both objects.
• Inversely proportional to the distance between the objects.

Law of Universal Gravitation

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

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• F_grav = G

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• Where G is a constant of proportionality.
• G = 6.67 x 10^-11 N m²/kg²

Mm

r ²

Inverse Square Law

• 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.

An Inverse-Square Force

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.

Action at a Distance

• 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.”

Gravitational Force

• 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 F_grav = mg.
• If g is the gravitational field strength at some point (in N/kg), then the free fall acceleration at that point is also g (in m/s²).

Earth’s Tides

• There are 2 high tides and 2 low tides per day.
• The tides follow the Moon.

Why Two Tides?

• Tides are caused by the stretching of a planet.
• Stretching is caused by a difference in forces on the two sides of an object.
• Since gravitational force depends on distance, there is more gravitational force on the side of Earth closest to the Moon and less gravitational force on the side of Earth farther from the Moon.

Why Two Tides?

• Remember that

Why the Moon?

• The Sun’s gravitational pull on Earth is much larger than the Moon’s gravitational pull on Earth. So why do the tides follow the Moon and not the Sun?

Why the Moon?

• Since the Sun is much farther from Earth than the Moon, the difference in distance across Earth is much less significant for the Sun than the Moon, therefore the difference in gravitational force on the two sides of Earth is less for the Sun than for the Moon
• The Sun does have a small effect on Earth’s tides, but the major effect is due to the Moon.

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THANK YOU…….