Rotating Space Tether for Lunar Rendezvous and Adjustment

For those interested in space tethers, a rotating tether (often called a rotovator) can facilitate low-energy transfers between a planetary surface and orbit. In this lunar scenario, the tether rotates around its center of mass (COM), which orbits the Moon at 1,600 m/s. The tip rotates oppositely at 1,600 m/s relative to the COM, making the tip momentarily stationary relative to the lunar surface at its lowest point (periapsis). This allows for a gentle rendezvous with payloads launched from the surface.

The tether is 55 km long, with the ballast 5 km from the COM and the tip 50 km from the COM. At rendezvous (t=0), the tip is 100 m above the surface and stationary. We calculate the tip's speed relative to the Moon and its distance from the rendezvous spot in the 12 seconds leading up to t=0, using the arc length along the cycloid path as the distance.

Similarly, a spring-launched payload from the surface reaches 100 m with zero velocity at t=0. Using lunar gravity (g = 1.62 m/s²), the required launch is 11.11 seconds before rendezvous. We track the payload's speed and distance from the rendezvous spot over the same period.

These tables allow comparison of the tip and payload approaches, showing how their positions and speeds align for a smooth hookup.

Tip Motion Countdown to Rendezvous

Payload Motion Countdown to Rendezvous

The launcher needs to launch the payload 11.11 seconds ahead of rendezvous time.

Tip Height Adjustment

To raise or lower the tip (e.g., for precise alignment), the 300 kg mobile ballast uses a 10 hp motor to climb or reel the 100 kg Spectra tether. The force propagates at the speed of sound in Spectra (~10 km/s), introducing a delay of 5.5 seconds for the 55 km tether. The table estimates the tip displacement (up or down) over 1-20 seconds, assuming constant velocity of 40.5 m/s after the delay based on power limits and wave propagation.