The "Big Wheel" Concept: We can visualize a rotating space tether around the Moon as a giant wheel rolling through the sky. In this scenario, we have a 55 km tether. The Center of Mass (CM) orbits at 1,600 m/s. The tip, located 50 km from the CM, rotates backward at 1,600 m/s.
Like the patch of rubber on a rolling tire that momentarily touches the road, the tether tip comes to a momentary stop relative to the Moon's surface at the bottom of its swing. We designate a "Rendezvous Spot" 100 meters above the lunar surface where the tip and payload meet at Time = 0.
The table below shows the behavior of the tether tip in the final 12 seconds before the catch. Note the dramatic difference between the tip's speed and position compared to the payload in Part 2. While the payload "hangs" in the air, the tether tip sweeps in at high velocity.
| Time to Catch (s) |
Tip Speed relative to Moon (m/s) |
Distance from Rendezvous (m) |
|---|---|---|
| -12.0 | 606.8 | 3,745.0 |
| -11.8 | 596.8 | 3,622.7 |
| -11.6 | 586.8 | 3,502.2 |
| -11.4 | 576.8 | 3,383.6 |
| -11.2 | 566.9 | 3,266.8 |
| -11.0 | 556.9 | 3,151.9 |
| -10.8 | 546.9 | 3,038.9 |
| -10.6 | 536.9 | 2,927.8 |
| -10.4 | 527.0 | 2,818.5 |
| -10.2 | 517.0 | 2,711.2 |
| -10.0 | 507.0 | 2,605.7 |
| -9.8 | 497.1 | 2,502.2 |
| -9.6 | 487.1 | 2,400.6 |
| -9.4 | 477.1 | 2,300.9 |
| -9.2 | 467.2 | 2,203.1 |
| -9.0 | 457.2 | 2,107.3 |
| -8.8 | 447.2 | 2,013.4 |
| -8.6 | 437.3 | 1,921.5 |
| -8.4 | 427.3 | 1,831.5 |
| -8.2 | 417.3 | 1,743.5 |
| -8.0 | 407.4 | 1,657.4 |
| -7.8 | 397.4 | 1,573.3 |
| -7.6 | 387.4 | 1,491.2 |
| -7.4 | 377.4 | 1,411.1 |
| -7.2 | 367.4 | 1,333.0 |
| -7.0 | 357.5 | 1,256.9 |
| -6.8 | 347.5 | 1,182.8 |
| -6.6 | 337.5 | 1,110.7 |
| -6.4 | 327.5 | 1,040.6 |
| -6.2 | 317.5 | 972.6 |
| -6.0 | 307.5 | 906.6 |
| -5.8 | 297.5 | 842.7 |
| -5.6 | 287.5 | 780.8 |
| -5.4 | 277.5 | 721.0 |
| -5.2 | 267.5 | 663.2 |
| -5.0 | 257.5 | 607.5 |
| -4.8 | 247.5 | 553.9 |
| -4.6 | 237.5 | 502.4 |
| -4.4 | 227.5 | 452.9 |
| -4.2 | 217.4 | 405.6 |
| -4.0 | 207.4 | 360.4 |
| -3.8 | 197.3 | 317.4 |
| -3.6 | 187.3 | 276.5 |
| -3.4 | 177.2 | 237.9 |
| -3.2 | 167.1 | 201.5 |
| -3.0 | 157.1 | 167.3 |
| -2.8 | 147.0 | 135.5 |
| -2.6 | 136.8 | 106.1 |
| -2.4 | 126.7 | 79.0 |
| -2.2 | 116.5 | 54.4 |
| -2.0 | 106.3 | 32.7 |
| -1.8 | 96.0 | 13.8 |
| -1.6 | 85.7 | 0.0* (Tip passes through altitude, non-zero horiz dist) |
| -1.6 | 85.7 | 14.4 (Checking calculation...) |
| -1.6 | 85.7 | 65.6 |
| -1.4 | 75.3 | 50.2 |
| -1.2 | 64.8 | 36.9 |
| -1.0 | 54.2 | 25.6 |
| -0.8 | 43.5 | 16.4 |
| -0.6 | 32.7 | 9.2 |
| -0.4 | 21.8 | 4.1 |
| -0.2 | 10.9 | 1.0 |
| 0.0 | 0.0 | 0.0 |
To match the tether tip, we use a spring launcher to throw the payload up 100 meters.
It must reach the apex (zero vertical speed) exactly at T=0.
Launch Requirement: To reach a 100m apex in Lunar gravity (1.625 m/s²), the payload must launch 11.1 seconds before rendezvous with an initial speed of 18.0 m/s.
| Time to Catch (s) |
Payload Speed (m/s) |
Distance from Rendezvous (m) |
|---|---|---|
| -12.0 | 0.0 | 100.0 (On Ground) |
| -11.8 | 0.0 | 100.0 (On Ground) |
| -11.6 | 0.0 | 100.0 (On Ground) |
| -11.4 | 0.0 | 100.0 (On Ground) |
| -11.2 | 18.0 | 100.0 (Launch!) |
| -11.0 | 17.9 | 96.4 |
| -10.8 | 17.6 | 92.8 |
| -10.6 | 17.2 | 89.4 |
| -10.4 | 16.9 | 86.0 |
| -10.2 | 16.6 | 82.6 |
| -10.0 | 16.3 | 79.4 |
| -9.8 | 15.9 | 76.1 |
| -9.6 | 15.6 | 73.0 |
| -9.4 | 15.3 | 69.9 |
| -9.2 | 15.0 | 66.8 |
| -9.0 | 14.6 | 63.9 |
| -8.8 | 14.3 | 61.0 |
| -8.6 | 14.0 | 58.1 |
| -8.4 | 13.7 | 55.4 |
| -8.2 | 13.3 | 52.7 |
| -8.0 | 13.0 | 50.1 |
| -7.8 | 12.7 | 47.5 |
| -7.6 | 12.4 | 45.0 |
| -7.4 | 12.0 | 42.6 |
| -7.2 | 11.7 | 40.3 |
| -7.0 | 11.4 | 38.0 |
| -6.8 | 11.1 | 35.8 |
| -6.6 | 10.7 | 33.7 |
| -6.4 | 10.4 | 31.6 |
| -6.2 | 10.1 | 29.6 |
| -6.0 | 9.8 | 27.7 |
| -5.8 | 9.4 | 25.8 |
| -5.6 | 9.1 | 24.0 |
| -5.4 | 8.8 | 22.2 |
| -5.2 | 8.5 | 20.5 |
| -5.0 | 8.1 | 18.9 |
| -4.8 | 7.8 | 17.3 |
| -4.6 | 7.5 | 15.8 |
| -4.4 | 7.2 | 14.3 |
| -4.2 | 6.8 | 12.9 |
| -4.0 | 6.5 | 11.6 |
| -3.8 | 6.2 | 10.3 |
| -3.6 | 5.9 | 9.1 |
| -3.4 | 5.5 | 8.0 |
| -3.2 | 5.2 | 6.9 |
| -3.0 | 4.9 | 5.9 |
| -2.8 | 4.6 | 4.9 |
| -2.6 | 4.2 | 4.0 |
| -2.4 | 3.9 | 3.2 |
| -2.2 | 3.6 | 2.5 |
| -2.0 | 3.3 | 1.9 |
| -1.8 | 2.9 | 1.3 |
| -1.6 | 2.6 | 0.9 |
| -1.4 | 2.3 | 0.5 |
| -1.2 | 2.0 | 0.2 |
| -1.0 | 1.6 | 0.0 |
| -1.0 | 1.6 | 0.8 |
| -0.8 | 1.3 | 0.5 |
| -0.6 | 1.0 | 0.3 |
| -0.4 | 0.7 | 0.1 |
| -0.2 | 0.3 | 0.0 |
| 0.0 | 0.0 | 0.0 |
Can we pull the tip up to avoid a collision or adjust the catch height?
The Constraints:
| Time Motor Running (s) |
Adjustment at Tip (m) |
Notes |
|---|---|---|
| 1.0 | 0.0 | Wave traveling down tether... |
| 2.0 | 0.0 | Wave traveling down tether... |
| 3.0 | 0.0 | Wave traveling down tether... |
| 4.0 | 0.0 | Wave traveling down tether... |
| 5.0 | 0.0 | Wave arrives at tip |
| 6.0 | 3.2 | Tip begins to move |
| 7.0 | 6.4 | |
| 8.0 | 9.6 | |
| 9.0 | 12.8 | |
| 10.0 | 16.0 | |
| 11.0 | 19.2 | |
| 12.0 | 22.4 | |
| 13.0 | 25.6 | |
| 14.0 | 28.8 | |
| 15.0 | 32.0 | |
| 16.0 | 35.2 | |
| 17.0 | 38.4 | |
| 18.0 | 41.6 | |
| 19.0 | 44.8 | |
| 20.0 | 48.0 |