Planetary Motions and Lessons in Science

Can One Prove that the Earth is Round? Shadow of the Earth during a lunar eclipse Height of Polaris above the horizon

Eratosthenes experiment Can One Prove that the Earth is Round? Shadow of the Earth during a lunar eclipse Height of Polaris above the horizon Inferred size of Earth: 250,000 stadia This is either 20% off, or good to about 1%, depending on the definition of stadia.

Can One Prove that the Earth goes Around the Sun? Proof of motion is through parallax An object’s position will appear to shift due to change in the observer’s position. This MUST occur!!! Since parallax was not seen, the Earth must not be moving!

Geocentric Properties of the Original Planets (Mercury, Venus, Mars, Jupiter, Saturn) The word “planet” means “wanderer”. The planets always stay close to the ecliptic plane, i.e., they move through the zodiac constellations. Mercury and Venus are inferior planets – they are never seen very far from the Sun (Mercury never more 23°, Venus never more than 46°). Mars, Jupiter, and Saturn are superior planets, and can be found anywhere in the zodiac. Planets usually move west-to-east against the fixed stars. But sometimes the planets move backwards (east-to-west). This is called retrograde motion.

Retrograde Motion Path of a planet with respect to the background stars

Retrograde Motion Path of a planet with respect to the background stars

Retrograde Motion

The Science of Aristotle Aristotle’s ideas:  Heavy objects fall faster than light objects  Objects have inertia – all objects prefer to be at rest  The heavens are perfect and immutable  All heavenly objects travel about the Earth at a constant speed in a perfect circle So how did Aristotle explain retrograde motion?

Explaining Retrograde Motion: Aristotle’s Model (350 B.C.) Earth at the center (since it is not moving). Sun and Moon orbit the Earth (west to east). Planets move at a constant speed around small circles called epicycles. Epicycles orbit around Earth (west-to-east) at a constant speed in a circle called a deferent. Combination of orbital and epicyclic motion creates retrograde motion.

Explaining Retrograde Motion: Aristotle’s Model (350 B.C.) Earth at the center (since it is not moving). Sun and Moon orbit the Earth (west to east). Planets move at a constant speed around small circles called epicycles. Epicycles orbit around Earth (west-to-east) at a constant speed in a circle called a deferent. Combination of orbital and epicyclic motion creates retrograde motion. Trouble is, it doesn’t do a very good job of predicting exact positions.

Explaining Retrograde Motion: Ptolemy’s Refinement (140 A.D.) Put the Earth slightly off center at a point called the eccentric State that epicycles only move at a constant speed about the deferent when viewed from a special place called the equant Model is more complicated, and, though it does better, it still doesn’t predict the exact positions of the planets.

Explaining Retrograde Motion: The Copernican Model (1530 A.D.) Since the planets are in the heavens, they must move in perfect circles at a constant speed. But …  The heavenly bodies do not all move around the same center.  The Earth is not at the center of the planetary system (i.e., the universe). Only the Moon goes around the Earth.  The Sun is at the center of the planetary system.  Compared to the distance of the fixed stars, the distance from the Earth to the Sun is negligible.  The daily revolution of the sky is due to the Earth’s rotation.  The Sun’s annual motion is due to the Earth’s orbit around the Sun.  Retrograde motion is due to the Earth’s orbit around the Sun.

Explaining Retrograde Motion: The Copernican Model (1530 A.D.) Retrograde motion is explained by the Earth “passing” (or being passed by) another planet in its orbit.

Explaining Retrograde Motion: The Copernican Model (1530 A.D.) Retrograde motion is explained by the Earth “passing” (or being passed by) another planet in its orbit.

The Heliocentric Model But the model is no better at predicting the positions of the planets than Aristotle’s model. (And are the stars really so far away that we can’t see parallax???) The Heliocentric model also naturally explains the difference between inferior and superior planets.

Galileo’s Experiments Galileo tried something new – doing experiments! Dropping balls to measure gravity Rolling balls to examine inertia Observing the sky through a telescope!

What Galileo Saw An imperfect Sun (sunspots)

What Galileo Saw An imperfect Sun (sunspots) A Moon with mountains and craters

What Galileo Saw An imperfect Sun (sunspots) A Moon with mountains and craters The “ears” of Saturn

What Galileo Saw An imperfect Sun (sunspots) A Moon with mountains and craters The “ears” of Saturn Four moons orbiting Jupiter

What Galileo Saw An imperfect Sun (sunspots) A Moon with mountains and craters The “ears” of Saturn Four moons orbiting Jupiter The Milky Way’s stars

What Galileo Saw An imperfect Sun (sunspots) A Moon with mountains and craters The “ears” of Saturn Four moons orbiting Jupiter The Milky Way’s stars The Phases of Venus

Next time -- Gravity