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Gravitation and the Waltz of the Planets

From Ancient to modern astronomy

Geocentric view

Heliocentric view

Galileos observations

Keplers laws of

planetary motion

Columbia Launch: October 18,1993

Columbias crew: STS 93

The Greeks tried to EXPLAIN and UNDERSTAND, not just

PREDICT.

To them, the universe was the basically solar system -the Sun,

Earth, Moon and 5 planets known at that time.

They observed that: - over the course of a night, the stars slid smoothly across the sky. - over the course of a month, the moon moved smoothly in the sky relative to the

stars.

- over a course of a year, the Sun progressed along the ecliptic.

- 5 other bodies known to them were Mercury, Venus, Mars, Jupiter and Saturn. Planetes- wanderer----> do not behave in as regular and predictable manner. They seem to speed up and slow down and appear to loop back and forth relative to stars. Sometimes they stop. Sometimes their brightness change.

Prograde motion: Eastward (forward or direct)

Retrograde motion: Westward (backward)

The Geocentric View (Greek Astronomy)

He gave PROOFS that the Earth was

SPHERICAL:

objects all fell towards its center

perpendicular to ground sphere.

noted shadows cast on moon during eclipse were always round.

Earth - at the CENTER of Universe

- is heaviest thing around therefore it shouldn't move.

The Sun and the Moon revolve with

uniform motion around a circle with

Earth at its center.

This simple model could not account for

the variation in planetary brightness and

their retrograde motion.

. Each planet was taken to move uniformly around a small circle, called an epicycle,

whose center moved uniformly around

Earth on a second and larger circle, known

as the deferent.

Greek philosopher Aristotle - (384-322 B.C.) : The Greek astronomers (& philosophers) Aristotle (384 -322 B.C.)

and Ptolemy (127--151 A.D.) created the GEOCENTRIC MODEL to

explain the motions of the Sun, Moon and planets around the Erath.

To account for the paths of Sun, Moon and the five planets known at that time his model required a series of nearly 80 distinct circles.

While complex, IT WORKED ---

used for 1300 years (~13

centuries)

The Geocentric Model

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Nicholas COPERNICUS (1473--1543), a Polish cleric,

argued in favor of :

1. HELIOCENTRIC COSMOLOGY --- THE EARTH IS NOT THE CENTER OF THE UNIVERSE .

2. The center of the Earth is the center of gravity and for the MOON.

3. The other PLANETS REVOLVE around the SUN.

4. The STARS are MUCH FARTHER from the EARTH than is the SUN.

5. STELLAR (and SOLAR) MOTIONS ARE APPARENT: all are due to motion of the earth.

6. PLANETARY MOTIONS are also substantially due to the Earth's motions.

7. RETROGRADE PLANETARY MOTIONS are also a consequence of Earths motion.

THE COPERNICAN REVOLUTION

Copernicus' model still assumed perfectly circular orbits

and did not dispense with epicycles --- but now the main

orbits went around the Sun and they could be smaller.

While this model fit the data available then, it was only

slightly better and certainly not proven.

SO WHY WAS IT ``BETTER''?

HELIOCENTRIC MODEL was SIMPLER and more

BEAUTIFUL than the Ptolemaic geocentric model.

Still, it gained few adherents:

--- went against common sense --- and written in Latin

Retrograde Motion (The Copernican model)

Two scientists Galileo Galilei and Johannes Kepler :

--- made ineradicable imprints in astronomy

--- popularized the Copernican viewpoint

GALILEO Galilei (1564--1642)

He taught mathematics and astronomy at Padua, Italy.

He performed EXPERIMENTS:

e.g., balls rolling down inclined planes and learned about INERTIA.

He is now widely regarded as father of experimental science.

He built a TELESCOPE in 1609 but not for commercial or military use.

The Birth of Modern Astronomy

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Galileo was the first man who POINTED the

TELESCOPE at THE SKY and DISCOVERED: The Lunar surface was irregular: it had mountains, valleys and

crater etc. Moon wasn't a perfect sphere.

Planets looked like disks, stars still looked like

points.

Milky way comprised of many stars --- many

fainter stars could be seen between those visible

to the naked eye.

The Sun had spots --- the most perfect of all heavenly bodies

had blemishes that moved across the face of Sun- Sun rotates.

Jupiter had four moons --- something other than earth had

things going around it. (One of the strongest supports in the favor

of Copernican model and against Aristotle/Ptolemys model)

Venus went through phases (including a full phase, not possible

in Ptolemaic model) -- reflecting light from the sun.

Galileo discovered that Venus, like the Moon, undergoes a series of phases

as seen from Earth. In the Ptolemaic (geocentric) model, Venus would be

seen in only new or crescent phases. However, as Galileo observed, Venus

is seen in all phases, which agrees with the Copernican model as shown.

Venus appears smallest at gibbous phase and largest at crescent phase.

The Changing Appearance of Venus

Galileo also discovered moons in orbit

around the planet Jupiter. This was

further evidence that the Earth was

not the center of the universe.

Jupiter and its Largest Moons

Observations made by Jesuits in 1620

The Moon in Galileos Sidereus Nuncius

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Galileo's Sunspot Drawings

Credit: http://galileo.rice.edu/

He was a German mathematician and an accomplished amateur

observer, who had already accepted the basic Copernican picture.

In contrast to Galileo, he was a pure theorist. His groundbreaking work about planetary motions was principally a collection of his employer, Tycho Brahe.

MARS MOVED

IN AN ELLIPSE, WITH THE SUN AT ONE

FOCUS. This broke

with the longstanding assumption

that combinations of

circles were the only way to

explain things;

after all, a circle is just a

special ellipse,

with ECCENTRICITY = 0.

By 1609 he had also realized that

Mars' orbit

swept out equal areas in equal

times

TYCHO Brahe (1546--1601), a Danish noble, built his own observatory at Denmark named Uraniborg

and designed HUGE instruments

including:

sextants (for measuring angles) astrolabes (for locating positions on the sky) These allowed for PRECISION MEASUREMENTS,

accuracies of about 1 arc min in planetary and

stellar positions were achieved.

Tycho was the first to quote errors along with his

measurements.

Johannes KEPLER (1571--1630)

1. All planets follow elliptical orbits,

with the Sun located at one focus.

Kepler's laws of Planetary Motion

2. Every planet sweeps out equal areas in equal

times as it orbits the Sun.

[In other words, planets move fastest when closest to the Sun (near

perihelion) and slowest when farthest away (aphelion).]

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KEPLER'S

First Law Second Law

Credit: Bill Drennon (Central Valley Christian High School, Visalia, CA USA)

3. The square of a planets orbital period is

proportional to the cube of its semi-major axis

(distance from the Sun).

P = a

2 3

(in earth years) (in astronomical units)

1 Astronomical unit (AU) = 1.5 x 10 Km (150 million Km) 8

Keplers laws are called empirical laws: not based on any physics or mathematics but just on observations.