About Kepler's Laws & Vis-Viva Orbital Mechanics Calculator
Unified astrophysical solver for Johannes Kepler's Three Laws of Planetary Motion. Solves 1st Law ellipse geometry (semi-major axis a, semi-minor axis b, focal distance c, eccentricity e), 2nd Law areal velocity and Vis-Viva instantaneous orbital speed, and 3rd Law harmonic orbital period relationships around stars of any mass.
Key Capabilities & Features
- Complete 1st Law ellipse geometry: semi-major a, semi-minor b, focal distance c, and periapsis/apoapsis
- Vis-viva equation: v = √(GM(2/r - 1/a)) solving orbital speed at periapsis, apoapsis, and any radius
- Kepler 3rd Law harmonic equation solving orbital period in Earth years and days
- Constant areal velocity (dA/dt) calculation demonstrating equal areas swept in equal times
How to Use Kepler's Laws & Vis-Viva Orbital Mechanics Calculator
Input Semi-Major Axis
Enter orbital semi-major axis in Astronomical Units (AU) or kilometers.
Adjust Orbital Eccentricity
Slide eccentricity from 0.0 (circular) to 0.95 (highly eccentric comet orbit).
Set Central Star Mass
Specify primary mass in Solar Masses (defaults to 1.0 for the Sun).
Review Complete Orbital Profile
Examine periapsis and apoapsis distances, orbital speeds, period, and geometry.
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Orbital mechanics equations solve 100% client-side with instant reactivity.
Frequently Asked Questions
What does the Vis-Viva equation calculate in orbital mechanics?
The Vis-Viva equation (Latin for "living force") expresses the orbital speed of an object at any point in its Keplerian orbit as a function of its current distance (r) and its semi-major axis (a): v² = GM(2/r - 1/a).