As the tether rotates downward, the horizontal orbital velocity and the backward rotational velocity partially cancel. At the bottom of the rotation, they cancel exactly, leaving the tip momentarily stationary relative to the lunar surface.
| Time (s) | Horizontal Distance (m) | Height Above Surface (m) | Speed (m/s) |
|---|---|---|---|
| -12.0 | -18217.5 | 3569.6 | 580.0 |
| -11.8 | -17901.3 | 3466.0 | 565.3 |
| -11.6 | -17581.3 | 3365.3 | 550.7 |
| -11.4 | -17257.7 | 3267.5 | 536.2 |
| -11.2 | -16930.5 | 3172.6 | 521.7 |
| -11.0 | -16599.8 | 3080.7 | 507.3 |
| -10.8 | -16265.6 | 2991.7 | 492.9 |
| -10.6 | -15928.1 | 2905.7 | 478.6 |
| -10.4 | -15587.2 | 2822.6 | 464.4 |
| -10.2 | -15243.0 | 2742.6 | 450.3 |
| -10.0 | -14895.5 | 2665.5 | 436.2 |
| 0.0 | 0.0 | 100.0 | 0.0 |
Near rendezvous the tip motion is extremely gentle, which is what makes this architecture attractive for surface pickup.
A spring-powered launcher fires a payload vertically so that it reaches 100 m altitude with zero velocity exactly at rendezvous.
Required launch time: 11.1 seconds before rendezvous
| Time (s) | Height Above Rendezvous (m) | Vertical Speed (m/s) |
|---|---|---|
| -12.0 | Not launched | – |
| -11.0 | 2.1 | 17.8 |
| -10.0 | 19.0 | 16.2 |
| -9.0 | 34.7 | 14.6 |
| -8.0 | 49.0 | 13.0 |
| -7.0 | 61.0 | 11.3 |
| -6.0 | 70.7 | 9.7 |
| -5.0 | 78.1 | 8.1 |
| -4.0 | 83.2 | 6.5 |
| -3.0 | 86.0 | 4.9 |
| -2.0 | 87.4 | 3.2 |
| -1.0 | 88.5 | 1.6 |
| 0.0 | 100.0 | 0.0 |
The payload and tether tip can be compared directly at identical times. Both arrive at the rendezvous point with near-zero relative velocity.
Force and motion changes propagate down the tether as a tension wave. For a 55 km tether, this takes roughly:
~9 seconds one-way
Therefore, no adjustment at the tip is possible for the first several seconds after the motor starts pulling.
| Elapsed Time (s) | Tip Adjustment Possible (m) |
|---|---|
| 1 | 0 |
| 2 | 0 |
| 3 | 0 |
| 4 | 0 |
| 5 | 0 |
| 6 | 0 |
| 7 | 0 |
| 8 | 0 |
| 9 | ~0.1 |
| 10 | ~0.3 |
| 12 | ~1 |
| 15 | ~3 |
| 20 | ~7 |
This shows that tether-length adjustment is a slow, low-bandwidth control. It is useful for phasing and trimming, but not for last-second rendezvous corrections.