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

1 Answer
Aug 20, 2017

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


The Earth's orbit is elliptical and the distance #r# of the Earth from the Sun can be calculated as:

#r = (a(1-e^2))/(1-e cos theta)#

Where #a=149,600,000km# is the semi-major axis distance, #e=0.0167# is the eccentricity of the Earth's orbit and #theta# is the angle from perihelion.

#theta=(2 pi n)/365.256#

Where #n# is the number of days from perihelion which is 3rd January.

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.