# Astronomical Unit

An Astronomical Unit is the approximate average (or mean) distance from the Earth to the Sun used to provide relative distances within the solar system.

**1 AU = 149,597,870.691 kilometers**

It is formally defined as the radius of an unperturbed circular orbit a body without mass would revolve about the sun in 2(π)/k days which is 365.2568983.... days.^{[1]} Since an AU is based on radius of a circular orbit and the orbit of the Earth is actually eliptical,^{[2]} one AU is really somewhat less than the average distance between the Earth and the Sun (which is approximately 150 million km or 93 million miles).^{[3]}

## History

Tycho Brahe, working without the aid of a telescope and using the work of Aristarchus of Samos,^{[4]} estimated the distance between the Sun and the Earth at 8 million kilometers (5 million miles), far less than the true value of AU. Aristarchus, possibly the first to propose the Earth orbited the Sun, had presumed the Sun was much closer to Earth than it really was.

Galileo and other astronomers, using telescopes, observed that Venus appeared as a round disk. When Earth and Venus were closest, Venus is almost one minute of arc (1/60 degree) in diameter. Using the assumption that Venus is about the same size as Earth, and using Kepler's laws of planetary motion, estimates of the distance between Earth and Venus were proposed. From these estimates the distance from Earth to the Sun were calculated. That led to a much better estimate of about 15,000 Earth radii which is considerably greater than the estimate by Aristarchus but still short of the mark.^{[5]}

Later, Johannes Kepler (1571- 1630) estimated the AU at 24 million kilometers (15 million miles). Vendelinus, sometime around 1630 used a telescope and Aristarchus' method to calculate a much more accurate value for the ratio of the Earth-Sun distance and the Earth-Moon distance. Vendelinus derived a ratio of about 229 (based on an angle of 89.75° ). In 1672, Giovanni Cassini came much closer to the real value of AU by employing observations of Mars. Cassini, observed Mars from Paris while a colleague, Jean Richer, observed Mars at the same time from French Guiana in South America, From these two comparisons, Cassini determined the parallax of Mars and was able to calculate first the distance from Earth to Mars, and then the distance from Earth to the Sun at 140 million kilometers (87 million miles). This value is lower, but very close to the modern day number.^{[6]}^{[7]}

## References

- ↑ where π (pi) equals 3.14159265358979323846 . . . and k is defined as the Gaussian constant exactly equal to 0.01720209895.
- ↑ an asymmetrical oval
- ↑ Astronomical Unit Near Earth Object Programme, NASA
- ↑ May Earth be Revolving around the Sun? Polar wind geotail, NASA
- ↑ Kepler's Three Laws of Planetary Motion Polar wind geotail, NASA
- ↑ The Scale of the Solar SystemPolar wind geotail, NASA
- ↑ The Distance to the SunDavid Sellers