Rotating Lunar Tether Rendezvous Analysis

Concept Overview

A rotating space tether is an elegant momentum-exchange system that can catch and release payloads without using propellant. Picture a long tether orbiting the Moon like a spoke on a giant wheel. The tether rotates opposite to its orbital direction, so when the tip swings down toward the surface, it momentarily becomes stationary relative to the Moon's surface—creating a perfect opportunity for rendezvous.

This analysis examines the precise timing and dynamics needed for a payload launched from the lunar surface to rendezvous with the rotating tether tip. We'll also explore the tether's ability to adjust its tip position in real-time to accommodate minor trajectory variations.

System Parameters

Table 1: Tether Tip Motion (12 seconds to rendezvous)

This table shows how the tether tip approaches the rendezvous spot. The angular velocity is ω = v/r = 1600/50000 = 0.032 rad/s. The center of mass moves at 1,600 m/s horizontally while the tip rotates opposite at the same rate.

Time to Rendezvous (s) Angular Position (deg) Horizontal Distance (m) Vertical Distance (m) Total Distance (m) Tip Speed rel. to Moon (m/s)

Table 2: Payload Trajectory (12 seconds to rendezvous)

The payload is launched vertically to reach 100 m altitude with zero velocity. Initial velocity needed: v₀ = √(2gh) = √(2 × 1.62 × 100) = 18.0 m/s. Time to reach apex: t = v₀/g = 18.0/1.62 = 11.11 seconds.

Launch Timing: The payload must be launched 11.11 seconds before the rendezvous time (t = 0).
Time to Rendezvous (s) Flight Time (s) Altitude (m) Distance from Rendezvous (m) Payload Speed (m/s)

Table 3: Tether Tip Adjustment Capability

The ballast can climb the tether to adjust the tip position. Key considerations:

Important: Because the signal takes 5.5 seconds to propagate along the 55 km tether, no tip adjustment is possible in the first 6 seconds. After that, the ballast's movement creates tip motion amplified by the lever arm ratio (50 km tip / 5 km ballast = 10× amplification).
Response Time (s) Ballast Displacement (m) Tip Adjustment (m) Notes

Analysis and Implications

Key Findings:

1. Launch Window Precision: The payload must launch exactly 11.11 seconds before rendezvous. At t = -12s, the tether tip is approximately 19,200 meters away horizontally and moving at about 384 m/s relative to the Moon.

2. Velocity Matching: At rendezvous (t = 0), both the tether tip and payload are stationary relative to the Moon and each other—perfect conditions for a gentle capture.

3. Real-time Adjustment Limitations: The tether system cannot make tip adjustments in less than 6 seconds due to signal propagation delay. After 10 seconds, modest adjustments of 30-50 meters are possible. This means the initial trajectory must be highly accurate, though small corrections can be made if detected early enough.

4. Practical Considerations: The ballast motor (10 hp) can move the 300 kg ballast at roughly 2-3 m/s against lunar gravity forces transmitted through the tether. With a 10:1 lever arm, this translates to 20-30 m/s tip velocity potential, but the propagation delay is the primary limiting factor for quick adjustments.

Why This Matters

This rotating tether system enables propellant-free payload capture from the lunar surface. Unlike rocket rendezvous which requires continuous thrust and propellant, the tether provides a mechanically fixed rendezvous point that appears stationary from the surface's perspective for a brief moment. The spring launcher can be a simple, reusable mechanical device.

The main challenges are timing precision (launch must occur within milliseconds of the correct moment) and trajectory accuracy (the payload must reach the exact altitude at the exact horizontal location). The limited real-time adjustment capability means most of the accuracy must come from the launch system itself, with tether adjustments serving only to handle minor variations or multiple rendezvous attempts during a single pass.