From the Earth-centered to the Sun-centered Model

Tuesday, January 8

For 2000 years, geocentricgeocentric model for the universe was widely assumed.

Spherical Earth at center of universe

Moon, Sun, planets, between Earth & stars

Stars affixed to celestial sphere

Dante, AD 1300

Most famous advocate of geocentric model: the astronomer

PtolemyPtolemy (2nd century AD).

Developed elaborate model to describe

motionmotion of stars, Sun, Moon, & planets.

Stars:Stars:Circular motion around north celestial

pole (near the North Star, Polaris)

Time to complete circle = 23 hours, 56 min. = 1 sidereal daysidereal day

Stars look as ifas if they were glued to rigid spherical shell rotating once

every 23 hr, 56 min.

(You can’t tell, without a telescope, that some stars are closer than others.)

Andromeda Galaxy: 2 million light-years away

Comet Hale-Bopp: 10 light-minutes away

No No sensesense of depth! of depth!

Sun:Sun:

Circular motion around celestial pole: part of circle is below horizon, so we say

Sun “rises” and “sets”.

Time to complete circle = 24 hours.

ObservedObserved motions of the Sun: humanity’s first clock.

1 solar daysolar day = time from one noon to the next = 24 hours

SunriseSunrise

NoonNoon

SunsetSunset

IFIF the Sun orbited the Earth once

per day:

SunriseSunriseNoonNoon

SunsetSunset

MidnightMidnight

×ObserverObserver

× ×

×

SINCESINCE the Earth rotates

once per day:

NoonNoonSunsetSunsetMidnightMidnightSunriseSunrise

×

Observed motions of the Sun can be described if eithereither

1) The Sun goes around the Earth once per day, oror

2) The Earth rotates about its axis.

Q: Why did ancient astronomers believe the Earth is not moving?

A: Well, do you feel any motion?

Rotation speed at Earth’s equator = circumference / rotation period = 40,000 kilometers / 24 hours =

1667 kilometers/hour

Describing motions of starsstars and Sun Sun (and also MoonMoon) was fairly simple in the geocentric model.

Describing motion of planetsplanets was very difficult.

Planet = “Wanderer”

To naked eye, a planet looks like a star - a

tiny blob of light.

Planets are distinguished by their motionmotion relative to stars.

↑ NORTH

Planets usually move west to east, but sometimes east to west (retrograde),

relative to stars.

Ptolemy’s explanation of retrograde motion:

Planet (P) moves in a small circle called the epicycleepicycle.

Center of epicycle (A) moves in a large circle called the deferentdeferent.

Combination of small and large circles creates “loop-the-loop” retrograde motion.

Detailed structure of Ptolemy’s geocentric model:

Earth

Complicated!

A bold minority opinion:

Aristarchus (3rd cent. BC) proposed that the Earth

rotates on its axis & goes around the Sun.

First heliocentricheliocentric (Sun-centered) model.

Heliocentric model was rejectedrejected by the contemporaries of Aristarchus.

Aristarchus was accused of impiety.

Why did Aristarchus bother with a heliocentric model, given the grief

he received?

Questions posed by Aristarchus:

How far away is the Sun?

How large is the Sun?

A sphere (like the Sun) will be 1/2° across when its distance is 110 times110 times its diameter.

How far away is the Sun?Farther away than the Moon!

Moon comes between between Sun and Earth during

a solar eclipse.

Moon, like Earth, is an opaque sphere, capable

of blocking light.

Phases of the Moon: The Moon is an opaque sphere

illuminated by the Sun.

s EM

Half close to Sun is

illuminated.

Half away from Sun is dark.

Gibbous, crescent shapes: result of perspective.

How Aristarchus found the relative distances of Sun and Moon.

“First quarter” or “last quarter” Moon: we see bright portion of Moon

as a perfect half-circle.

When we see the Moon as a half-circle, Earth-Moon-Sun angle must bemust be 90°.

When Aristarchus saw the Moon as a half-circle, he measuredmeasured the Moon-Earth-Sun

angle to be 87°.

90°

87°

Trigonometry Alert!

x yθ

cosy

xx

xy 19

87cos

Aristarchus: Sun is 19 times farther away Aristarchus: Sun is 19 times farther away (and thus 19 times bigger) than Moon.(and thus 19 times bigger) than Moon.

(This is actually an (This is actually an underestimateunderestimate of the Sun’s immense size.)of the Sun’s immense size.)

Aristarchus: Earth is 3 times size of Moon Aristarchus: Earth is 3 times size of Moon (from size of Earth’s shadow on Moon).(from size of Earth’s shadow on Moon).

Despite the arguments of Aristarchus (“Why should huge Sun orbit tiny Earth?”),

heliocentric model ignored for 18 centuries.

Reviver of “heliocentrism”: Nicolaus Copernicus (Polish: 1473 – 1543)

Basic structure of Copernicus’ model:

Earth

Sun

Geocentric model (Ptolemy):

◦ Earth in central location

◦ Celestial sphere rotating about axis

◦ Sun orbiting around Earth

Heliocentric model (Copernicus):

◦ Sun in central location

◦ Earth rotating about axis

◦ Earth orbiting around Sun

Thursday’s Lecture:

Reading:

Chapter 1

Planets and Stars and Galaxies (Oh my!)