Very little is known about Hipparchus. None of his major work survives, and most of what is known is due to what Ptolemy says in the Almagest. He was born in Nicaea, which is now the modern town of Iznik in Turkey. He lived and worked in Rhodes and Alexandria.
Hipparchus is often called the first real astronomer, as he was the first Greek to actually make systematic observations of the sky. He was also a very talented mathematician who made great strides in the development of the classic Greek model of the solar system.
Hipparchus catalogs the position and brightness of over 800 stars. He was the first person to record the actual angular positions using the ecliptic as a base line. He ranked the stars according to a brightness scale of six magnitudes.
He discovered the slight wobble in the axis of the earth's rotaion, also called the "Precession of the Equinoxes." The axis of the earth's rotation currently points to a spot near the Polaris - hence it is called the North Star as it doesn't move very much over the course of the night. Because of a slight gravitational effect, the axis is slowly rotating with a 26,000 year period, and Hipparchus discovers this because he notices that the position of the equinoxes along the celestial equator were slowly moving.
He calculates the length of the year to be 365 days, 5 hours, 55 minutes and 12 seconds long and calculates his error to be no more than 15 minutes. (It turns out he was only 6 minutes off.)
He also came up with another way to determine the distance to the moon. Using parallax, he was able to calculate that the moon was between 59 and 67 earth radii away. (The correct average distance is 60.) He did this from a solar eclipse. During a solar eclipse, the moon just covers the sun (remember that they are both about 1/2 degree in angular size.) However, only a very small portion of the earth can actually witness the eclipse in totality, because the shadow of the moon on the earth is fairly small. Hipparchus used data from a solar eclipse viewed from 2 different locations. The diagram below would represent a solar eclipse as viewed from 2 different places on the earth, labeled A and B.
Someone at A on the earth would see a total eclipse. Someone at B would only see a partial eclipse of the sun. In Hipparchus' case, he knew there was a total eclipse in the Hellespont (now called the Dardanelles) while the eclipse was only about 4/5 total in Alexandria, which is almost due south of the Hellespont. He would have known the latitudes of the 2 locations, and therefor know their angular separation. In the picture above, looking at the "bottom" edge of the moon, the small angle shown would be about 1/5 the size of the sun, or about 0.1 degrees. This lets him calculate the distance to the moon. One can approximate this as in the diagram below:.
Basically, we have 2 triangles with a common side. The distance between A and B is an arclength (and equal to the radius of the earth times the angular separation of And B.) One could also say that the distance between A and B is basically the arclength created as seen from the moon, so that it is equal to the distance to the moon times the small 0.1 degree angle Hipparchus had found. Both angles are small enough that we can assume that the arclengths are basically equal. (In the packet, I made up a problem using parallax that you can do without any approximations.)
Hipparchus also created the first reasonably accurate model of the motion of the sun and moon. Using the idea of epicycles, probably introduced by the mathematician Apollonius of Perga, he was able to create a model that accurately predicted some key positions of the moon's motion. He created a similar model to predict the position of the sun. (See the Ptolemy page for more information on epicycles and its subsequent use in the planetary models.) His model didn't work for all cases, but it marked the real beginning of trying to create a predictive model that matched data.
Even though the orbits are circular and going around the earth, the earth is not at the exact center of the orbits of the sun and moon. (They were eccentric orbits.) Hipparchus needed to use the epicycles and eccentric orbits because the observed motion of the sun around the ecliptic was not at a constant rate - in the winter the sun moved a little bit faster and in the summer the sun moved a little bit slower. Using an eccentric orbit for the sun and moon, and using small epicycles, Hipparchus gives the foundations of the classic Greek model of the solar system that approximately predicts the positions of the moon and sun that matched positions and predicted key dates and events pretty well. Eventually, Ptolemy takes this Hipparchan model and fully applies it to the motion of the planets - and eventually produces a full, working model of the solar system.
On a side note, Hipparchus was also a pioneer in the development of trigonometry, and was the first person to make and use a table of chords (similar to the sine function.) This makes it much easier to solve a general problem involving triangles. Because of this, some historians argue that Hipparchus really changed Greek astronomy from a more theoretical exercise to the developing an actual predictive model of the solar system.