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Phys 181-701Phys 181-701

AstronomyAstronomy

Galileo’s Apparatus – Deutches Museum, Munchen, Germany

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“Numero pondere et mensura Deus omnia condidit.” Sir Isaac Newton – Principia Mathematica

“If I have been able to see further, it was only because I stood on the shoulders of giants.” Newton, in a letter to Robert Hooke

“To command the professors of astronomy to confute their own observations is to enjoin an impossibility, for it is to

command them to not see what they do see, and not to understand what they do understand, and to find what they

do not discover.”Galileo Galilei – In Science

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Review

REVIEW:

Kepler Develops Three Laws:

•Law of Ellipses

•Law of Areas

•Harmonic Law

P

ak

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3 constant

We now understand HOW the planets move… but not WHY they move.

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Galileo: The Death of the Earth Centered Universe

1564-1642

•Contemporary of Kepler

•Demonstrated that all objects are accelerated by gravity by the same amount

•Moving objects remain in motion

•Built a telescope in 1609* and observed the Sun, Moon, Milky Way, Moons of Jupiter and the phases of Venus.

*Hans Lippershey invented the telescope in 1608

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If we assume (incorrectly) that the Tower of Pisa is 20m tall, the ball will take 2s to hit the ground.

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Even if the ball is thrown horizontally from the tower, the acceleration toward the earth is still 10m/s2.

As a result, the ball that is dropped and the ball that is thrown both hit the ground after 2 seconds!!!

We will return to this essential idea in a few slides…

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Sir Isaac Newton

Newton’s Laws:

1. All objects at rest shall remain at rest and all objects in motion shall remain in motion in a straight line, unless compelled by a FORCE to do otherwise.

2. The ACCELERATION of any object is directly proportional to the FORCE applied to it and inversely proportional to its MASS.

3. For every force applied to an object, there is an equal and opposite force applied by the object on the actor.

1642-1727

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Newton’s Laws Relative to Galileo’s Experiment:

1. When the ball is dropped it ceases to be at rest. Therefore there must be a force, directed downward, to cause the acceleration.

2. The acceleration will be equal to the force that gravity exerts on the ball divided by the mass of the ball, that is, the acceleration is equal to the force per unit mass.

3. If the Earth exerts a gravitational force on the ball, the ball must exert an equal and opposite force on the Earth!!!!

Newton v.s. Galileo

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Law of Universal Gravitation

Newton knows that the more mass an object has, the greater the force of Gravity on it.

FG= m g

Where “g” is the special name given to the acceleration that is caused by gravity. 10 m/s2

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Inverse squareThe inverse square law…

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The Law

13Example

Example:

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Mass of baby

Mass of doctor

Distance between baby and doctor

Assumptions

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“Knowns”

Mass of Mars

Mars-Baby Distance

Universal Gravitational Constant

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“Weighing” the Earth…

A & B have equal masses and therefore equal weights.The rod is balanced.

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The very small mass is needed to balance the gravitational force of

the very large mass. “G” can be calculated!

Knowing G and Kepler’s Law’s allows us to calculate the mass of the Earth, Sun and all of the planets moons and asteroids in the solar system

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Return to Pisa

Return to Pisa…The earth is not flat…

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Curved Earth

After one second the projectile has fallen five meters…But the earth has curved away.

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Question

kP

a

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Question…

If the earth is curved such that it “curves away” 5 meters for every 8000 meters traveled, how fast would the projectile need to be going so that, after falling 5 meters, it was still 5 meters above the earth?

8000 m/s!!!

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Summary•Universal Gravitation used to determine the mass of the Earth•Satellite motion possible•Solar system travel made possible

•Newton invents calculus•Newton Proves Kepler’s Laws•Tides understood•Moon “lock” understood

WE NOW UNDERSTAND…

WE ARE UNCLEAR ON…

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Calculus and Planetary Motion…

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R

R

v t

h

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WHICH IS NOT THE RIGHT ANSWER….

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This does not represent the true motion….

The true motion is revealed when weMake the time very, very, very small…

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Newton Tells us that…

An that, for gravity in particular…

We have just discovered that…

We may deduce then that…

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Determine the mass of the SUN….

R = 1.496 x 1011 m

T = 3.156 x 107 s

G = 6.673 x 10-11 Nm2/kg2

M = 1.99 x 1030 kg

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Forces are Balanced on a Spherical Moon

Forces in Competition on a Prolate Moon

Forces are Balanced when Collinear on a Prolate Moon

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Summary II

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IMPORTANT

• Objects fall at the same rate.• Newton’s Laws• Inverse Square Law of Gravity• Nature of Orbits• Renaissance Astronomers

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Electromagnetic Radiation

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