The “Geocentric Model” Aristotle vs. Aristarchus (3 rd century B.C.): Aristotle: Sun, Moon, Planets and Stars rotate around fixed Earth. Ancient Greek astronomers knew of Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. Difficulty with Aristotle's "Geocentric" model: "Retrograde motion of the planets". Aristarchus: Used geometry of eclipses to show Sun bigger than Earth (and Moon smaller), so guessed Earth orbits Sun. Also guessed Earth spins on axis once a day => apparent motion of stars. However, Ptolemy (c. A.D. 140) invented a model where planets circle in “epicycles” that orbit the Earth. This helped to explain retrograde motion for a long time, until astronomical observations became more precise. The Ptolemaic Model.

"Heliocentric" Model ● Rediscovered by Copernicus in 16 th century. ● Put Sun at the center of everything. ● Much simpler. Almost got rid of retrograde motion. ● But orbits circular in his model. In reality, they’re elliptical, so it didn’t fit the data well. ● Not generally accepted then. Copernicus

Galileo ( ) Built his own telescope in years ago. Discovered four moons orbiting Jupiter => Earth is not center of all things! Co-discovered sunspots. Deduced Sun rotated on its axis. Discovered phases of Venus, inconsistent with geocentric model.

Johannes Kepler ( ) Born near Stuttgart Studied philosophy and theology at Tubingen Developed love for astronomy as a child Showed high level of mathematical skill Had a reputation as a skilled astrologer Wanted to be a minister; became instead a teacher of astronomy and math in Graz, Austria Became assistant to Tycho Brahe in 1601 Developed Laws of Planetary Motion

Kepler's First Law The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse. eccentricity = e = distance between foci major axis length CIRCLEELLIPSEELLIPSE e = 0moderately sohighly elliptical Kepler's Second Law A line connecting the Sun and a planet sweeps out equal areas in equal times. Translation: planets move faster when closer to the Sun. faster slower

Kepler's Third Law The square of a planet's orbital period, P, is proportional to the cube of its semi-major axis, a. P 2 α a 3 (for circular orbits, a=radius). Translation: the larger a planet's orbit, the longer the period. With the scale of the Solar System determined, can rewrite Kepler’s Third Law as: P 2 = a 3 as long as P is in years and a in AU. So compare Earth and Pluto: Object a (AU) P (Earth years) Earth Pluto

Newton ( ) Kepler was playing with mathematical shapes and equations and seeing what worked. Newton's work based on experiments of how objects interact. His three laws of motion and law of gravity described how all objects interact with each other.

Newton's Correction to Kepler's First Law The orbit of a planet around the Sun has the common center of mass (instead of the Sun) at one focus. x Star center planet of mass Center of mass is not at the geometric center of the star, but because stars are so much more massive than planets, it’s usually beneath the surface of the star.

Timelines of the Big Names Copernicus Galileo Brahe Kepler Newton

The Celestial Sphere Features: - Does not rotate with Earth - Poles, Equator : Projections of Earth’s Pole’s and Equator out onto the sky An ancient concept, as if all objects at same distance. But to find things on sky, don't need to know their distance, so still useful today. North Celestial pole South Celestial pole Celestial Equator

Inclined view of the Earth’s orbit The Year The Earth revolves around the Sun in days (“sidereal year”). Spring Winter N. Hemisphere tilted away from the Sun Fall Summer N. Hemisphere tilted towards the sun Earth’s rotation axis is inclined (tilted) 23 1/2 degrees to the plane of its orbit. Sun Direction of Earth’s motion in orbit Note: the projection of Earth’s orbital plane onto the sky (the Celestial sphere) is called the Ecliptic

The "Solar Day" and the "Sidereal Day" Solar Day How long it takes for the Sun to return to the same position in the sky (24 hours). Sidereal Day How long it takes for the Earth to rotate 360 o on its axis. These are not the same!

The Motion of the Moon The Moon has a cycle of "phases", which lasts about 29 days. Half of the Moon's surface is lit by the Sun. During this cycle, we see different fractions of the sunlit side. Which way is the Sun in each case? Cycle of phases slightly longer than time it takes Moon to do a complete orbit around Earth. Cycle of phases or "synodic month" Orbit time or "sidereal month" 29.5 days 27.3 days

Eclipses Lunar Eclipse When the Earth passes directly between the Sun and the Moon. Sun Earth Moon Solar Eclipse When the Moon passes directly between the Sun and the Earth. Sun Earth Moon

Solar Eclipses Total Diamond ring effect - just before or after total Partial Annular - why do these occur?

Lunar Eclipse

A: Look at Moon's orbit tilted compared to Earth-Sun orbital plane: Sun Earth Moon Also, moon's orbit slightly elliptical: Earth Moon Side view Top view, exaggerated ellipse Distance varies by ~12% 5.2 o Q: Why don't we get eclipses every month? Q: How can there be both total and annular eclipses?

Types of Solar Eclipses Explained Total Annular Partial Sun Moon Earth

Certain seasons are favorable for eclipses. Solar “eclipse season” lasts about 38 days. Likely to get at least a partial eclipse somewhere. It's worse than this! The plane of the Moon's orbit precesses, so that the eclipse season occurs about 20 days earlier each year.