How to Calculate the Eccentric Anomaly

The parameter known as eccentric anomaly is an important part of celestial mechanics and is used to define the movement of a body along an elliptical Kepler orbit in terms of its position. The eccentric anomaly can be regarded as the value of an angle formed by drawing a vertical line from any point P situated on the orbit of an ellipse to the major axis of the ellipse. This parameter is also part of the three values used to define the position of an element on an orbit.

Things You'll Need

  • Calculator
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Instructions

    • 1

      Draw an ellipse and choose any point P situated on it.

    • 2

      Write down the two basic formulas for calculating the eccentric anomaly. These are "cos E = x / a" and "sin E = y / b", where "x" and "y" are the coordinates of the point you chose in the previous step. "A" and "b" represent the semi-major and semi-minor axes of the ellipse respectively.

    • 3

      Compute one of the two values with a calculator. That is, compute "x/a" or "y/b." You may compute both to double-check your work in the next step.

    • 4

      Use the acos or asin function to calculate the eccentric anomaly E, depending on which value you computed in the previous step. If you calculated "x/a" in step 3, you will use the acos function. If you calculated "y/b" in step 3, you will use the asin function. You may calculate both to double-check your work.

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