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Lectures
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Table of Contents
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Astro 100 |
The Origin of Modern Astronomy
Planetary Motions and the Historical Foundations of Astronomy
Outline
- Classical Greek Astronomy
- The Copernican Revolution
Terms to Know
Retrograde Motion
Parallax
Geocentric
Heliocentric
1. Classical Greek Astronomy: An Earth-Centered
Universe
The Data:
- All the planets (like the Sun and Moon) stay
close the ecliptic
- Venus and Mercury never seem to stray far from the Sun
- The other naked-eye planets (Jupiter, Mars, Saturn) move mostly
west-to-east among the stars, but sometimes do loop backwards (retrograde
motion), and then continue in the original direction.
- There is no parallax (apparent regular back-and-forth motion,
like the difference in view between your right eye and left eye) of celestial
bodies visible to the naked eye.
Aristotle (Greek, 384-322 BC), one of the world's greatest
philosophers (though not a true scientist by today's definition), proposed
a model Universe with the Earth at the center (geocentric), and the Sun,
Moon, planets, and stars carried around the Earth on transparent, crystalline
spheres.
Ptolemy refined Aristotle's theories by adding mathematical
equations and epicycles, or circle-on-a-circle, to the geocentric model.
Each epicycle moved around a deferent (larger circle), and the Earth was
placed not at the center of the deferent but at an equant (offset point).
Even though it didn't predict the positions of the planets very well, this
picture of the Universe lasted almost 2000 years!
The Ptolemeic model was favored because the sky
was thought to be made of the "most perfect" shape -- the circle. What
else could it possibly be made of?
2. Copernicus and the Sun-Centered Universe
Nicolaus Copernicus (1473-1543), a Polish church
official, launched modern astronomy by proposing a heliocentric (sun-centered)
model of the solar system. His model still assumed circular orbits, so the
ability to predict planet motions was little better than in the Ptolemeic
system. But epicycles were no longer necessary -- and the Earth was no longer
at the center of the Universe!
Copernicus' model put Mercury and Venus' orbits
inside ("inferior") the Earth's orbit, and Mars, Jupiter, and
Saturn's orbits outside ("superior") the Earth's orbit, thus explaining
why Mercury and Venus were never observed far from the Sun.
This is the basic picture of the solar system with
which we are all familiar today.
Copernicus' ideas were revolutionary and controversial.
Why?
Gravity, Orbits, and the Birth of Modern Astronomy
Outline
- Brahe, Kepler, Galileo, and Newton: The Birth of Modern
Science
- Kepler's Laws of planetary orbits
- Newton's Laws of motion
Terms to Know
Ellipse
Kepler's Laws
Newton's Laws
Newton's Law of Gravity
1. Brahe, Kepler, Galileo, and Newton: The Birth
of Modern Science
Tycho Brahe (Danish, 1546-1601)
- made very careful measurements of star and planet positions
- rejected the Copernican model because he could detect no parallax
among the fixed stars (why couldn't he?), and rejected the Ptolemeic
model because of its poor ability to predict planet locations.
- proposed a new, complex model with the Sun and Moon revolving
around the Earth, and the other planets revolving around the Sun
Johannes Kepler (German, 1571-1630 -- Tycho's successor)
- Studied the data Tycho had carefully collected on planetary
motions
- Realized that the planets move on ellipses, not perfect circles
- Supported a heliocentric (Copernican), not geocentric, view.
- Showed that the planets change speed during their orbit (faster
when close to the Sun, slower when far from the Sun)
Galileo Galilei (Italian, 1564-1642) (99 years after
Copernicus' death!)
- was first person to turn a telescope on the sky
- was first to see moons of Jupiter; sunspots; mountains on the
Moon; phases of Venus; stars in the Milky Way; rings ("ears", "handles")
around Saturn.
- proved that Earth could not possibly be the center of the Universe,
thus supporting Copernican system
Isaac Newton (English, 1642-1727) (born the same
year Galileo died!)
- studied the work of Galileo, Kepler, and apple trees
- figured out the laws of optics, gravity, and calculus
- came up with the physics to explain Kepler's Laws
- realized that mass and distance were both important
in the Law of Gravity, and derived that fact mathematically
2. Kepler's Laws of planetary orbits
- Orbits of planets are ellipses with the Sun at one
focus
- The area swept out by a planet in its orbit around the
Sun is always the same in a given time interval (i.e., planets move faster
when closer to the Sun)
- P2 = a3, where P=Orbital
Period (years) and a = Distance from Sun (A.U.)
3. Newton's Laws of Motion
- Law of Inertia: A body remains at rest or moving
in a straight line unless acted upon by some external force
- F = ma : A force F applied to a body with mass
m will cause it to accelerate (change speed and/or direction)
at rate a.
- Action and Reaction: Every force (or action) applied by
one body on a second body results in an equal but opposite force (or
action) by that second body back on the first body.
Newton's Law of Gravity:
- Since the Moon travels in an orbit
around the Earth (and thus not in a straight line), Newton's First Law
requires that some force must act upon the Moon.
- Newton's insight: This force is the same one that pulls objects
to the ground on the Earth.
- Newton determined a quantitative relationship for the gravitational
force between two masses (m1 and m2)
separated by a distance r12.
- G is just a number -- the gravitational constant.
If you measure mass in kilograms, separation in meters, and force
in newtons(!), then G=6.67 x 10-11.
- Any two masses attract one another gravitationally, each one
-- according to the Third Law -- exerting an equal attractive force on
the other.
- The greater the masses, the greater the force.
- The smaller the separation, the greater the force.
- This law provides the physical explanation for Kepler's observations.
Lectures
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Table of Contents
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Astro 100 |
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