Specific Orbital Energy Calculator Formula

Understand the math behind the specific orbital energy calculator. Each variable explained with a worked example.

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Formulas Used

Specific Orbital Energy

specific_energy = -6.674e-11 * central_mass / (2 * semi_major_axis)

Variables

VariableDescriptionDefault
semi_major_axisSemi-Major Axis(m)6771000
central_massCentral Body Mass(kg)5.972e+24

How It Works

Specific Orbital Energy

epsilon = -G M / (2a)

  • Negative energy = bound (elliptical) orbit
  • Zero = parabolic escape
  • Positive = hyperbolic trajectory

    • This quantity is constant along the entire Keplerian orbit.

    Worked Example

    ISS orbit with semi-major axis a = 6 771 km around Earth.

    semi_major_axis = 6771000central_mass = 5.972e+24
    1. 01epsilon = -G M / (2a)
    2. 02G M = 3.986e14
    3. 032a = 1.354e7
    4. 04epsilon = -3.986e14 / 1.354e7 ≈ -29.4 MJ/kg

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