Kepler's first law states the sun is at one of two focii of an ellipse (orbit of the planet), not the center; the distance between a planet and the sun is always changing as the planet goes around its orbit. Kepler's second law states the line which joins a planet to the sun covers equal areas in equal times as a planet completes its orbit. Therefore, as a planet nears the sun it moves faster. According to Kepler's third law of planetary motion, a planet's orbit size is directly related to the time it takes for a planet to orbit the sun.
To calculate orbit, Kepler's third law calculation is used, which states that the cube of the semi-major axis of a planet (a) is equal to the square of the period of the orbit (P): a^3 = P^2. Plug in the given semi-major axis of the planet into the equation. The semi-major axis is always labeled in astronomical units (AUs). For example, if the semi-major axis of a planet is 20, you would set 8,000 (20^3) equal to T squared.
Solve for the unknown variable. In this example, if 8,000 = P^2, find the square root of both sides to solve for P. Determine the value of P, in years. For example, if 8,000 = P^2, then determining the square root of 8,000, T equals approximately 89. Therefore, the calculated planetary orbit is 89 years. You may calculate the semi-major axis (a) of a planet if you are given the orbital period (P). Merely use the same calculation, and plug in the variable information for P while solving for a.