* The Babylonians accumulated records of astronomical observations for many centuries. The records enabled them to see repeated patterns in the motions of the celestial objects. They used the patterns to predict the positions of the Moon and planets.
* The idea that the celestial bodies were
spheres and that they moved on perfectly circular paths originated
with Pythagoras and his students.
* Aristotle tought that all celestial motion must be circular
and that celestial bodies were spheres. He argued that the Earth
must be motionless at the center of the universe.
* Aristarchus showed that it is possible to use geometry to find the distance of the Moon and the relative distances of the Moon and Sun. By doing so he showed that the universe is enormous compared with the size of the Earth.
* The small angle equation describes the relationship of the angular diameter of an object to its linear diameter and its distance. If any two of these variables are known, the third can be found.
* Aristarchus proposed that the Sun, not
the Earth, is the center of the universe, but this idea was not
accepted by most other Greek astronomers.
* Eratosthenes found the difference in the altitude of the noonday
Sun at Syene and Alexandria. He showed that this is the same as
the difference in latitude of the two cities. This difference
allowed him to find the ratio of the circumference of the Earth
to the distance between Syene and Alexandria
* Hipparchus discovered Precession when he compared his measurements of stellar positions with those of earlier Greek astronomers. The celestial coordinates of stars change with time because of precession, the slow circular shifting of the celestial poles with respect to the stars.
* Greek astronomy culminated with the epicyclic system of Ptolemy. In Ptolemy's model the retrograde motion of a planet was produced by the combination of two circular motions.
* Epicycle . One of the circles upon which a planet moved according to the Ptolemaic (geocentric) model of the solar system. The center of the epicycle moved on a larger circle, called the deferent
* Deferent .One of the circles on which a planet moved according to the Ptolemaic model of the solar system
* A planet moved in a circle on an Epicycle,
which itself moved on a Deferent. The system could predict accurately
the positions of the planets and was in use for nearly 1500 years.
Astrology. Deferent. Epicycle. Equant. Geocentric. Precession
1. Precession is. The slow motion of the Earth's rotation axis on the celestial sphere
2. Something which is 100 km away has an angular size of 2 seconds
of arc. Approximately how tall is it . 1 m
3. An object with an angular size of 1 degree moves three times
farther away. What is its new angular size? 20 minutes of arc
4. Which of the following is a reason that the ancient Greek astronomers
rejected Aristarchus' heliocentric model of the solar system?
They could detect no stellar parallax
5. What quantity did Aristarchus have to estimate in order to
find the relative distances of the sun and the moon? The angle
between the sun and moon at the time of quarter moon
6. How did Eratosthenes determine the size of the Earth? By observing
the lengths of shadows at different locations
7. What evidence did Aristotle offer for his argument that the
Earth is a sphere? The shadow of the Earth during a lunar eclipse
is curved
8. An astronaut lands on an unknown planet. After walking a distance
of 200 km toward the north pole of the planet, she notices that
the pole star for that planet is 5 degrees higher in the sky.
What is the circumference of the planet? 14,400 km
9. Why were epicycles used in Ptolemy's model of the solar system?
To explain the retrograde motions of planets
10. What role did the equant play in Ptolemy's model of the solar
system? It made planets move among the stars at the right speed