Tool 11 · Rendezvous & Relative Motion

Rendezvous Planner

Plan a simple impulsive rendezvous in the LVLH frame using HCW targeting. Enter the chaser's initial relative position, choose a desired final point near the target, select a transfer time, and compute the burn required to arrive at that point.

What this tool computes

This planner uses the Hill–Clohessy–Wiltshire equations as a linear targeting model. Instead of only showing natural drift, it solves for the initial velocity change needed to move the chaser from its current relative position to a desired final relative position after a selected transfer time.

  • Required initial relative velocity after burn
  • Required burn vector \(\Delta\mathbf v_1\)
  • Arrival relative velocity at the final point
  • Optional stopping burn \(\Delta\mathbf v_2\)
  • Total two-impulse rendezvous cost
  • 3D LVLH transfer path and range history

Targeting idea

HCW propagation can be written in state-transition form:

\[ \begin{bmatrix}\mathbf r_f \\ \mathbf v_f\end{bmatrix} = \begin{bmatrix}\Phi_{rr} & \Phi_{rv} \\ \Phi_{vr} & \Phi_{vv}\end{bmatrix} \begin{bmatrix}\mathbf r_0 \\ \mathbf v_0\end{bmatrix} \]

To hit a desired final position, solve the position equation for the required initial velocity:

\[ \mathbf v_0 = \Phi_{rv}^{-1}\left(\mathbf r_f - \Phi_{rr}\mathbf r_0\right) \]

Rendezvous interpretation

The first burn places the chaser onto a relative trajectory that reaches the desired final point at the chosen time. If the goal is to stop relative to the target at arrival, a second burn removes the arrival relative velocity.

  • Burn 1: inject into the targeted relative transfer path.
  • Coast: follow HCW relative dynamics.
  • Burn 2: optional braking burn to reduce final relative velocity.

Safety insight

A mathematically valid HCW transfer is not automatically a safe rendezvous. Real missions use approach corridors, keep-out zones, abort logic, navigation uncertainty bounds, and plume/sensor constraints.

Educational simplification

This planner is for learning targeting logic. It does not enforce collision avoidance, line-of-sight cones, docking corridors, or operational safety rules.

Interactive rendezvous planner

Current chaser relative position (m)

Current chaser relative velocity before burn (m/s)

Desired final relative position (m)

Presets demonstrate common relative targeting ideas, not certified approach rules.

Results

Required velocity after Burn 1

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Burn 1 vector

—

Burn 1 magnitude

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Arrival relative velocity

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Stopping burn magnitude

—

Total Δv

—

Interpretation

Run the planner to compute a targeted HCW rendezvous transfer.

3D rendezvous trajectory in LVLH frame
In-plane path: radial x vs along-track y
Range to target over time

Assumptions and limitations

This tool assumes:

  • Circular target orbit
  • Linear HCW relative dynamics
  • Impulsive burns
  • No collision-avoidance or keep-out-zone enforcement
  • No J2, drag, eccentric target orbit, finite burns, or navigation uncertainty
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