Orbital Mechanics Calculator

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

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Recommended Tools

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Fundamentals of Astrodynamics (Bate, Mueller & White) - The inexpensive Dover classic on orbits, transfers and trajectories.
Six Easy Pieces (Feynman) - Feynman's short, brilliant introduction to the core ideas of physics.

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=2\pi\sqrt{\frac{a^3}{\mu}}

, circular velocity is

v_c=\sqrt{\frac{\mu}{r}}

, vis-viva is

v=\sqrt{\mu\left(\frac{2}{r}-\frac{1}{a}\right)}

, escape speed is

v_e=\sqrt{\frac{2\mu}{r}}

, and specific orbital energy is

\varepsilon=-\frac{\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.

Reference Book

University Physics with Modern Physics

Hugh D. Young and Roger A. Freedman · Pearson

A common undergraduate physics text covering mechanics, electricity, waves, energy, and introductory modern physics.

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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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