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| Eratosthenes |
The philosopher Eratosthenes (276-194BC) was the first to use a geometric technique called parallax to calculate the Earths diameter and circumfrance. Eratosthenes later used this same technique to approximate the distance from te Earth to the Sun and the Earth to the Moon. Although people of his time didn't take Eratosthenes seriously, his calculations were actually pretty close. Today parallax, along with more precise instruments and calculations provide us with the ability to very accurately measure distances from the Earth to the Moon, Sun, asteroids, and other planets.
What is "parallax"?
The technique called trigonometric parallax uses geometric calculations to determine the distance from an observer to a remote object.
Parallax the the apparent change in position of an object, like an asteroid, when observer moves.
The above diagram (from Rochester Institute of Technology) is a good example of parallax, showing how two observers on Earth would see the moon 'in front of' a different place in the stars.
The angle (shown as theta on the picture), along with the distance between the two observers, can be used to tell the distance from the earth to the moon. This same technique can be used to find distances to asteroids, and other planets. Finding this distance over a period of time can give you the shape of an objects orbit.
What does parallax have to do with Eros?
In 1900 the orbit of Eros brought it about 29 million miles from Earth, and using Eros astronomers were able to calculate a much more precise distance from the Earth to the Sun than they had been able to acheive before.
In 1921 an astronomer named Noteboom, was able to derive the mass of the Earth from "From the strong perturbations of Eros caused by the earth", which led to an even better parallax calculation. His method of finding the parallax was called the "dynamical Eros method". This method uses Newton's laws of gravity, and the Earth/Moon mass to calculate parallax.
In 1931 Eros came even closer: about 16 million miles from Earth. A massive project was started that included about 40 observatories world wide. 10 years of extracing data from observations of Eros led to an extremely accurate understanding of the orbit of the asteroid.
In 1975 Eros made the closes pass by Earth since it was discovered in 1888. Using radar, astronomers were able to directly measure the distance from Earth to Eros. Radar works by sending out a radio pulse, and by listening to the echos (reflected by Eros). Since the radio pulse moves at the speed of light, the time it took for the echos to return allowed astromers to determine the distance from Earth to Eros.
No other significant findings were produced about Eros until the NEAR project set its sights on it.
More Information:
For a breif history of Eratosthenes, go to Eratosthenes of Cyrene
To learn more about parallax, see Distances within the Solar System
To find out more about how radar works, got to How Stuff Works: How Radar Works