Orbital Mechanics Calculator

Complete orbital mechanics calculations. Kepler's laws, Hohmann transfers, delta-v, Lagrange points, escape velocities, and relativistic effects.

Progress0%

Step 1 of 2

Calculation Type

Central Body Mass (M☉)

Semi-Major Axis (AU)

How to Use This Calculator

Use the Kepler module to enter semi-major axis (AU) and central mass (solar masses) to compute Orbital Period and Mean Velocity.
In the Hohmann Transfer section, enter departure and arrival orbit radii to get Total Delta-V (km/s) and Transfer Time (days).
Check Lagrange Points to find stable gravitational equilibria — L4 and L5 are stable, L1/L2/L3 are unstable.
Use the Roche Limit and Hill Sphere outputs to determine where a satellite will survive vs. be tidally disrupted.
Review the orbital comparison chart against the solar system planets to contextualize your orbit.

What each input means

Calculation Type: Calculation mode to use.
Central Body Mass (M☉): Mass in solar masses
Semi-Major Axis (AU): Average orbital distance
Eccentricity: 0 = circle, <1 = ellipse, 1 = parabola
Inclination (degrees): Angle from reference plane
Starting Orbit (AU): Earth orbit = 1 AU
Target Orbit (AU): Mars orbit ≈ 1.52 AU
Parent Body Mass (Earth masses): Sun ≈ 333,000 Earth masses
Primary Mass (M☉): Larger body (e.g., Sun)
Secondary Mass (M☉): Smaller body (Earth ≈ 3e-6 M☉)
Orbital Radius (AU): Mercury ≈ 0.387 AU
Object Velocity (km/s): Mercury ≈ 47.87 km/s

How this is calculated

Formula

T² = (4π²/GM)a³ (Kepler's 3rd) | v = √(GM/r) | ΔV = v_transfer - v_circular

Worked example, using the default values

Identify Input Parameters
4 parameters
Calculation Type = 0, Central Body Mass (M☉) = 1, Semi-Major Axis (AU) = 1, Eccentricity = 0.017 = 18 input(s) provided
Calculate Orbital Period
Orbital Period
0.9998918722467838 = 0.9998918722467838
Calculate Mean Velocity
Mean Velocity
29.7888993205065 = 29.7888993205065
Calculate Orbital Period
Orbital Period
365.21050633813775 = 365.21050633813775
Calculate Perihelion
Perihelion
0.983 = 0.983

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

Astrophysics & Astronomy

Stellar Physics Calculator

Complete stellar physics calculations. Analyze luminosity, temperature, nuclear fusion, stellar evolution, black body radiation, and stellar distances.

Astrophysics & Astronomy