Early Discoveries about the Earth and Sky (cont.)
Examples of deductive reasoning
- Is the Earth flat or round?
- early sea-faring peoples noticed that ships disappeared over
the horizon, but most ships returned
- Aristotle concluded the Earth was spherical for several other good
- Which is closer to the Earth, the Sun or the Moon? Aristarchus of Samos figured it out in about 280 B.C. How can you tell? Hint:
Go here for an animation showing the phases of the Moon.
- Moon reflects sunlight
- how does Moon look to us for different Sun, Moon, Earth arrangements?
- at 90 degrees, if Moon was further than Sun, it would look fully illuminated
- at 90 degrees, if Moon was closer than Sun, it would look 1/2 illuminated ---> thus, Moon closer than Sun
- Which is larger, the Earth or the Moon? How can you tell? Hint:
Go here for an animation showing an
- lunar eclipse -- how many Moon's fit in Earth's shadow? about 3 Moons
- What is the distance to the Moon?
- What is Earth's size? Eratosthenes, 200 B.C., Alexandria
- compared length of shadows at same time of day at two different locations
- difference in length of shadows related to the angle at which you are looking at Sun, to Earth's curvature from Syene and Alexandria
(1/50 of Earth's circumference)
- relating angular difference to linear distance gives you
the circumference of Earth
- calculation was only off true value by 20%!
- How do we know the Earth's tilt? Eratosthenes again...
- measured difference between noontime elevation of Sun in winter and summer
- divide the difference by two to get the angle of the tilt
- deduced that Earth's equator is tilted by 23.5 degrees
- difference in height of Sun at different times gives latitude
- What causes
Go here to relate the composer Vivaldi's ``The Four Seasons''
to the motion of the Earth.
- light from a flashlight is more intense when focused over a smaller area
- light from a flashlight is less intense when it is spread out by tilting the flashlight
- similarly, the tilt of Earth's rotational axis and the Earth's orbit around
the Sun work together to create the seasons
- because the Earth's axis tilts toward Sun in summer, the Northern
Hemisphere receives concentrated light
- because the Earth's axis tilts away from the Sun in summer, the Northern
Hemisphere receives light that has been spread out ---> less of the
Sun's energy heats a given area of the surface ---> cooler
The Copernican Revolution
A brief history of cosmology
- in 350 B.C.,
Aristotle proposes that Sun and all other heavenly bodies orbit Earth
- in 250 B.C., Aristarchus proposes Sun-centered, or
heliocentric, model, but not accepted because
- in 140 A.D., Ptolemy revives Aristotlean cosmology
- but planets show retrograde motion! Ptolemy was forced to
explain such motion with a complicated system of epicycles
- in 1500, Copernicus adopts heliocentric model
- beautiful and elegant in its explanation of retrograde motion (click on figure for retrograde animation)
The Copernican explanation of retrograde motion.
As Earth overtakes Mars (a-c), it appears to slow
its eastward motion. As Earth passes Mars(d),
it appears to move westward (retrograde). As Earth
draws ahead of Mars (e-g), it resumes its eastward
motion against the background stars.
The positions of Earth and Mars are shown at equal
intervals of 1 month.
- not totally correct, as it predicted that the planets all move in
circular orbits around the Sun
Birth of modern astronomy
- Galileo's observations
- tests of Copernican theory
- sunspots and Sun's rotation (click image to see the Sun rotate)
- Jupiter's four large (Galilean) moons
- phases of Venus (full when smallest ---> full on far side of Sun ---> orbiting Sun)
- rate of change of velocity
- independent of weight or composition
- example: feather and hammer fall to ground at same time on Moon (astronaut movie)
- resistance of any object to a change in its motion
- example: ball dropped from ship's mast
- frame of reference
- atmosphere carried with Earth, so we don't feel our motion
- cabin of smoothly sailing ship
- astronauts on Space Shuttle
- Kepler's Laws