Lecture 2: The Shape & Size of Earth Astronomy 1143 – Spring 2014

Key Ideas: The Earth is Round Height of Constellations Above the Horizon Shadow of Earth during a Lunar Eclipse Measuring Length -- Meters Measuring Angles Degrees, Minutes and Seconds Angular Distances & Sizes Measuring the Earth's Size Angle of Sun at two different locations

Classical Greece & Spheres The Ancient Greeks were intoxicated by geometry, form, and symmetry. A sphere is the most perfect geometric solid 500 BCE: Pythagoras proposed a spherical Earth on purely aesthetic grounds 400 BCE: Plato espoused a spherical Earth in the Phaedra.

Aristotle gets Physical... Aristotle ( BCE) proposed a spherical Earth on geometric grounds, Backed up with physical evidence: People living in the south see southern constellations higher above the horizon than people living in the north. The shadow of the Earth on the Moon during a lunar eclipse is round. Matter settling onto Earth would naturally shape itself into a spherical shape

The Basic Idea If the Earth is round, then people on different parts of Earth will see stars at different heights above the horizon. Sees North Star directly overhead Sees North Star on horizon

The Basic Idea This is much more realistic, considering the scale of the solar system. Sunlight

Looking South from Syene Egypt Latitude: 24º N Scorpius Looking South from Athens Greece Latitude: 38º N Scorpius

Orion: North and South

Thanks to a spherical Earth Southern constellations appear higher in the sky as you move south The North Star appears lower in the sky as you move south Constellations/the Moon/etc appear “upside-down” in the Southern Hemisphere compared to the Northern Hemisphere Some constellations are not visible in the Northern Hemisphere and vice versa for the Southern Hemisphere

Earth Shadow during Lunar Eclipse Multiple Exposure Photograph

No Flat Earth (or Moon) Aristotle’s demonstration was so compelling that a spherical Earth was the central assumption of all subsequent philosophers of the Classical era. He also used the curved phases of the Moon to argue that the Moon must also be a sphere like the Earth. We’ve established its shape, what’s its size? Need to use GEOMETRY

Units: A Useful Digression

The Metric System Astronomers use the Metric System: Length in Meters Mass in Kilograms Time in Seconds All scientists use Metric Units Only the United States, Liberia & Myanmar (Burma) still use “English” Units.

If you are not paying attention to units, bad things can happen 1.Your roller coaster could fall apart In 2004, an axle at Tokyo Disneyland’s space mountain broke mid-ride, because of problems in converting the English units to metric units 2.You could lose a $125 billion satellite In 1999, NASA lost the Mars Climate Orbiter. It was off course by 60 miles by the time it reached Mars because Lockheed Martin was sending the thruster force calculation in pounds and NASA was expecting Newtons

If you are not paying attention to units, bad things can happen 3.Your jet could turn into a glider In 1983, an Air Canada Boeing 767 flying between Montreal and Edmonton ran out of fuel and had to glide to a landing at a former Air Force base in Gimli, Manitoba. Among other mistakes, the crew had calculated the amount of fuel needed in pounds, rather than kilograms, but thought they had the correct number of kilograms. As a result, they had less than ½ the amount they needed 4.You could lose points on your homework

How many kilometers are in 10,000 meters? Or: convert 10,000 meters to kilometers

How seconds in a year?

Units of Length The basic unit of length is the meter (m) Traditional Definition: 1 ten-millionth the distance from the North Pole to the Equator of the Earth. Modern Definition: The distance traveled by light in a vacuum in 1 / th of a second. Commonly use meters and kilometers.

Measuring Angles A complete circle is divided into 360-degrees The Babylonians started this convention: 360 is close to 365, the days in a year. 360 is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120 & 180 without using fractions. Start by quartering the circle (90 degrees), then subdividing further using geometry. 1 degree of arc

Subdividing the Degree Degrees are divided into Minutes of Arc ('): 1 degree divided into 60 minutes of arc from “pars minuta prima” (1 st small part) 1 minute = 1 / 60 th of a degree Minutes are divided into Seconds of Arc ("): 1 minute divided into 60 seconds of arc from “parte minutae secundae” (2 nd small part) 1 second = 1 / 60 th of a minute or 1 / 3600 th of a degree (very small)

Question: Why 60? Answer: Blame the Babylonians is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, & 30 without using fractions. The Babylonians subdivided the degree as fractions of 60, for example: 7 14 / 60 degrees Claudius Ptolemy introduced the modern notation: 7º 14' 00" Subdividing the Degree (cont’d)

Eratosthenes of Cyrene Born in Cyrene (now Shahhat Libya) in 276 BCE, lived until about 195 BCE 2nd Librarian of Alexandria. At noon on the Summer Solstice in Syene Egypt (modern Aswan), the Sun was straight overhead and cast no shadows. On the same day, the noon Sun cast shadows in Alexandria, located north of Syene, 5000 stades away.

Tropic of Cancer Alexandria Syene

Shadowless in Syene No shadows on the Summer Solstice means that Syene is on the Tropic of Cancer. Alexandria is north of Syene along the Earth’s curved surface and shadows are cast. Measuring the angle of the Sun in Alexandria at noon on the Summer Solstice when it was overhead in Syene lets you measure the circumference of the Earth if you assume that the Sun is very, very far away!

Syene Alexandria Earth High Noon on the Summer Solstice Sunlight 7 12 / 60 º

Noon on the Summer Solstice At Syene: Sun directly overhead, no shadows cast At Alexandria: Sun 7 12 / 60 degrees south of overhead, casting a shadow Since a full circle is 360 degrees, the arc from Alexandria to Syene is

The Road to Syene The circumference of the Earth is 50 times the distance from Alexandria to Syene. How far is Alexandria from Syene? 5000 Stades How big is 1 Stade? 600 Greek Feet Best guess is 1 stade = 185 meters (Attic stade)

The Circumference of the Earth Eratosthenes computed the circumference of Earth as: 50  5000 stades = 250,000 stades 250,000 stades  185 meters/stade = 46,250 kilometers The modern value: 40,070 kilometers Eratosthenes' estimate is only ~15% too large

Units matter – historical example Columbus was not only convinced that he could reach the treasures of the East by sailing west, but also that it would be a short, relatively easy trip. Just a few days between Spain and the India! He presented sponsors, such as Queen Isabella and King Ferdinand, with small numbers from two main mistakes: Too large estimates for the size of Eurasia Misinterpreting number of Arabic miles as number of Roman miles (shrunk Earth by 25%) The rest, as they say, is history

Describing the Sky We do not “see” a 3-dimensional night sky We can describe brightnesses and colors and motions Stars appear as single points of light Planets are close to points of light (at least to the naked eye) Sun and Moon appear as actual extended objects Describe separation of stars on the sky and the apparent size of objects by angular distance and angular size

Angular Size

Angular Distance & Size

Angular Size Changes with Distance The angular size of a dime and quarter can be the same, even though their physical sizes are different

Measuring big distances Measuring distances and physical sizes in astronomy is very difficult Obvious methods such as meter sticks are out (there’s that whole lack of oxygen thing) We don’t usually have reference objects here on Earth to help us out Answer: Use geometry