Orbital Mechanics Calculator

Compute orbital period, characteristic velocities, specific orbital energy, and a simple Hohmann transfer estimate.

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What This Calculator Does

This calculator summarizes the core quantities of a Keplerian orbit from the gravitational parameter, semi-major axis, and eccentricity. It also estimates the delta-v required for a circular-to-circular Hohmann transfer to a target altitude around the same central body.

It combines Central Body, Gravitational Parameter μ, Body Radius, Semi-Major Axis to estimate Orbital Period, Circular Velocity, Periapsis Velocity.

Formula & Method

Core equations: Orbital period is T=2pisqrt{rac{a^3}{mu}}, circular velocity is v_c=sqrt{rac{mu}{r}}, vis-viva is v=sqrt{muleft(rac{2}{r}-rac{1}{a} ight)}, escape speed is v_e=sqrt{rac{2mu}{r}}, and specific orbital energy is arepsilon=-rac{mu}{2a}.

Notation used in the formulas: R = Orbital Period; x_{1} = Central Body; x_{2} = Gravitational Parameter μ; x_{3} = Body Radius; x_{4} = Semi-Major Axis; x_{5} = Eccentricity; x_{6} = Hohmann Target Altitude.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when comparing low-eccentricity parking orbits, checking how eccentricity changes periapsis and apoapsis speed, or estimating the transfer cost to raise a circular orbit to a new altitude.

Inputs Used

Central Body: Used directly in the calculation.
Gravitational Parameter μ: Used directly in the calculation.
Body Radius: Used directly in the calculation.
Semi-Major Axis: Used directly in the calculation.
Eccentricity: Used directly in the calculation.
Hohmann Target Altitude: Used directly in the calculation.

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