# What is the mathematical equation used to calculate the distance between earth and the sun at any given day of the year?

##### 1 Answer

A good approximation to calculating the distance from the sun is to use Kepler's first law.

#### Explanation:

The Earth's orbit is elliptical and the distance

Where

Where

Kepler's law gives a fairly good approximation to the Earth's orbit. In actual fact the Earth's orbit is not a true ellipse as it constantly being changed by the gravitational pull of the other planets.

If you want a really accurate value you need to use numerical integration data such as NASA's DE430 data. This data consists of a large number of coefficients for a series of polynomial equations which have been derived from observations and satellite data.