Eratosthenes (3rd century B.C.)

Eratosthenes was able to measure the circumference of the Earth using very simple trigonometry and geometry. Eratosthenes knew that sunlight would shine directly down a well in Syene at noon on the summer solstice. On that same day, a building in Alexandria would cast a shadow which could be measured. By measuring the length of the shadow and the height of the building, the angle between Alexandria and Syene could be established. This angle was found to be approximately seven degrees. Since the distance between the two cities was known, the circumference of the Earth could be established.

Hipparchus (2nd century BC)

Perhaps three main concepts in astronomy may be attributed to Hipparchus. The first of these was the concept of epicycles and deferents which would be refined by Ptolemy years later. The second of these was the discovery of precession as was discussed earlier. Hipparchus was able to do so by comparing star chart which he had created with those of Babylonian astronomers some 300 years before. The last idea established by Hipparchus was the concept of magnitudes. The magnitudes system is the way astronomers rank the brightness of stars. Hipparchus considered the brightest stars in the sky to be first magnitudes stars and the faintest stars in the sky to be sixth magnitude stars.

To this day astronomers still use the magnitude system created by Hipparchus. However, the system has been refined more mathematically than Hipparchus had established 2000 years ago. The magnitude system is a logarithmic system. Each change of 1 in the star's magnitude is a change of 2.5 times the brightness. So a magnitude one star is 2.5 times brighter than a magnitude two star. Similarly, a magnitude two star is 2.5 times brighter than a magnitude three star. Therefore, a magnitude one star is 2.5 * 2.5 = 6.25 times brighter than a magnitude three star. Or a magnitude one star is about six times brighter than a magnitude three star. Always keep in mind that the smaller the number the brighter the star. This concept will be very important later in the course.

Ptolemy (2nd century A.D.)

Ptolemy refined the system of epicycles and deferents created by Hipparchus. This has been discussed in previous pages.

This page was last updated on 06/06/01.