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Orbital Mechanics Calculator

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

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How to Use This Calculator
  1. Follow the step-by-step wizard — complete each step before moving to the next. This guided approach ensures you provide all the necessary information in a logical order.
  2. Calculation Type — Calculation mode to use. Choose from: Kepler's Laws & Orbits, Hohmann Transfer & Delta-V, Escape Velocity & SOI, Lagrange Points, Relativistic Effects. default: 0.
  3. Central Body Mass (M☉) — Mass in solar masses default: 1.
  4. Semi-Major Axis (AU) — Average orbital distance default: 1.
  5. Eccentricity — 0 = circle, <1 = ellipse, 1 = parabola default: 0.017.
  6. Inclination (degrees) — Angle from reference plane default: 0.
  7. Central Body Mass (M☉) — enter a numeric value. default: 1.
  8. Starting Orbit (AU) — Earth orbit = 1 AU default: 1.
  9. Target Orbit (AU) — Mars orbit ≈ 1.52 AU default: 1.524.
  10. Body Mass (Earth masses) — enter a numeric value. default: 1.
  11. Body Radius (Earth radii) — enter a numeric value. default: 1.
  12. Parent Body Mass (Earth masses) — Sun ≈ 333,000 Earth masses default: 333,000.
  13. Orbital Distance (AU) — enter a numeric value. default: 1.
  14. Primary Mass (M☉) — Larger body (e.g., Sun) default: 1.
  15. Secondary Mass (M☉) — Smaller body (Earth ≈ 3e-6 M☉) default: 0.000003.
  16. Separation (AU) — enter a numeric value. default: 1.
  17. Central Mass (M☉) — enter a numeric value. default: 1.
  18. Orbital Radius (AU) — Mercury ≈ 0.387 AU default: 0.387.
  19. Object Velocity (km/s) — Mercury ≈ 47.87 km/s default: 47.87.
  20. Once all inputs are set, review your results in the Results panel. Here's what each output means:
  21. Orbital Period (years) — shown as a numeric value. This is the primary result of this calculator.
  22. Mean Velocity (km/s) — shown as a numeric value. This is the primary result of this calculator.
  23. Total Delta-V (km/s) — shown as a numeric value. This is the primary result of this calculator.
  24. Escape Velocity (km/s) — shown as a numeric value. This is the primary result of this calculator.
  25. L1 Distance (M km) — shown as a numeric value. This is the primary result of this calculator.
  26. L2 Distance (M km) — shown as a numeric value. This is the primary result of this calculator.
  27. Time Dilation (%) — shown as a numeric value. This is the primary result of this calculator.
  28. Orbital Period (days) — shown as a numeric value.
  29. Perihelion (AU) — shown as a numeric value.
  30. Aphelion (AU) — shown as a numeric value.
  31. Perihelion Velocity (km/s) — shown as a numeric value.
  32. Aphelion Velocity (km/s) — shown as a numeric value.
  33. Orbit Type — your calculated result.
  34. Departure ΔV (km/s) — shown as a numeric value.
  35. Arrival ΔV (km/s) — shown as a numeric value.
  36. Transfer Time (days) — shown as a numeric value.
  37. Phase Angle (°) — shown as a numeric value.
  38. Launch Window (years) — shown as a numeric value.
  39. Surface Gravity (g) — shown as a numeric value.
  40. Sphere of Influence (km) — shown as a numeric value.
  41. Hill Sphere (km) — shown as a numeric value.
  42. Roche Limit (km) — shown as a numeric value.
  43. Sync Orbit Altitude (km) — shown as a numeric value.
  44. L4/L5 Distance (AU) — shown as a numeric value.
  45. L4/L5 Stability — your calculated result.
  46. Orbital Period (days) — shown as a numeric value.
  47. Schwarzschild Radius (km) — shown as a numeric value.
  48. Precession ("/century) — shown as a numeric value.
  49. Gravitational Redshift (ppm) — shown as a numeric value.
  50. Lorentz Factor — shown as a numeric value.
  51. View the Orbital Comparison below for a visual breakdown of how the numbers relate to each other.
  52. Check the Orbital Parameters for a detailed row-by-row breakdown. This is useful for spotting trends or finding values at specific points.
  53. Explore the related calculators below if you need deeper analysis or want to approach this topic from a different angle.
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Formula

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

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