Orbital Energy Calculator

How it is calculated

The tool first finds the standard gravitational parameter, μ = G · M, with G = 6.67430×10⁻¹¹ m³ kg⁻¹ s⁻² and M the mass of the central body in kilograms. The semi-major axis a is typed in kilometres and converted to metres (× 1000). The specific orbital energy is then ε = −μ / (2a), in joules per kilogram of the orbiting body. Both results are printed in scientific notation with five significant figures. Mass and semi-major axis must be greater than zero, otherwise no result is produced. Because the formula always gives a negative number for a positive a, the tool describes bound (elliptical or circular) orbits; the energy is the same wherever the body is on that orbit. Note that a is measured from the centre of the central body, not from its surface.

Common mistakes

• Typing the semi-major axis in metres. The field expects kilometres, so entering 7000000 for a low Earth orbit makes the energy 1000 times too small in size.
• Entering the altitude above the surface instead of the semi-major axis. For Earth, a 600 km altitude orbit has a ≈ 6371 + 600 = 6971 km, because a is measured from the centre.
• Putting the mass in grams, solar masses or Earth masses. The field takes kilograms, so Earth is 5.972e24, not 1.
• Expecting the result to change with eccentricity or with the satellite's current position. Only a matters; a more elongated orbit with the same a has exactly the same energy.
• Confusing specific energy (J/kg) with the total energy of the spacecraft. Multiply by the spacecraft's mass to get joules.