General Astronomy

Historical Attempts to Model the Solar System

The Historical Quest to Model the Solar System

• The Theme through the Ages has been:– What is it?– How does it work?– How is it going to affect ME?

• For each different era, there is a different emphasis

Ancient AstronomyBabylon (Religious-Mystical)• The earth is a flat disk which rises out of the ocean with an

inverted bowl (sky) over it. The stars are fixed into place on the bowl.

• The planets move about against the steady background (major gods)

• Astronomy began as a systematic study when the priest-astrologers started to keep a careful watch on the movements of the gods in order to warn their kings about what the gods might be planning.

• Babylonians are responsible for dividing the sky into 12 equal zones (zodiac) through which the gods moved.

• Calendar was Lunar; a month started at sundown on the day that the crescent moon was first seen in the west. This leads to 29-30 day months with 12-13 months per year.

Ancient AstronomyEgypt (Religious-Mystical)• Even less scientific approach• No system at all; everything is blamed on or due to the gods.

– The Sky is the goddess Nut; Stars are part of her body.– Horus, the hawk-headed god identified with the Pharaoh, had his

left eye damaged in battle with Set, the god of hostility and chaos. His eye was later restored by Thoth, the ibis-headed god of the moon. This loss and restoration, of course, explains the phases of the moon.

• The major contribution was a Solar calendar having 12 months of 30 days each (adjusted at year’s end)– primary use was agriculture; i.e., when Sirius rose in the east just

before the sun, the Nile would flood.

Ancient AstronomyGreece (Mystical-Scientific)

The Greeks inherited volumes of data and observations from the Egyptians and Babylonians. At a formal level, at least, astronomy was still linked to religion; e.g., the sun was Apollo’s chariot.

• Thales of Miletus (640? - 546BC)– Thought the earth was flat, but still gave the first

recorded prediction of a solar eclipse.– Believed the sun to be self-luminous and the moon to

shine by reflected light.– Taught the Greeks to navigate using the ‘Little Dipper’

(close to the pole at that time).

Greek Astronomy• Pythagorus (582 - 500 BC)

– A mystic who believed that mathematics was all that was needed (Numerology).

• For example, since 10 is a ‘perfect’ number, 1+2+3+4 = 10, and he could only identify 9 heavenly bodies, 5 planets, the sun, moon, earth and fixed-stars, then there must be a 10th, the ‘counter-earth’ which revolved opposite the earth - forever out of sight. It was on the other side of the ‘Central fire’ about which everything revolved; including the sun.

• The friction of revolution caused the Music of the Spheres which played for the gods on Olympus.

• Taught that the Earth was round based on the belief that the sphere is the perfect shape used by the gods.

• Had some success in developing a relation describing the lengths of the sides of a right-triangle.

AB

CA2 + B2 = C2

Greek Astronomy• Eudoxus of Cnidus (4th century BC)

– Geocentric Model– Modeled solar system as spherical shells each rotating

independently from the center out (Fails to explain variation in brightness of planets)

Greek AstronomyAristotle (384 - 322 BC)

The greatest of all philosophers! Succeeded in single-handedly setting back the course of astronomy and geology for centuries.

– Regarded the earth as a sphere; the sun and moon as pure (emphasis on purity) aether instead of matter

• Aether is a substance whose ‘natural motion’ is circles about the earth.

• Matter is a substance whose ‘natural motion’ is up and down.• Since matter can only move if pushed, the moon and planets

had animate souls whose job it was to steer these bodies about the sky.

– Geocentric Model of Solar System• Failure to observe parallax

Aristotole's Universe

Greek Astronomy• Aristarchus of Samos (300BC)

– Determined the relative distances of the sun and moon from the earth

• Showed that the sun was much further away than the moon despite the similar apparent sizes

– Estimated the relative sizes of sun and moon (Timed lunar eclipses)

– Estimated distance to the sun (using a solar eclipse)– Created a heliocentric model of the solar system

– In his Sand-Reckoner, Archimedes (d. 212 BCE), discusses how to express very large numbers. As an example he chooses the question as to how many grains of sand there are in the cosmos. And in order to make the problem more difficult, he chooses not the geocentric cosmos generally accepted at the time, but the heliocentric cosmos proposed by Aristarchus of Samos (ca. 310-230 BCE), which would have to be many times larger because of the lack of observable stellar parallax.

Greek AstronomyEratosthenes (276 - 196 BC)

– 1st to determine the Earth's DiameterHe noted that at Syene (Aswan) on June 21the sun shown directly down a deep well; onthe same date at Alexandria, it hit the wallof the well at 7 degrees. Knowing thedistance between Syene and Alexandria was 7/360 of the earth'scircumference he could calculatethe diameter.

Greek AstronomyHipparchus (150 BC)• Created the first formal observatory• Devised a system of Magnitudes• Created the first Star Catalog• Determined that the Earth was precessing• Invented trigonometry• Geocentric Model

– Wanted perfect circles with uniform circular motion, so he invented epicycles

Geocentric Model

Deferent

Epicycle

Earth

Geocentric ModelsWhy were Aristotle, Hipparcus and others

insisting on the Earth being at the center of the Solar system?

1. ParallaxIt was clear to them that if the earth was orbiting the

Sun, the stars should exhibit parallax. However, the stars are much farther away then they imagined and the parallax much too small to be seen with the naked eye.

2. If the earth were moving, one should sense the motion.

3. How would the moon stay in orbit if the earth was moving away from it?

Geocentric ModelsWhat observations must be

explained by the model?• Retrograde motion • Variation of brightness• Mercury and Venus never stray too

far from the Sun (28° and 48 ° respectively)

Motions of Inner Planets

Motions of Inner Planets

Motions of Outer Planets

The Retrograde motion of the planets presents a challenge for the geocentric model.

The Geocentric Model: ConvolutionsGreek astronomers invented the epicycle and

deferent scheme to account for retrograde motion.

Greek AstronomyPtolemy• Adapted and improved

Hipparchus' geocentric model to account for discrepancies found by improved observations.

• Produced the Almagest, which both summarized the state of Astronomy and extended it.

• Used eccentrics and equants to refine the model

The Ptolemaic Universe

Ptolemy's geocentric (earth-centered) model of the universe.

Middle AgesEurope• The earth is a flat disk which rises out of

the ocean with an inverted bowl (sky) over it. The stars are fixed into place on the bowl.

• In 1200 AD, Aphonso X of Castile had the planetary position tables calculated. In noting the ~88 epicycles, equants and eccentrics necessary, is reported to have stated " Had I been present at the Creation, I could have offered excellent advice…"

Islam

Astronomy kept alive due to need to know the direction of Mecca

Carried forward Greek astronomy

Developed new Mathematics, aided calculations

Great observers - Many star names are Arabic.

Painting, 1581

Nicolas Copernicus (1473 - 1543 AD)

• Chiefly a mathematician, he attempted to summarize all the existing models

• Developed the idea of relative motion. This having been done, he realized that the sun moving about the earth and the earth moving about the sun results in the same observations.

• Developed a new model of the solar system in a book, De Revolutionibus – Generally considered a 'crank'

Nicolas Copernicus• Had life-long association with the church -

was a Canon.• The church did not immediately view his

model as radical.• His model was simply a hypothesis. It was

simpler mathematically and easier to use.• De Revolutionibus was not forbidden by the

church until 73 years after publication.• It became forbidden in 1616 after word of

Galileo was getting around.

Copernicus proposed a heliocentric (sun-centered) model for the universe.

Opponents argued, in addition to earlier parallax and other items, that if earth were revolving about its axis it would 'fly apart'

His answer was that the Celestial spheres would do the same, even faster since they are larger.

Heliocentric Hypothesis• There were some preconceptions:

– The Universe is spherical– All heavenly bodies must move in combinations of

perfect circles– All heavenly bodies must move in uniform circular

motion• He placed them in order:

– Sun, Mercury, Venus, Earth (and Moon), Mars, Jupiter and Saturn.

– He deduced that the nearer the planet to the sun, the faster its motion.

– He worked out the approximate scale of the solar system

– He can account for the three observations we noted earlier in a much simpler manner - without epicycles

Heliocentric HypothesisLooking at the InnerPlanets from Earth

At any point in Earth'sorbit, the maximumelongation of Mercuryis limited - We cannever see it too far from the Sun

The same effect for Venus, only the elongation is larger

Heliocentric Hypothesis

Variation in Brightnessoccurs when planets are1. Closer together and2. are better illuminated by the Sun

Heliocentric HypothesisRetrograde Motion is now easily seen without theuse of epicycles:

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A ABC

D

B

CD

ObservationTycho Brahe (1546 - 1601

AD)Tycho Brahe's contributions to astronomy were enormous. • He not only designed and built instruments, he also calibrated them and

checked their accuracy periodically. • He thus revolutionized astronomical instrumentation.

• He also changed observational practice profoundly. • Whereas earlier astronomers had been content to observe the positions

of planets and the Moon at certain important points of their orbits (e.g., opposition, quadrature), Tycho and his cast of assistants observed these bodies throughout their orbits. As a result, a number of orbital anomalies never before noticed were made explicit by Tycho. Without these complete series of observations of unprecedented accuracy, Kepler could not have discovered that planets move in elliptical orbits.

• Tycho was also the first astronomer to make corrections for atmospheric refraction. In general, whereas previous astronomers made observations accurate to perhaps 15 arc minutes, those of Tycho were accurate to perhaps 2 arc minutes, and it has been shown that his best observations were accurate to about half an arc minute.

Instruments

Tycho Brahe observed a supernova, bright enough to see in the daytime. He attempted to use parallax of a supernova to test the Copernican model.

No parallax observed

Stars either very far away, or not moving at all

Led him to reject the heliocentric model

Actual parallaxes are 100 times smaller than he could detect

Results of the parallax experiment

Tycho's Model• Hybrid model – combined geocentric

and heliocentric– Earth in center; Sun orbits Earth– Other planets orbit the Sun (and so, also

the Earth) – Tychonic system adopted by Catholic

Church for many years as official Astronomical conception of universe

Tycho's ModelTycho Brahe's model is a combination of the Geocentric and Heliocentric.

The Earth is at the center about which orbit the Sun and Moon. All other planets (and Tycho's Comet) orbit the Sun

and TheoryJohannes Kepler (1571 - 1630

AD)Kepler worked on a number of projects. He was basically a mathematician. As can be seen from his model of the spacing of the planets:

Spacing was according to some mystical use of regular polygons

Kepler• Kepler was hired by Brahe (by direction of Brahe's patron) • He was assigned the analysis of the orbit of Mars.

– This was the most difficult of all the planetary orbits– Many feel that Brahe assigned this one to Kepler because

he was afraid that this bright, young man would upstage him.

• The choice of Mars was fortunate. While difficult it leads directly to Kepler's Laws of Planetary Motion

• When Brahe died, Kepler had access to volumes of measurements – 20 years worth – for analysis

Kepler's LawsFirst Law:

The orbits of the planets are ellipses with the Sun at one of the foci.

Kepler's LawsSecond Law:

Equal Areas of the orbit are swept out in equal intervals of time

one monthdifference

one monthdifference

Kepler's LawsThird Law:

The square of the period is equal to the cube of the average distance

P2 = a3

This assumes units of 1 earth year for period and 1 Astronomical Unit (AU) for average distance

Searching For The Underlying Laws

Galileo Galilei• Foundations of experimental

physics• Falling bodies• Discovered:

Mountains, 'Seas' and Craters on the Moon

Sunspots Moons of Jupiter Phases of Venus

“I do not feel obliged to believe that the samegod who has endowed us with sense, reason andintellect has intended us to forgo their use.” - Galileo

Galileo’s telescope revealed that Jupiter had moons which orbited Jupiter instead of Earth.

Gasp! Not all heavenly bodies orbited about the Earth!

The telescopic appearance of Venus in the Ptolemaic model.If the system was geocentric, Venus would look like this:

The telescopic appearance of Venus in the Copernican model.Galileo saw Venus like this, a heliocentric system:

Searching For The Underlying Laws

Sir Issac Newton

Newton's Laws of Motion1. An object in a state of rest or

uniform motion will remain in that state unless acted on by an external force

2. F = m a

3. Every action has an equal and opposite reaction

Inertial mass

Newton’s 1st Law

At rest – until acted on!

Uniform motion – until acted on!

Newton’s Second Law• F = m a• “Mass resists acceleration”

Newton’s Third LawForces have equal strength, but accelerations may

differ:

MORE MASS, LESS ACCELERATION

BOAT’S FORCE ON MANMAN’S FORCE ON BOAT

FORCEFORCE

Searching For The Underlying LawsNewton's Law of Universal

Gravitation

F = G m M

r2

Gravitational mass

Mass versus Weight• Mass is a measure of the total

amount of material in the object Remains the same everywhere

• Weight is the force with which an object ispulled down while on the ground (due to gravity’s attraction)Changes depending on the body you are standing on

Searching For The Underlying Laws

Newton's Form of Kepler's Third Law

(m + M) P2 = a3

Kepler’s version assumed Solar Mass as a unit since he used Mars’ measurements M = 1And since Mars was so small compared to the Sun m = 0

P2 = a3

Back to a basic question…

We've discovered quite a few 'Laws' and have gathered lots of data.

So how do we prove the Earth is rotating about its axis?

Any ideas?

Foucault's Pendulum

Consider a pendulum centered over the north pole. Assuming it doesn’t slow down and stop, it will trace out a complete circle in 24 hours as the Earth turns beneath it.

Back to another question…

Now how do we prove the Earth is rotating about the Sun?

Any ideas?

Time out for a ChallengeLet's suppose there is a heavy rain, but no

wind. I'll give you a long, perhaps 8 foot cardboard tube about 2 inches in diameter.

I want you to run from one side of the parking lot and back and get a single raindrop to pass completely down the tube without striking the side.

How would you do it?

The Aberration of Starlight• Bradley determined that our

challenge was the same as looking at a star in a telescope. Earth is 'running' around and the light is traveling down a long tube without striking the sides. So do we have to tilt the telescope slightly as Earth moves?

• Yes – This slight, but measurable angle proves that the Earth is orbiting the Sun.

Parallax (again)• In 1838, Bessel announced that 61 Cygni had a

parallax of 0.314 arcseconds; which, given the diameter of the Earth's orbit, indicated that the star was about 3 parsecs (9.8 light years) away.

• Again showing that the Earth orbits the sun