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 Astronomy Babylon (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 Astronomy Egypt (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 Astronomy Greece (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 A2 + B2 = C2 Pythagorus (582 - 500 BC) B A C 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. B A C A2 + 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 Astronomy Aristotle (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 Astronomy Eratosthenes (276 - 196 BC) 1st to determine the Earth's Diameter He noted that at Syene (Aswan) on June 21 the sun shown directly down a deep well; on the same date at Alexandria, it hit the wall of the well at 7 degrees. Knowing the distance between Syene and Alexandria was 7/360 of the earth's circumference he could calculate the diameter.

Greek Astronomy Hipparchus (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 Models Why were Aristotle, Hipparcus and others insisting on the Earth being at the center of the Solar system? Parallax It 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. If the earth were moving, one should sense the motion. How would the moon stay in orbit if the earth was moving away from it?

Geocentric Models What 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: Convolutions Greek astronomers invented the epicycle and deferent scheme to account for retrograde motion.

Greek Astronomy Ptolemy 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 Ages Europe 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…"

Astronomy kept alive due to need to know the direction of Mecca 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 Hypothesis Looking at the Inner Planets from Earth At any point in Earth's orbit, the maximum elongation of Mercury is limited - We can never see it too far from the Sun The same effect for Venus, only the elongation is larger

Heliocentric Hypothesis Variation in Brightness occurs when planets are 1. Closer together and 2. are better illuminated by the Sun

Heliocentric Hypothesis Retrograde Motion is now easily seen without the use of epicycles: * * * * * D * * D C * * C * B * A B A * *

Observation Tycho 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 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.

Results of the parallax experiment 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

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 Model Tycho 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 Theory Johannes 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 Laws First Law: The orbits of the planets are ellipses with the Sun at one of the foci.

Kepler's Laws Second Law: Equal Areas of the orbit are swept out in equal intervals of time one month difference one month difference

P2 = a3 Kepler's Laws Third 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 “I do not feel obliged to believe that the same god who has endowed us with sense, reason and intellect has intended us to forgo their use.” - Galileo Galileo Galilei Foundations of experimental physics Falling bodies Discovered: Mountains, 'Seas' and Craters on the Moon Sunspots Moons of Jupiter Phases of Venus

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 Motion An object in a state of rest or uniform motion will remain in that state unless acted on by an external force F = m a Every action has an equal and opposite reaction Inertial mass

Searching For The Underlying Laws Newton's Law of Universal Gravitation Gravitational mass G m M F = r2

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 is pulled 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 = 1 And since Mars was so small compared to the Sun m = 0

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 Challenge Let'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