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Preliminary Analysis of an Asymmetric Resonant Ecliptic Capture Orbit Sling Transport System

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Preliminary Analysis of an Asymmetric Resonant Ecliptic Capture Orbit Sling Transport System 9/6/2018 capture-orbit-sling http://localhost:8888/nbconvert/html/capture/capture-orbit-sling.ipynb?download=false 1/173 9/6/2018 capture-orbit-sling Preliminary analysis of an asymmetric resonant ecliptic capture orbit sling transport system Bryan Killett, 2018 Puig-Suari et al. 1995 (http://web.archive.org/web/20171006015505/https://engineering.purdue.edu/people/james.m.longuski.1/JournalAr and Jokic and Longuski 2004 (http://web.archive.org/web/20170923011520/https://eprints.usq.edu.au/8092/1/Jokic_Longuski_JSR_v41n6_PV.pd designed tether slings on Phobos and Deimos for transporting payloads to Earth. However, their slings' tether masses scale quickly with the required payload hyperbolic excess speed, partly because the small Oberth effect at Phobos and Deimos necessitates high sling tip speeds. If a hyperbolic excess speed higher than ~5 km/s is required, a lower total system mass can be obtained by using multiple slings. A 'moon sling' on Phobos or Deimos throws payloads and counterbalance masses into a capture orbit with a periapsis just above the atmosphere of Mars. The capture orbit is resonant with the chosen moon to allow for repeated throws, and it's ecliptic because trans-Earth injection velocities are close to lying in the ecliptic plane. A coupled pair of asymmetric 'capture slings' in the capture orbit rendezvous with those payloads and counterbalances, then use solar power to spin up both slings by torquing against each other. Both payloads and both counterbalances are then thrown at periapsis to maximize the Oberth effect. Asymmetric capture slings allow the counterbalance orbits to be specified approximately independently of the payload velocities, but asymmetric slings force a certain ratio between the payload masses and require ballast mass to keep the slings' centers of mass at the desired rotational axis. The capture slings can use tether reeling to avoid collisions with the moons and to rotate their periapsis velocity vector to throw payloads in different directions in the ecliptic plane. Steps: 1. Specify the maximum payload tip speed and acceleration. 2. Choose the payloads' hyperbolic excess speeds, tether material, safety factor, etc. 3. Choose an orbital resonance for the capture slings. 4. Estimate the required tip speed to compare with the tip speed specified in step 1. 5. Initialize lists and define functions. 6. Solve for each capture sling's radius, rotation rate, counterbalance ratio, etc. 7. Print the capture slings' payload trajectories and counterbalance orbits. 8. Calculate the delta-v from the chosen moon's orbit to the inclined capture sling orbit. 9. Print the moon sling's payload and counterbalance orbits. 10. Solve for the ballast mass needed to keep an asymmetric sling's center of mass at the rotational axis. 11. Define the slings' moments of inertia and rotational kinetic energy. 12. Solve for the third capture sling which zeroes the total rotational angular momentum of the capture sling system whether it's full or empty. 13. Solve for the moon sling payload based on mt4ct and the total mass to be thrown. 14. Check the centers of mass of all slings while empty and full. 15. Calculate required power and solar panel mass for spinning the slings. 16. Animate the capture sling throw. 17. Make a 3D plot of the payloads and counterbalances to assess the risk of collisions. 18. Calculate mass of equivalent rocket. http://localhost:8888/nbconvert/html/capture/capture-orbit-sling.ipynb?download=false 2/173 9/6/2018 capture-orbit-sling 19. Print summary. 20. Appendix A: Counterbalance mass ratios above 4.6033 cause collisions. 21. Appendix B: Indirect paths from the moon to the capture orbit. This notebook was initially written to reproduce values in Jokic and Longuski 2004 (http://web.archive.org/web/20170923011520/https://eprints.usq.edu.au/8092/1/Jokic_Longuski_JSR_v41n6_PV.pd table 3. To do that, set grapple_fraction = 0, moon_name = 'Phobos', safety = 1.0, material = 'Zylon', tip_accel_max = 3*g, payload_mass = 11.2*1000 or 70*1000, cbrs[0] >= 1, cbrs[1] = 0, best_case_offset = 0.0, Isp = 379, s2p = 0.15. The moon sling payload tether mass, length, diameters, single-stage rocket propellant mass and mu_single reported in the summary at the bottom will then ~reproduce values in Jokic and Longuski 2004 table 3. Look through phone for other things. Radiator sun shield doesn't show up! Add longitudinal supports to the hawsepipe. Add a light right outside the hub, for clarity. NOTE THAT THE CAPTURE TO MOON ROTATION MATRIX DOESN'T REALLY MAKE SENSE ANYMORE AFTER THE CELL CHANGED FROM MOON FRAME TO CAPTURE_FRAME! IN SEVERAL PLACES THE PERIAPSIS VS INFINITY HYPERBOLIC DEFLECTION ANGLE IS CALCULATED. MAKE SURE THAT IN ALL SUCH PLACES, THE CALCULATIONS ARE EITHER FOR THE MOON SLING OR THEY'RE FOR THE CAPTURE SLING BUT BOTH V_INFS ARE USED!!! DAMNIT! THE RETROGRADE ANCHOR NEEDS TO BE REALLY DIFFERENT MASSES BEFORE AND AFTER THE THROW! Changed all RR( to RDF( for speed https://ask.sagemath.org/question/9950/what- are-the-different-real-numbers-in-sage/ (https://ask.sagemath.org/question/9950/what-are-the-different-real-numbers-in- sage/) AT THE SAME TIME, CHANGE capture_frame_string to ecliptic_frame_string, inc_moon to inc_m2c (OR SOMETHING?!?!), H_cs_unit to H_cs_n to match others, etc?? Because tether reeling becomes less effective with more circular orbits, might consider making the destination counterbalance orbit elliptical. However, that would complicate gravity gradient stabilization of habitats and getting the counterbalances to rendezvous with those habitats. Finish writing string for payload longitude (and rename it!), specifically start and finish the part dealing with the capture sling longitudes which don't require any tether reeling in between picking up payloads from one of the moon sling's nodes (either going out or going in). http://localhost:8888/nbconvert/html/capture/capture-orbit-sling.ipynb?download=false 3/173 9/6/2018 capture-orbit-sling Eclipses aren't considered in calculations of power requirements. LINK here (http://www.csc.caltech.edu/references/Hopkins-Phobos-Deimos-Paper.pdf) FOR MOON ECLIPSES, FOR CAPTURE SLING ECLIPSES, LINK TO THESIS AND/OR THAT RECENT TETHER ANALYSIS I DOWNLOADED (CAN'T FIND IT ON TABLET, MIGHT HAVE TO LOOK IN TETHER EMAIL AND/OR THAT KHAYMAN FOLDER WITH ALL THE PAPERS THAT NEED TO BE NAMED)? capture_frame_string should probably be called ecliptic_frame_string, and it shouldn't mention the capture slings if cbrs[1]==0. Consider adding equatorial capture sling option. This means inc_moon needs to become inc_m2c (inclination of moon wrt capture orbit). Also have inc_q2l (equator wrt ecliptic BUT THIS IS ALREADY IN CODE AS axial_tilt_planet!) and inc_c2q or inc_c2l??? Finish J2 precession calcs. Still not dealing with nodal precession due to the Sun, which precesses the orbit around the normal to Mars's orbital plane. ". For each satellite the net precession is retrograde about the normal to its Laplace plane, a plane lying between the Mars equator and Mars orbit;" http://www.planetary.brown.edu/planetary/geo287/PhobosDeimos/papers/Jacobson 2014.pdf (http://www.planetary.brown.edu/planetary/geo287/PhobosDeimos/papers/Jacobso 2014.pdf) GREAT website overall, and this function should replace GAIA's distance function! http://web.archive.org/web/20110825045635/https://www.projectpluto.com/dist.cpp (http://web.archive.org/web/20110825045635/https://www.projectpluto.com/dist.cpp Limitations: Simple rigid tether model- no elasticity, oscillations, tumbling, chaotic motion, etc. There's no coupling between orbital and rotational angular momenta. The capture slings rotate as though they're in free space and their center of mass isn't accelerating. Completely separately, the capture sling center of mass moves in a Keplerian orbit as if it were a point mass. Only centrifugal forces are included, so forces due to gravitational gradients aren't considered. Gravitational forces due to Deimos, Phobos, and the oblateness of Mars (and all other gravitational perturbations) are ignored. Deimos and Phobos are treated as being in circular orbits that are inclined relative to the ecliptic plane. Hyperbolic payload trajectories lie in the ecliptic plane, so plane-change corrections are needed because planetary orbits aren't all in the ecliptic. The specified maximum acceleration and tip speed only apply to the payload, so if a sling uses a counterbalance ratio < 1.0, its counterbalance acceleration and tip speed will be above the specified maximums. In that case, the counterbalance arm could also reach below the target altitude of the counterbalances, which is a safety hazard. This notebook was written mostly from scratch. While this was fun and educational, the code has only been tested by one person. That's a serious limitation compared to code from Project Pluto http://localhost:8888/nbconvert/html/capture/capture-orbit-sling.ipynb?download=false 4/173 9/6/2018 capture-orbit-sling (https://www.projectpluto.com) which has been tested by many people. In particular, functions like xyz2kepler() and kepler2xyz() should probably be replaced with code from Project Pluto. On a related note, this notebook is sort of designed to allow the origin planet to be changed (e.g. so the capture slings throw payloads from Jupiter rather than Mars), but that hasn't really been tested. If you want to throw payloads from a planet that isn't Mars then beware of software bugs. You can manually run each cell by hitting Shift-Enter, but it's safer to run the entire notebook at once by clicking on Kernel -> Restart & Run All . (Unintended output can sometimes occur when running cells repeatedly or out of order.) Haven't estimated the masses of the radiators, electric motors and the central hub that transmits torque from one capture sling to the other. The summary prints values for these masses as reminders to produce rigorous estimates, but right now those values are either all zero (if estimate_misc is set to 0) or they're just copies of the solar panel mass estimate (based on Juno's solar panels).
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