The “Geocentric Model”

Aristotle vs. Aristarchus (3rd 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 16th 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 1473-1543

Galileo (1564-1642)

Built his own telescope in 1609.400 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• (1571 - 1630)• 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 LawThe 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

CIRCLE ELLIPSE ELLIPSE e = 0 moderately so highly elliptical

Kepler's Second LawA line connecting the Sun and a planet sweeps out equal areas in equal times.

Translation: planets move fasterwhen closer to the Sun.

faster

slower

Kepler's Third LawThe square of a planet's orbital period, P, is proportional to the cube of its semi-major axis, a.

P2 α a3

(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:

P2 = a3 as long as P is in years and a in AU.

So compare Earth and Pluto:Object a (AU) P (Earth years)

Earth 1.0 1.0Pluto 39.53 248.6

Newton (1642-1727)

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

Newton1473-1543 1546-16011473-1543

1564-1642

1571-1630

1642-1727

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 365.256 days (“sidereal year”).

Spring

Winter

N. Hemispheretilted away fromthe Sun

Fall

Summer

N. Hemispheretilted towardsthe sun

Earth’s rotation axis is inclined (tilted)23 1/2 degrees to the plane of its orbit.

Sun

Direction ofEarth’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 360o on its axis.

These are not the same!

The Motion of the MoonThe 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 EarthMoon

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 EarthMoon

Also, moon's orbit slightly elliptical:

Earth

Moon

Side view

Top view, exaggerated ellipse

Distance varies by ~12%

5.2o

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.