rationale
8. In both Hipparchian and Ptolemaic systems, the planets are assumed to move in a small circle called an epicycle, which in turn moves along a larger circle called a deferent. Both circles rotate clockwise and are roughly parallel to the plane of the Sun's orbit (ecliptic). Despite the fact that the system is considered geocentric, the planets' motion was not centered on the Earth but on what is called the eccentric. The orbits of planets in this system are epitrochoids.
The epicycle rotated and revolved along the deferent with uniform motion. However, Ptolemy found that the rate at which the deferent revolved was not constant unless he measured it from another point at an equal distance from the eccentric, which he called the equant. It was the angular rate at which the deferent moved around the equant that was constant. It was the use of the equant that distinguished the Ptolemaic system.
Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest. All of his calculations were done with respect to a normalized deferent. This is not to say that he believed the planets were all equidistant. He did guess at an ordering of the planets. Later he calculated their distances in the Planetary Hypotheses.
For superior planets the planet would typically move through in the night sky slower than the stars. Each night the planet would "lag" a little behind the star, in what is called prograde motion. Occasionally, near opposition, the planet would appear to move through in the night sky faster than the stars, called retrograde motion. Ptolemy's model, in part, sought to explain this behavior.
The inferior planets were always observed to be near the sun, appearing only shortly before sunrise or shortly after sunset. To accommodate this, Ptolemy's model fixed the motion of Mercury and Venus so that the line from the equant point to the center of the epicycle was always parallel to the earth-sun line.
17. Supernova in Cassiopeia.
Although,
The epicycle rotated and revolved along the deferent with uniform motion. However, Ptolemy found that the rate at which the deferent revolved was not constant unless he measured it from another point at an equal distance from the eccentric, which he called the equant. It was the angular rate at which the deferent moved around the equant that was constant. It was the use of the equant that distinguished the Ptolemaic system.
Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest. All of his calculations were done with respect to a normalized deferent. This is not to say that he believed the planets were all equidistant. He did guess at an ordering of the planets. Later he calculated their distances in the Planetary Hypotheses.
For superior planets the planet would typically move through in the night sky slower than the stars. Each night the planet would "lag" a little behind the star, in what is called prograde motion. Occasionally, near opposition, the planet would appear to move through in the night sky faster than the stars, called retrograde motion. Ptolemy's model, in part, sought to explain this behavior.
The inferior planets were always observed to be near the sun, appearing only shortly before sunrise or shortly after sunset. To accommodate this, Ptolemy's model fixed the motion of Mercury and Venus so that the line from the equant point to the center of the epicycle was always parallel to the earth-sun line.
17. Supernova in Cassiopeia.
Although,