Editing Equant (section)

===Hipparchus===
In models of planetary motion that precede [[Ptolemy]], generally attributed to [[Hipparchus]], the eccentric and epicycles were already a feature. The Roman writer [[Pliny the Elder|Pliny]] in the 1st century CE, who apparently had access to writings of late Greek astronomers, and not being an astronomer himself, still correctly identified the [[line of apsides|lines of apsides]] for the five known planets and where they pointed in the zodiac.<ref>{{cite book |author-link=Pliny the Elder |author=Gaius Plinius Secundus |title=Naturalis Historia |trans-title=Natural History |title-link=Natural History (Pliny) |at=Book 2, Chapter 13 |section=An account of the world and the elements: Why the same stars appear at some times more lofty and some times more near |section-url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D2&force=y |access-date=7 August 2014}}</ref> Such data requires the concept of eccentric centers of motion.  

Before around the year 430&nbsp;BCE, [[Meton]] and [[Euktemon]] of Athens observed differences in the [[Season#Astronomical|lengths of the seasons]].<ref name=Evans/> This can be observed in the lengths of seasons, given by equinoxes and solstices that indicate when the Sun traveled 90&nbsp;degrees along its path. Though others tried, Hipparchos calculated and presented the most exact lengths of seasons around 130&nbsp;BCE.

According to these calculations, Spring lasted about {{nobr| {{sfrac|94|1| 2 }} days}}, Summer about {{sfrac|92|1| 2 }}, Fall about {{sfrac|88|1| 8 }}, and Winter about {{sfrac|90|1| 8 }}, showing that seasons did indeed have differences in lengths. This was later used as evidence for the zodiacal inequality, or the appearance of the Sun to move at a rate that is not constant, with some parts of its orbit including it moving faster or slower. The Sun's annual motion as understood by Greek astronomy up to this point did not account for this, as it assumed the Sun had a perfectly circular orbit that was centered around the Earth that it traveled around at a constant speed. According to the astronomer Hipparchos, moving the center of the Sun's path slightly away from Earth would satisfy the observed motion of the Sun rather painlessly, thus making the Sun's orbit eccentric.<ref name=Evans/>

Most of what we know about Hipparchus comes to us through citations of his works by Ptolemy.<ref name=Ptolemy-Almagest/> Hipparchus' models' features explained differences in the length of the seasons on Earth (known as the "first anomaly"), and the appearance of retrograde motion in the planets (known as the "second anomaly"). But Hipparchus was unable to make the predictions about the location and duration of retrograde motions of the planets match observations; he could match location, or he could match duration, but not both simultaneously.<ref>{{cite AV media |series=The New Astronomy |title=Equants, from Part&nbsp;1 of Kepler's ''Astronomia Nova'' |publisher=science.larouchepac.com |url=http://science.larouchepac.com/kepler/astronomianova/part1/5 |access-date=1 August 2014}} — An excellent video on the effects of the equant</ref>