ISS Hill Equation Simulator

Mission Layer • Trajectory Domain
v1.0.0 MIT License Updated: 2025-08-23

Interactive 2D simulation of relative motion near the International Space Station using Hill/Clohessy-Wiltshire equations. Analyze relative orbits, approach ellipses, and keep-out spheres for spacecraft proximity operations.

References

Clohessy, W. H., & Wiltshire, R. S. (1960). Terminal guidance system for satellite rendezvous. Journal of the Aerospace Sciences, 27(9), 653-658. Hill, G. W. (1878). Researches in the lunar theory. American Journal of Mathematics, 1(1), 5-26.

2.8 m/s
15 s
2 rev
ΔV Magnitude: 1.5 m/s
Status: Ready
Position (R,V): 0.0, 0.0 m
Velocity (Ṙ,V̇): 0.0, 0.0 m/s
Radial Distance: 0.0 m
Radial Velocity: 0.0 m/s
Elapsed Time: 00:00:00
Min Miss Distance: -- m
Initial Conditions: --
Click canvas to set initial position
LVLH Frame: R-bar (radial), V-bar (velocity)
Trajectory
Spacecraft
Approach Ellipse
Keep-Out Sphere

How to Use

  • Click on canvas to set initial spacecraft position in LVLH frame
  • Set ΔV magnitude and direction (R-bar/V-bar only)
  • Click Run to start simulation, Pause to pause, Reset to clear
  • Use Export buttons to save trajectory data or visualization

Hill/Clohessy-Wiltshire Equations

The Hill equations describe relative motion in the LVLH (Local Vertical, Local Horizontal) frame:

  • ẍ - 2nẏ - 3n²x = aₓ
  • ÿ + 2nẋ = aᵧ

Where n = mean motion (≈ 0.001166 rad/s for ISS at ~408km altitude), (x,y) = (R-bar, V-bar) position, (aₓ,aᵧ) = accelerations.

Safety Zones

  • Approach Ellipsoid (AE): 4km × 2km safety zone around ISS
  • Keep-Out Sphere (KOS): 200m radius critical safety zone