Kepler’s Laws of Planetary Motion help us calculate the position of stars.

The positions of planets are calculated using a series of algorithms (mathematical formulas) *based upon* Kepler’s Laws of Planetary Motion. Johannes Kepler was a mathematician and astronomer who lived in the late 16th and early 17th centuries. He developed three laws based upon his belief that the planets revolved around the sun. These laws help scientists, teachers, students and anyone with an interest in astronomy calculate the positions of the planets in relation to the sun and Earth.

## Instructions

## Calculating Planetary Positions

1. The position of the planet in relation to the sun is known as heliocentric.

Calculate the ecliptic longitude and latitude of the planet. After choosing your planet, you must formulate its ecliptic position in relation to the sun. For this you will need to calculate the semi-major axis of the planet’s orbit, distance from the sun to the planet, point of closest passage to the sun, and angle of the planet in relation to its point of closest passage to the sun. You will use astronomical units to determine distance and time measured in years. This calculation is the heliocentric (sun-centered) position of the planet.

2. The celestial equator is elliptical and coordinates are based on different variables.

Convert the heliocentric position into a geocentric position. Continuing to use algorithms set forth by Kepler’s Laws, you must determine the position of the planet in relation to Earth. This is the planet’s geocentric position. Formulation of this position will provide you with the ecliptic coordinates of the planet in relation to Earth.

3. Coordinates must be remapped because planetary positioning changes every day.

Determine the equatorial coordinates through converting ecliptic coordinates. On Earth, we use equatorial coordinates to determine position of locations on the planet. The equator is used to determine longitude and latitude. Determining the location of a planet, in relation to Earth, requires using the celestial equator, which has a right ascension and declination. Use Greenwich Mean Time when calculating these coordinates, as set forth in Kepler’s Laws. Determine where the right ascension of the planet meets with the ecliptic. This formulation will provide you with the planet’s position in relation to Earth. Your coordinates will not be exact, but providing you complete the equations correctly, you will calculate the position within a few minutes of accuracy.