## 5 The Challenge of the Bolo Rendezvous and Catching  
This Section defines the interface between highly speculative momentum transfer architecture and hardware outlined in Sections 1-4 and existing rocket propulsion hardware. A literature review on payload capture and tentative overview of hardware components for payload capture will be provided in this section. Catch of payload by LEO bolo has very strict requirements for speed, location, and time-matching between the payload and bolo tip. A space-docking experience is not applicable for rendezvous with momentum transfer tethers. In 2006, [PERSON] [38] investigated the low-speed tether capture dynamic. A conclusion was that, to avoid transient loads, the capture time must be at least two orbital revolutions--an unsuitably long interval for bolo tip capture. For high-speed rendezvous, an asteroid grapple was proposed in 2000 by [PERSON] [39] for a tethered swing-by of the asteroids to modify the spacecraft's speed vector. Such an approach is intrinsically unreliable and far beyond the capability of the existing throwing grapples. Historically, most resembling the bolo capture was the air recovery of Corona satellites, Stardust sample recovery, or attempted recovery of the Genesis sample capsule. A satellite being recovered closely resembles the bolo tip, while recovery aircraft mostly resemble the suborbital, maneuvering payload. The Corona satellite was captured at high relative velocities (up to 60 m/s) using a combination of hooks hanging from aircrafts and loops created by parachute ropes attached to the Corona satellite. It is a flight-proven solution. Research is currently in progress, specifically for bolo by [PERSON] [40] at the Tennessee Tech University, but only on room-scale, open-loop models. The grappling aperture of Newton [40] is heavy, weighing 10% of the payload mass. Furthermore, a capture happens at zero relative velocity--a feature requiring multi-second speed adjustment phase in the actual flown, close-loop controlled payload. The speeds of the bolo tip and payload cannot be matched far away from the rendezvous point because of the natural uncertainties of the payload trajectory. Most of the uncertainty happens due to interaction with winds, turbulence, unsteady rocket engine thrust, fuel slosh, and rocket stage pointing errors. It is common for the last stage of the orbital vehicle to be left within ~10 m/s of the desired speed, even if bi-propellant liquid-fuel engines are used. Solid-fuel engines have an even worse final speed spread (Pegasus XL official 3-sigma error is 150 m/s [41]). Therefore, a multiple correction maneuvers must occur at the last moments, guided most likely by bolo tip radio beacon, GPS, and laser rangefinder. Even as such, intervals of a few seconds of the bolo tip and payload at low relative speed (<30 m/s) are desirable to roughly adjust range and orientation errors, given the typical low agility of the modern orbital boosters. Requirements for the orbital booster (or payload only) to have an increased agility in order to be caught will surely result in payload-bearing modules having too much deadweight, out-weighing any benefit from any \(\Delta\)v savings provided by the bolo. Given these constraints, the only currently achievable flight profile leading to successful bolo rendezvous is reuse of the main engine in the last stage of the orbital booster to roughly match the acceleration of the bolo tip for a few seconds before the catch moment. Typical upper stages have linear accelerations up to 30 m/s\({}^{2}\), throttleable down to 60% of nominal thrust, and have angular accelerations up to 4 rad/s\({}^{2}\) (typical for Falcon-1e upper stage). To equalizelongitudinal and transverse agility, these parameters result in free acceleration of 6 m/s\({}^{2}\) with acceleration lagging about 0.2 s after controls.