Benefit of astronomy to ancient cultures Usefulness as a tool to predict the weather (seasons) Usefulness as a tool to tell time (sundials) Our calendar is based on astronomical objects Length of day = time Sun takes to complete one circuit in the sky 7 days of the week = seven moving solar system objects Central Africa (6500 B.C.) Many ancient cultures built structures to mark the seasons The structures were often aligned North-South, East-West Purpose - astronomical and social (rituals)? Alignments Stonehenge Sunlight pierces the center of carved spiral only at noon on summer solstice Modern Science and the Greeks The Greeks are credited for developing the scientific method Instead of using superstition, they were the first to use logic and geometry to explain nature They understood the power of reasoning from observations
How do we know the Earth is round? Ships sailing out to sea disappear from the bottom up. Were the Earth flat they would just get smaller Thales: the first astronomer First to ask What is the universe made of? Model: Universe is mostly water, and the Earth is a flat disk floating on the infinite ocean Even wrong ideas are good - they get people thinking and coming up with (hopefully!) better models horizon How do we know the Earth is round? Ships sailing out to sea disappear from the bottom up. Were the Earth flat they would just get smaller horizon How do we know the Earth is round? Ships sailing out to sea disappear from the bottom up. Were the Earth flat they would just get smaller The edge of the Earth s shadow on the Moon is always part of a circular arc. Only a sphere always casts a circular shadow
How do we know the Earth is round? Ships sailing out to sea disappear from the bottom up. Were the Earth flat they would just get smaller The edge of the Earth s shadow on the Moon is always part of a circular arc. Only a sphere always casts a circular shadow The altitude of the constellations changes as one moves northsouth. This cannot happen if the Earth is flat (Anaximander) Equator S N Observer Horizon How do we know the Earth is round? Ships sailing out to sea disappear from the bottom up. Were the Earth flat they would just get smaller The edge of the Earth s shadow on the Moon is always part of a circular arc. Only a sphere always casts a circular shadow The altitude of the constellations changes as one moves northsouth. This cannot happen if the Earth is flat (Anaximander) Equator S N Horizon Pythagoras: the Earth is a sphere within a celestial sphere. The reasoning was that the sphere is geometrically perfect Aristotle: the Earth s curved shadow during lunar eclipse proves that the Earth is spherical Aristarchus: the Earth orbits the Sun 1) Distance to the Moon 2) The moon is closer to us than the Sun 3) The size of the Earth 4) The distance of the Sun from the Earth
Brief trigonometry review - 1) Distance to the Moon y R sin = y R, cos = x R, tan = y x x θ arc length radius θ For small, tan = So, arc length radius Parallax - the apparent displacement of an object caused by the motion of the observer A near moon Earth moon (courtesy of Mike Zingale)
A far moon Large parallax observed
Smaller parallax observed 2) How do we know the Moon is closer to us than the Sun? R D = Radius of Earth Distance to Moon Solar eclipses I.e., the moon, being closer, blocks the light from the Sun D R
3) Size of the Earth 3) Size of the Earth Earth Shadow Area Earth Shadow Area Because the Sun is so far away, the shadow of the Earth is more-or-less cylindrical. The image above illustrates this fact - a nearby light source causes an Earth to cast a wide-angle shadow, but the angle of the shadow approaches that of the dotted parallel lines as the light source is moved farther from the Earth Because the Sun is so far away, the shadow of the Earth is more-or-less cylindrical. The image above illustrates this fact - a nearby light source causes an Earth to cast a wide-angle shadow, but the angle of the shadow approaches that of the dotted parallel lines as the light source is moved farther from the Earth 3) Size of the Earth 3) Size of the Earth Distant Sun Earth Projected Shadow moon Because the Sun is so far away, the shadow of the Earth is more-or-less cylindrical. Thus, the size of the Earth can be estimated from the size of its shadow The Earth s radius is 3 times that of the Moon s eclipsed moon
3) Size of the Earth 3) Size of the Earth eclipsed moon eclipsed moon Way too small! Too small! 3) Size of the Earth Matching fit eclipsed moon 4) Size of the Sun Aristarchus (280 b.c.) used geometry When the moon is half illuminated, the Earth-Moon- Sun angle is 90 o By measuring the Moon- Earth-Sun angle, the relative distances between the Moon and the Sun, and thus relative size can be calculated.
Size of the Sun (cont ) Aristarchus answers: the Sun is 20 times farther away than the Moon, & thus 20 times its size. Since the Earth is 3 times the size of the Moon, the Sun must be 7 times the Earth s size Real numbers: The Sun is 400 times the size of the Moon & 100 times the size of the Earth The Moon-Earth-Sun angle is extremely difficult to measure! Size of the Sun (cont ) Punchline: Aristarchus was right in principle, but wrong in detail. He did, however, conclude that the Sun, the largest (and brightest) object in the known universe, must be at the center, and that the Earth must orbit the Sun Eratosthenes Measured Earth s Size Syene: Sun passes directly overhead at summer solstice Alexander: Sun comes within 7 o of zenith at summer solstice Thus, Alexandria is 7 o in latitude to the north of Syene Eratosthenes Measured Earth s Size 7 o 360 o = arc circumference 7 o arc
Eratosthenes Measured Earth s Size Syene-Alexander distance = 5,000 stadia Thus, Apollonius and Hipparchus laid the foundation for the Ptolemaic, geocentric model of the Universe The equivalent value of his estimate in km is 42,000 km. The actual circumference of the Earth is 40,000 km. Geocentric Model: things to be explained The occasional retrograde motion of Mars, Jupiter and Saturn The fact that Venus and Mercury are always seen near the Sun The length of each object s orbital period Ptolemy pushed the idea of the Earthcentered (i.e., Geocentric) system A key feature was the use of epicycles to explain retrograde motion This model reigned in the Western culture for ~ 1500 years Claudius Ptolemy (100-170 A.D.)
Ptolemy pushed the idea of the Earthcentered (i.e., Geocentric) system A key feature was the use of epicycles to explain retrograde motion This model reigned in the Western culture for ~ 1500 years Claudius Ptolemy (100-170 A.D.) Copernicus (1473-1543 A.D.) Used the best data of planetary motions available and the earlier suggestion of a Suncentered (i.e., heliocentric) system by Aristarchus Worked out the detailed geometry of the solar system Flaw - motions must be perfect circles Tycho Brahe (1546-1601 A.D.) Tycho built of observatory for naked eye observations to make accurate measurements of the positions of stars & planets Such accurate astrometry, i.e., the measurements of the positions of astronomical objects, was necessary to pave the way to the correct model Johannes Kepler (1571-1630 A. D.) Apprentice of Tycho, made use of Tycho s high quality astrometry to make accurate models of the solar system Kepler gave up his personal belief in the idea of the circle s perfection because the data contradicted that model Kepler: If I had believed that we could ignore these 8 minutes [of arc], I would have patched up my hypothesis accordingly. But since it was not permissible to ignore, those 8 minutes pointed the road to a complete reformation of astronomy.
Kepler s first law: The orbit of each planet about the Sun is an ellipse with the Sun at one focus eccentricity = Eccentricity distance from center to focus semimajor axis = c a Eccentricity The value of c, and thus the eccentricity, goes to zero for a circle (courtesy of Mike Zingale)
Perihelion vs. Aphelion Perihelion vs. Aphelion c Perihelion = a - c = a (1 - e) c Aphelion = a + c = a (1+ e) a a Earth's Eccentric Orbit Earth s orbit has e = 0.017. What is its closest (perihelion) and furthest (aphelion) distance from the Sun? Earth's Eccentric Orbit Perihelion vs. Aphelion Sun
(2) Equal areas are swept out in equal time. Kepler s second law: An imaginary line connecting the Sun with a planet sweeps out equal areas in equal (courtesy of Mike Zingale) times as the planet moves about the Sun.!54 Kepler s third law: The cube of the distance from the Sun divided by the square of the time required to traverse the orbit is a constant, and is the same for every planet. I.e., distance 3 period 2 = constant Kepler s Laws of Planetary Motion Each planet moves in an elliptical orbit about the Sun, with the Sun at one focus of the ellipse. An imaginary line connecting the Sun with a planet sweeps out equal areas in equal times as the planet moves about the Sun. The cube of the distance from the Sun divided by the square of the time required to traverse the orbit is a constant, and is the same for every planet (i.e., distance 3 / period 2 = constant ). AU years 1
Planetary Speeds vs. Distance from the Sun Kepler noted that more distant planets move slowly relative to closer planets Kepler speculated that it might result from a force from the Sun Planets farther away move slower than planets close in Also, from Kepler s third law, we know that the period of the blue planet is twice that of the red planet a 3 blue P 2 blue = a3 red P 2 red (courtesy of Mike Zingale) Kepler s 3rd Law: Geosynchronous Satellites The orbital period is 24 hours to keep them in sync with Earth's rotation. What is the orbital radius? We can use the Moon's data: Pmoon = 27.3 days, amoon = 384,000 km & Kepler s Third Law to solve this problem 2/3 2/3 Psat 1 a sat = a moon =3.84 10 5 km = 42400 km P moon 27.3 Galileo Galilei (1564-1642 A.D.) Best known for using the telescope for astronomical purposes. His discoveries added support to the heliocentric model of the solar system Also known for testing gravitational acceleration by simultaneously dropping two different size masses from the top of the Tower of Pisa (see Chapter 4). 60
Objections to Kepler s model Aristotle had held that the Earth could not be moving because, if it were, objects such as birds, falling stones & clouds would be left behind as Earth moved along its way Galileo s rebuttal: A rolling ball - a moving object remains in motion unless a force acts to stop it. Objects sharing Earth's motion through space will continue to. Objections to Kepler s model Noncircular motion contradicted Aristotle s claim that the heavens - the realm of the Sun, Moon, planets & stars - must be perfect & unchanging Rebuttal: unchanging heavens - Tycho had observed a comet & a supernova, evidence that the heavens are not static. perfection - Sunspots and mountains on the Moon show deviations from perfection 61 Objections to Kepler s model No one had detected stellar parallax that should occur if Earth orbits the Sun Rebuttal: Lack of parallax - Galileo used a telescope to resolve the Milky Way into faint stars; stars are farther away and more numerous that Tycho & others believed 62 Additional Evidence: (1) Moons of Jupiter I.e., the moons could stay with a moving Jupiter Below is an image of Jupiter & 3 of the 4 moons Galileo saw (Io is behind Jupiter). Taken with the Mars Global Surveyor The moons of Jupiter: Galileo s Logbook 63
Additional Evidence: (3) Phases of Venus Phases of Venus Ptolemaic model = Venus would always be in a crescent phase Galileo (1564-1642) + telescope = Venus has phases, as expected if it orbits the Sun & its orbit is interior to the Earth s orbit Crescent Moon & Venus Prediction: Mercury Transit Kepler s laws had predicted the transit of Mercury across the face of the Sun...... which was observed in 1631
Galileo s fate A Catholic Church doctrine: the Earth is the center of the Universe In 1633, a 70-year old Galileo was brought before the Church in Rome to recant his claim. Which he did for fear of his life The Church did not vindicate Galileo until 1992 What is Science? Science: the intellectual & practical activity encompassing the systematic study of the structure & behavior of the physical & natural world through observation & experiment Scientific Method The principles & empirical processes of discovery & demonstration considered characteristic of or necessary for scientific investigation, generally involving The Scientific Method a) The observation of phenomena b) The formation of a hypothesis concerning the phenomena c) Experimentation to demonstrate the truth or falseness of the hypothesis d) & a conclusion that validates or modifies the hypothesis The method employed in exact science & consisting of a) Careful & abundant observation & experimentation b) Generalization of the results into formulated Laws & statements
A simple example of the process observation: a flashlight isn t working hypothesis: the batteries are dead prediction: if the batteries are replaced by new batteries, the flashlight will work test: replace the batteries hypothesis supported: flashlight works or... hypothesis not supported: flashlight still doesn t work new hypothesis: the bulb is burned out. etc., Hallmarks of Science E.g., Tycho s careful measurements of planetary motion motivated Kepler to come up with a better explanation for these measurements. Hallmarks of Science Hallmarks of Science Several competing models of the Universe were compared & tested Occam s Razor: The simplest explanation is likely to be the correct one E.g., A heliocentric model is much simpler than an geocentric model
Hallmarks of Science Each model could make precise predictions about the future motions of celestial objects. Failure resulted in modifications Hallmarks of Science Verifiable Observations A scientific method must make testable predictions E.g., the existence of UFOs is hard to verify. In contrast, Einstein s theory of relativity, though difficult to understand, makes testable predictions which one can verify UFO over Miami, February 1, 2010 Objectivity in Science Science is done by people, and people have biases E.g., in terms of early planetary motion models, the belief in the perfection of the circle Lack of objectivity can slow things down, but ultimately the scientific method prevails (i.e., Kepler s laws of motion usurping both Ptolemy s & Copernicus s models) Theory Theory: a model that makes predictions that survive repeated & varied testing We will talk soon about Newton s theory of gravity, which uses a simple set of physical principles to explain many observations & experiments Einstein s theory of relativity explains all of the observations covered by Newton s theory, as well as other observations not explainable with Newton s theory An even more general theory of gravity is in the works
Astrology astrology: the apparent positions of the Sun, Moon and planets among the stars in our sky influence human behavior Astrologers & astronomers used to be one in the same Astrology Superstition results from the lack of understanding of the true nature of things. I.e, if a catastrophic event happened when a comet appeared in the sky, the natural superstition is that a similar event may happen every time a comet appears Astrology The break point between astronomy & astrology astronomy was seen as a science that could help us to understand the Universe. I.e., the work of Kepler & Galileo Regardless... many well-known astronomers such as Kepler practiced astrology. Probably for money Astrology There is special meaning in the patterns of the stars in the constellations: We know that stars that are in the same part of the sky are not really associated with each other The position of the planets among the constellations is important: Planets only appear to be wandering among the stars, & planets are a lot closer to us than stars A proper horoscope accounts for the positions of all planets: But Uranus & Neptune were discovered relative recently. What about the positions of dwarf planets?
Loose Ends: Orbital Properties Loose Ends: Titius-Bode Rule (Bode s Law) Kepler s 3rd law: The eccentricity of most of the orbits is ~ 0.0. I.e., planetary orbits are circular. The inclination of most of the orbits is ~ 0 o. Bode s Law?? Bode s Law: Plus: Rule developed before asteroid belt was discovered Minus: No underlying physics. Minus: Neptune (& Pluto) do not fit Minus: n = - for Mercury?? Loose Ends: How Do We Know The Earth Rotates? Looking down onto the Earth along the polar axis Foucault pendulum swings in the same plane Earth's rotation makes it look like it twists Ground traversed at each latitude in time t NP Equator The higher the latitude, the smaller the circle traveled in one day, and the slower the ground speed
No rotation vs. Rotation No Rotation Eastward Westward View from over the north pole Air moving south No Rotation Rotation Eastward Westward Cumulative Effect - South-moving air veers to the southwest
Loose Ends: How Do We Know The Earth Rotates? Planet Rotation causes air moving on a planet to deviate from a straight line trajectory (coriolis effect) The coriolis effect is also felt on a spinning carousel Loose Ends: How Do We Know The Earth Rotates? Coriolis effect makes hurricanes spin counter-clockwise in the Northern hemisphere. It does not affect your toilet flush. Hurricane Katrina showing counterclockwise rotation due to the Coriolis effect. (NOAA) Circulation direction of a hurricane in the Northern hemisphere Loose ends: Leap years The length of a year is ~ 365.25 days, not 365 days. Thus, every fourth year has 366 days. Adding a day every 4 years helps to solve this problem