# Astronomical Unit

### earth distance value constant

An astronomical unit (AU) is a unit of length that astronomers use for measuring distances within the **solar system**. One astronomical unit is the **mean** distance between the **Earth** and the **Sun**, called the semimajor axis, or 92,919,000 mi (149,597,870 km).

The relative distances between the Sun and the planets, in astronomical units, were known long before the actual distances were established. Kepler, in developing his third law, showed that the **ratio** of the square of a planet's period (the **time** to make one complete revolution) to the cube of the semimajor axis of its **orbit** is a constant; that is, the ratio is the same for all the planets. Kepler's law can be summarized by the formula a^{3}/p^{2} = K where a is the semimajor axis of the planet's orbit, p is its period, and K is the proportionality constant, a constant that holds for all bodies orbiting the Sun. By choosing the period of the Earth as one year and its orbital radius as one AU, the constant K has a numerical value of one.

Kepler's third law (in a more accurate form derived by Isaac Newton) can be used to calculate a precise value of the AU, if the exact **distance** between the earth and another **planet** can be measured. An early attempt took place in 1671, when Jean Cassini in Paris and Jean Richer about 5,000 mi (8,000 km) away in Cayenne, Guiana, simultaneously determined the **parallax** of **Mars**. Their measurements, which allowed them to calculate the distance from earth to Mars by triangulation, showed Mars to be about 50 million mi (80 million km) from Earth. Since the relative distance between Earth and Mars was known, it was a simple matter to determine the actual value of an AU in miles or kilometers. Today, the value of the AU is known very accurately. By measuring the time for a **radar** pulse to reach **Venus** and return, the distance can be calculated because radar waves travel at the speed of **light**.

See also Kepler's laws.

## User Comments

about 2 years ago

This is very good.

I wish to know the derivation of a formula that gives earth-sun distance in astronomical units if one know the day of the year.

d= 1- 0.01672*Cos(0.9856*(Julian day-4))

Thanks and Rgeards,

seshadri