## 6 Example Missions Designs  
In this section, the conclusions on momentum transfer architecture (Sections 1 and 3), environment (Section 2), tether hardware (Section 4), and tether interface (payload capture, Section 5) are combined in a coherent LEO constellation delivery mission. This mission is compared against a similar mission, which uses only chemical propulsion--namely, Falcon-1e vehicles. To avoid potentially misleading economic and payload utilization considerations, mission merit is determined as mass of hardware placed on at least a 185 km LEO orbit by using equal numbers of Falcon 1e launches. Fractional launches (part of the rocket-delivering part of the payload) are also considered possible for simplicity. A software package was developed in the Scilab for the semi-automatic calculation of the mass budget of the space launch mission using momentum transfer tethers. The Scilab scripts are provided on request or available on the author's page at www.researchgate.net. A total of nine scripts were used and briefly described below. The mission budgets derived from auto-budget script outputs are provided in Table 3.  
The Tether_reentry.see script works as follows:  
1. The MSISE-90 atmospheric model is loaded and interpolated with a resolution of 1 km. 2. The distribution of atmospheric drag across the tether is calculated at five segments across the tether length for rotation angles with step 15 degrees. 3. The circular orbit altitude drop is calculated from energy and impulse conservation laws. Spacecraft assumed to collide inelastically with air molecules, therefore transferring the kinetic and potential energy of spacecraft to air, accelerating and ultimately heating it. The application of conservation laws is possible if the orbit decaying quasi-statically. Quasi-staticity mean drag acceleration several orders of magnitude below gravity acceleration, and gravity acceleration magnitude varying negligible per orbit. For this to happen, orbit must be near-circular and gravity field must be nearly-spherical. Real decaying low-earth orbits are slightly non-circular (orbital eccentricity is varying around 0.001 due non-spherical gravity fields). In addition, a few minutes before reentry, decay becomes not quasi-static due to increasing drag acceleration. 4. The time step is adapted to keep the orbit altitude drop rate in the 0.1-1 km/step range. 5. Simulation is terminated after the orbit is lowered to 100 km altitude. 6. The steps b-e are swept for various tether lengths and initial orbit altitudes. The tether rotation speed is derived from the Steady_ether_speed.sci script output. The Steady_ether_speed.sci script works as follows:  
1. The MSISE-90 atmospheric model is loaded and interpolated with a resolution of 1 km. 2. Initially assumed tip speed is 1 m/s and the speed adaptation coefficient is 1.4. 3. Torques arising from center of pressure and center of mass mismatch are calculated for nine tether segments and averaged over a rotation period with step 3 degrees. * If torque is found to be positive, estimated speed is multiplied by speed adaptation coefficient until torque becomes negative. * If torque is found to be negative, estimated speed is divided by speed adaptation coefficient until torque becomes positive. * When torque changes sign, the speed adaptation coefficient is set to the square root of itself. * The steps c-f are repeated until torque absolute value is reduced below the pre-determined accuracy. * The steps b-g are repeated while sweeping orbit altitude and tether mass. The Tether_spinup_time.sci script works as follows:  
* The MSISE-90 atmospheric model is loaded and interpolated with a resolution of 1 km. * The output of Steady_ether_speed.sci is divided by torque calculated for zero rotation speed, but averaged for all possible tether orientations with step 3 degrees. The tether_minspeed.sc script simply applies Equation (1) for the range of the tether lengths and circular orbit altitudes.