The Origins of Modern Astronomy

Mesopotamian astronomers kept long term astronomical records. used the location of the Sun among the 12 constellations of the zodiac to keep keep track of seasons. noted the “wandering” of Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn. made predictions based on repeating patterns, including the saros cycle. showed no interest in building models. Observed that Mars, Jupiter, and Saturn periodically slow down, get brighter, reverse direction (from eastward to westward), and then resume their usual eastward motion. developed astrology

Retrograde Motion of Mars in 2001 As seen from Earth, the superior (outer) planets usually move eastward relative to the stars. However, they periodically slow down, get brighter, reverse direction and move westward for a while, slow down again, get dimmer, and then resume their eastward motion. This is called retrograde motion. February 15,2001 September 12, 2001 N S E W

Aristotle (384-322 BC) Concluded that Earth is spherical. All falling bodies fall straight down. The shadow cast by Earth on the Moon during a lunar eclipse is always circular. Different stars are seen from different locations on Earth. Therefore Earth is spherical Concluded that Earth is the center of the universe and does not move. If the Earth were moving, there would be a strong wind. Falling objects would fall to the west instead of vertically down. Our changing viewpoint as we orbit the Sun would cause the stars to look brighter and farther apart when we are on the part of our orbit closer to them. Developed a geocentric (Earth –centered) model for the motions of the planets.

Relationship Between the Vertical and the Direction to the Sun at Noon on the Summer Solstice North Pole Z O' is an observer at a latitude of 23.5o, and O at the same longitude, but farther north. O S' O' ZOS = ZCS' is the angle between the vertical and the direction to the Sun at noon at the summer solstice. C E Latitude 23½º Angle ZOS = Angle ZCS' = Angle ZCE – Angle S'CE Angle ZOS = Latitude - 23½º South Pole ZOS = 0º for observer at a latitude of 23½º

Eratosthenes (276-195 BC) measured the circumference (C) of Earth using observations of the Sun at noon on the summer solstice at Alexandria (latitude 30.7º) and Syene (latitude 23.5º). North Pole Z S' s q = 7.2º q q s = 5,000 stadia C = 250,000 stadia This is close to the correct value of 40,100 km if the stadium was about 1/6 km. South Pole

Ptolemy (127 - 151 AD) Contributions to Astronomy The Ptolemaic Model developed a geocentric model, (based on Aristotle’s model) that was accepted by scholars for almost 1500 years. compiled a catalog of more than 1000 stars, including celestial coordinates and brightness. expressed brightness as “magnitude”. The Ptolemaic Model The center of a planet’s orbit moves along a circle called the “deferent”. The planet moves around that center in a circle called the “epicycle”. The center of the epicycle moves at a constant speed as viewed from a point called the “equant”.

Retrograde Motion in the Ptolemaic Model (Mars, Jupiter, Saturn) The center of a superior planet’s orbit moves in a circular orbit called the deferent. The planet itself moves around that center in a circle called the “epicycle”. Epicycle Deferent

Apparent Motion in the Ptolemaic Model (Mercury and Venus) The center of the epicycle for these planets must always lie along a line from Earth to the Sun. This accounts for the fact we see them move back and forth, between east of the Sun and west of the Sun. Earth Sun East

Renaissance Astronomy

Properties of Circular Orbits in Copernicus’ Heliocentric Model Contributions to Science Developed a heliocentric (Sun-centered) model of the solar system. Argued that such a model is simpler than the Ptolemaic model. Hoped that it could predict planet positions better. Properties of Circular Orbits in Copernicus’ Heliocentric Model The planets move in circular orbits with the Sun as center. The farther a planet is from the Sun, the slower it moves. All of the planets move eastward around the Sun.

Retrograde Motion According to Copernicus West Sun East Our line of sight usually moves eastward among the stars but, when we’re passing a superior planet, our line of sight moves westward. Earth, moves faster than a superior planet, so it catches up to the planet, and passes it.

Measuring the Distance from the Sun to an Inferior Planet e = greatest elongation (the maximum angle between The Earth-Sun line and the Earth-Planet line) S SP = r SE = 1 AU 1 AU = 1 astronomical unit = 1.496 x 108 km P The greatest eastern elongation of Mercury is 22.8o. Calculate its distance from the Sun. e E e = 22.8o

Tycho Brahe (1546 – 1601) Having measured the position of a new star (now known as Tycho’s supernova), and observed no parallax, he concluded that it was farther away than the Moon. This led him to question the Ptolemaic theory, according to which objects farther away than the Moon were celestial (therefore perfect) and could not change. was given an island to encourage his continuing his work in Denmark. built large metallic measuring instruments and measured positions of stars and planets with greater accuracy than his predecessors. proposed a model of the solar system in which the Sun and Moon orbit the Earth but the other planets orbit the Sun. hired Johannes Kepler.

Tycho’s Supernoiva Remnant

Johannes Kepler (1571 - 1630) Galileo (1564 – 1642) Worked for Tycho Brahe. Acquired Tycho’s data after Tycho died. Studied the data on Mars and devised three laws of planetary motion, which are still accepted. Galileo (1564 – 1642) Demonstrated that all bodies fall with the same acceleration: i.e., their speeds increase at the same rate (9.8 m/s every second). Built telescopes and used them to observe the Sun, Moon, and planets. Wrote a book that was influential in undermining confidence in the geocentric model of the universe, and got him into serious trouble with the Church.

Galileo’s Telescopic Observations Mountains and craters on the Moon. Spots on the Sun. Complete set of phases of Venus. 4 satellites orbiting Jupiter. Saturn’s “ears”. Many stars invisible to the naked eye.

Kepler’s Model of Planetary Motion

e = c/a = the “eccentricity” Properties of Ellipses Ellipse: a figure in which the sum of the distances from two fixed points is constant. Each of these points, labeled F1 and F2 in the diagram, is called a “focus”. The plural is “foci”. P B r r' F1P + PF2 = 2a q a = CA = CA' = “semi-major axis” A' A C F1 b = CB = CB' = “semi-minor axis” F2 F1C = CF2 = c e = c/a = the “eccentricity” B' If F2 is the Sun and P is a planet, then A' is aphelion and A is perihelion. aphelion = farthest point from the Sun . perihelion = point of closest approach to the Sun

Kepler’s laws of Planetary Motion The orbit of a planet is an ellipse with the Sun at one focus. The line from the Sun to a planet sweeps out equal areas in equal times. The square of the sidereal period of a planet is proportional to the cube of the semi-major axis of its orbit. P2 = ka3 If P is in years and a in AU’s, then k = 1.I

Kepler’s Second Law The line from the Sun to a planet sweeps out equal areas in equal times. S is the position of the Sun (at one focus of the ellipse). A, B, C, and D mark positions of the planet. If area SAB = area SCD, then the time it takes the planet to go from A to B is the same as the time it takes the planet to go from C to D. Since the distance AB is greater than the distance CD, the speed of the planet as it goes from A to B is greater than its speed as it goes from C to D. B C S D The perihelion speed of a planet is greater than its aphelion speed. A

Points Along the Orbit of Mercury at Two Day Intervals Sun

sidereal period in years Observational Evidence that P2 = ka3 for the Planets Planet sidereal period in years semi major axis in AU’s a3/P2 Mercury 0.241 0.387 0.998 Venus 0.615 0.723 0.999 Earth 1.000 Mars 1.881 1.524 Jupiter 11.86 5.203 1.001 Saturn 29.46 9.54 Uranus 84.81 19.18 Neptune 164.8 30.06 The data shown above confirm Kepler’s third law for the 8 planets of our solar system. The same law is obeyed by the moons that orbit each planet, but the constant k has a different value for each planet-Moon system.