Skyhooks

A totally different architecture for placing mass into orbit is using very long, orbiting cables. The classic example is the synchronous skyhook [7], a cable in geosynchronous orbit reaching down to be anchored at the planet's surface, and extending upward so the entire structure is in tension. It is possible for a mass to climb this skyhook, gaining potential energy directly, and taking momentum from the orbital momentum of the planet. [8] discusses another version, free-orbiting skyhooks counter-rotating to just cancel out the orbit and planet's rotation as the tip makes its closest approach. Such a skyhook can grab a payload, and pull it into orbit.

Skyhooks are generally much too long to support themselves if they are of constant thickness. The answer is to use cables tapered with the load so that they experience constant stress over their length. The ratio of the area of a skyhook at distance r from the planet to the area of the skyhook tip at the surface of the planet is expressed in equation (5) from [8]:

(1)

Where A(r) is the area of the skyhook at radius r from the planet's center, A(rp) is the area of the skyhook at the planet's radius, rp is the planet's radius, d is the skyhook material's density, t is the tensile strength, wo is the orbital rate of the satellite, and ws is the rotation rate of the satellite. For a synchronous skyhook, ws = wo = wp (where wp is the planet's rotational rate). One particularly favorable concept is for a rotating skyhook roughly 1/3 the radius of the planet. This can be designed to make its closest approaches near exactly six stable points on the surface. It is also close to the optimum rotating skyhook length.

One measure of skyhook feasibility is the taper ratio, the ratio between the widest point in the skyhook and the tips. The taper ratio is proportionate to the exponent of the density to tensile strength ratio. [8] derived taper ratios, assuming graphite crystals and a substantial safety factor. Properly scaling those taper ratios based on the material properties achievable with MNT, gives improved feasibility, as shown on table 4 below.

Table 4. Improved feasibility of skyhooks, using MNT materials. Taper ratios when using graphite come from [8].

Body	Taper Ratio for Synchronous Using Graphite	Taper Ratio for Synchronous Using MNT	Taper Ratio for 1/3 Planet Radius Using Graphite	Taper Ratio for 1/3 Planet Radius Using MNT
Mercury	2.22	1.71	1.42	1.27
Venus	123	25.2	8.32	4.13
Earth	100	21.9	10.1	4.69
Moon	1.3	1.19	1.12	1.08
Mars	2.41	1.8	1.56	1.35
Jupiter	2.8 x 10^26	5.3 x 10^17	7.0 x 10^15	4.1 x 10^10
Saturn	3.3 x 10^6	2.3 x 10^4	17,430	695
Uranus	2,350	182	101	22.1
Neptune	1 x 10^6	1 x 10^4	1,092