What Is the Clohessy-Wiltshire (Hill’s) Orbital Relative Motion Calculator?
The Clohessy-Wiltshire equations model the relative trajectory between two spacecraft orbiting in close proximity.
How Does the Clohessy-Wiltshire (Hill’s) Orbital Relative Motion Calculator Work?
Linearizes gravitational and centrifugal equations of motion in the rotating Local-Vertical Local-Horizontal (LVLH) frame.
Clohessy-Wiltshire (Hill’s) Orbital Relative Motion Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
x(t) = (4 - 3cos nt)x_0, quad y(t) = y_0 - 6(nt - sin nt)x_0, quad dot{y}_{ ext{drift}} = -1.5 n x_0
Linearized Hill-Clohessy-Wiltshire equations in the local-vertical local-horizontal (LVLH) frame.
How to Use the Clohessy-Wiltshire (Hill’s) Orbital Relative Motion Calculator
- Enter target chief orbit altitude, initial radial, along-track, and cross-track offsets, and propagation time.
Step-by-Step Example Calculation
ISS Spacecraft Proximity Rendezvous Approach
Input Values:
chiefOrbitAltitudeKm:400
initialRadialOffsetXMeters:25
initialAlongTrackOffsetYMeters:100
initialCrossTrackOffsetZMeters:0
timeElapsedMinutes:45
Worked Steps: Relative position after 45 min: x = 175.0 m, y = -368.5 m, total relative distance = 408.0 m.
Understanding Your Result
Shows chaser position relative to target and calculates the secular along-track drift rate resulting from radial offset.
Factors That Affect the Result
- Any initial radial offset x0 alters the semi-major axis, causing Keplerian orbital period differences and drift.
When Should You Use This Calculator?
- Automated docking, satellite proximity operations (RPO), space station resupply, and satellite servicing.
Assumptions & Limitations
- Assumes target in circular orbit and small relative separation (< a few km) compared to orbit radius.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard linear relative motion formulation in orbital mechanics.