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How to Calculate Planetary Orbit

Planetary orbit can be calculated simply using Kepler's third law of planetary motion. Kepler's third law states that the amount of time a planet takes to orbit the Sun, T, is related to its orbit's size, a. As long as you know the semimajor axis of a body orbiting the sun, the planetary orbit can be calculated by setting the cube of the semi-major axis (a) equal to the square of the period of orbit (T) in years. This is represented by the calculation a^3 = T^2.

Instructions

- 1
  Use the given semimajor axis of the planet whose orbit you desire to know. Plug it in for a in the equation a^3 = T^2.
- 2
  Calculate the cube (a^3) of the given information, and set it equal to T^2. (For example, if you know that the semimajor axis of Venus is 40, set the cube of 40 equal to T^2.)
- 3
  Determine the unknown quantity algebraically. If 40^3 = T^2, calculate the square root of both T^2 and 40^3.
- 4
  Solve for T, in years. In this example, then, since the square root of 40^3 (64,000) is approximately 253, the planetary orbit (T) is approximately 253 years.

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