## 3 The Inconvenience of the Tip Masses or Counterweights  
This Section is intended to outline the conditions when the momentum transfer tether with tip mass or counterweight may be useful. In addition, the related problem of matching rotation phase of the bolo with the payload trajectory will be discussed with a resulting conclusion on the inconvenience of tip masses or counterweights for launch-assist missions using LEO bolos.  
In 2001, [PERSON] [29] proposed to use momentum-transfer tethers for orbit apogee raising. [PERSON] [29] found that additional tip mass raises the transfer orbit apogee, but no tether reuse, spin-up, or catch requirements were considered.  
The bolo must not only be deployed to LEO, but also rotated to its operational tip velocity if aero-spinning alone cannot be relied upon. Such a spin-up requirement is non-trivial, and requires, most realistically, a hydrazine-powered (or electric-ion) low-thrust rocket pod on either end of the tether. Therefore, minimization of the energy required for spin-up will allow reduction of bolo launch mass. Such minimization of energy spent generally requires minimization of the moment of inertia of the entire bolo. Therefore, placement of any massive components on the bolo tip (as counterweight) will result in larger energy requirements for bolo spin-up, as illustrated in Figure 7. Any energy spent for bolo spin-up is lost for momentum transfer because payload is only subject to radial acceleration by the bolo.  
\begin{table}
\begin{tabular}{c c} \hline
**Particle size** & **Collision frequency for 1 m\({}^{2}\) single-side target** \\ \hline
100 \(\upmu\)m & 2.8 collisions/year \\
200 \(\upmu\)m & 0.48 collisions/year \\
500 \(\upmu\)m & 0.045 collisions/year \\
1 mm & 0.0077 collisions/year \\
2 mm & 0.0013 collisions/year \\
2.5 mm & 0.00074 collisions/year \\
3 mm & 0.00046 collisions/year \\ \hline \end{tabular}
\end{table}
Table 1: Collision frequencies for various debris sizes.  
In addition, it is advisable to reduce the bolo moment of inertia to allow easy adjustment of the rotation phase. Such an adjustment is necessary to catch payloads launched from the fixed Earth's location to the lowest point of tether.  
Relying on a booster rocket to provide cross-time to meet the bolo tip in its lower point will result in the booster flying long segments in non-ballistic trajectory, with resulting delta-v losses of 400-800 m/s.  
The phase of the bolo can be adjusted either by tip rockets (very expensive, in terms of propellant mass and added weight) or by reeling/unreeling the tether to the central hub. In 2006, [PERSON] [30] devised a method to change the spin rate of the rotovator (bolo) using Coriolis forces on the tether in a yo-yo configuration, without any reaction thrusters. The reeling/unreeling mechanism provides necessary cross-time capability for 1-10 W power levels (250 kg payload designs in Section 6) and reel speed below 1 mm/s. Maximal reeled length is 100 m for 43 s cross-time compensation within a two-day reeling maneuver. In 1998, [PERSON] [31] also proposed adjusting the aerodynamic drag of the tether with planetary atmosphere during flyby, by means of winding/unwinding the tether.  
Given the lesser role of aerospinning (described in Section 2) at altitudes above 300 km and the necessity to minimize the moment of inertia of bolo, the optimal bolo configuration would be the symmetric tether with powered spacecraft for bolo re-boost placed at or near the tether center. Counterweight may still be considered if heavy MMOD protection or the reduction of aero-spinning spin-up rate (for very low orbits) is important.