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

    Frequently Asked Questions

    Why is bound orbit energy negative?

    The gravitational potential energy (negative) exceeds the kinetic energy, so the total is negative and the body cannot escape.

    How does energy relate to orbit shape?

    Energy depends only on the semi-major axis, not eccentricity. A circle and an elongated ellipse with the same a have the same energy.

    What happens at exactly zero energy?

    The orbit is parabolic, corresponding to escape velocity at every point.

    Ready to run the numbers?

    Open Specific Orbital Energy Calculator