## 6 Example Missions Designs
The tether_mmod.sc script calculates the total weight of MMOD shield for a given length and diameter of tether, using tabulated MMOD shield area density extracted from [28]. The tether.sc script uses laws of energy and momentum conservation to calculate the following parameters as a function of payload weight to tether weight ratio:  
* The \(\Delta\)v imparted on the tether as a result of payload capture and release. * The \(\Delta\)v imparted on the payload after being carried by the tether from a capture point directly below the tether hub to a release point directly above the tether hub. The auto-budget scripts, (Tether_autobudget_UHMWPE.sce and Tether_autobudgetSteel.sce), do automatically calculate power and propellant requirements for the catch-release-rebosot momentum transfer cycle, given average orbit altitude and launch frequency. Optimization of these is left for the user. Other script outputs are used as input for auto-budget scripts. Average altitude of the tether capture orbit was swept to minimize orbital mass break-even time. Break-even time is the interval necessary for the bolo system to transfer, to orbit, additional (compared to purely rocket system) mass equal to the initial bolo weight (plus all ion motor fuel spent in the process). It was discovered that higher launch rates result in the reduction of orbital break-even time, up to a launch frequency of 180 per year. It was also found that a launch frequency above 52 launches/year (weekly) results in a bolo system that is undeliverable to orbit by medium-lift vehicles. Therefore, only bolo capture orbit average altitude was optimized, while launch frequency was fixed to 52 launches/year. For more robust optimization convergence, the gravity gradient on LEO was linearized. Therefore, all apogee and perigee data in Table 3 are approximations only. The tether strength data was derived from the Table 2. Typical satellite power density (1 W/kg) and solar panel energy output (150 W/m\({}^{2}\)) were used for columns 1, 2, and 4. Solar panels are assumed to have an effective drag factor of 1 in sunlight and 0.2 in shadow, corresponding to the \"night glider\" operation mode. The payload catch is assumed to happen near the perigee of the bolo orbit to avoid perigee lowering and excessive air drag during re-boost. The payload is released after a half-rotation of the bolo, still near the bolo perigee, to maximize momentum transfer (in line with [45]). After payload release, the tether orbit is considered circularized. In 2006, [PERSON] [46] explained how any conductivity of the tether on Earth's orbit will result in electromagnetic force, causing eventual tether de-orbit. Therefore, only insulating or semi-insulating tethers (with insulator junctions between segments) can be considered for long-term, low-loss operation. However, for sake of simplicity, that effect for steel (hence, conductive) tethers was not taken into account. Surprisingly, the concept that the re-boost engine specific impulse is a limiting factor, as stated in 2003 by [PERSON] [10], was proven wrong, as fuel spent for currently existing ion motors (1500 s ISP and 50% efficiency) was found to reduce tether-assisted payload increase for about 1/4 only. This conclusion is in line with analysis by [PERSON] [47], who rejected magnetic-reboosted (MXER) tethers. [PERSON] [47] states that a tether-magnetic system will be too heavy, compared to the electric propulsion, if orbital transfer times below one month are required due to poorer power efficiency and associated weight of the necessary photovoltaic panels. In addition, a small role of the material strength was found. Although bolo performance (pay-off time) moderately improves (by 27%) if steel tether is replaced for available high-strength UHMWPE rope (five times stronger for same weight), further doubling of tether strength results only in a 9% improvement in pay-off time. The main reason for such a performance stagnation is the limiting role of the payload catch specifications.