Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Rapid Interplanetary Tether Transport SystemsIAF-99-A.5.10Shift in Tether Center of MassThe shift of the center of mass of thetether system when a payload was attachedor released was determined by adding themoments of the unloaded tether about theloaded center of symmetry and dividing by theunloaded mass.Figure 20 illustrates the four generalcircumstances of tether operations: originpickup, origin release, destination capture anddestination release. The shift of the center ofmass of the tether system when a payload wasattached or released was determined byadding the moments of the unloaded tetherabout the loaded center of symmetry anddividing by the unloaded mass. Figure 20illustrates the four general circumstances oftether operations; origin pickup, originrelease, destination capture and destinationrelease. It turns out that the dynamics of anideal rigid tether system with a givenpayload can be fairly well modeled by simplyaccounting for the change in the position andmotion of the tether's center of mass as thepayload is caught and released.When the payload is caught, the center ofmass shifts toward the payload and thetether assumes a symmetrical state. Thevelocity of the tip around the loaded center ofmass is simply its velocity around theunloaded center of mass minus the velocity ofthe point which became the new center of massabout the old center of mass. The change in thetether orbital vector is fully described by thesum of the vector of the old center of mass andthe vector at the time of capture or release ofthe point that becomes the new center of massrelative to the old center of mass. Since thetether loses altitude with both the catch andthe throw, its initial altitude must be highenough so that it does not enter theatmosphere after it throws the payload.Once the payload is released, its velocityand position are converted to Keplerianorbital elements which are propagated to theoutgoing patch point. At this point, they areconverted back to position and velocity, andtransformed to the Sun frame of reference.The velocity of insertion into the orbit inthe Sun's frame of reference is essentially thevector sum of the hyperbolic excess velocitywith respect to the origin planet and theOrigin tethercapture detailunloadedtether tip circleloaded tethertip circler oi horizonr oc horizonvo ir c horizonOrigin tetherrelease detailϕ orloadedtether tip circleunloadedtether tip circleDestination tetherrelease detailunloadedtether tip circleloaded tethertip circler df horizonrdr horizonϕ fϕ irr horizonϕ ofr r horizonv oiLoiϕ oiϕ oc v oc Cvi = voi - vtir cvdf = v dr qdrv dr + v cϕ dfv cCL dvf = vdr + vtr dfLf = Ld + Cr rv drv tiDestination tethercapture detailr c horizonr dc horizonr i c horizonloaded tethertip circleunloadedtether tip circleϕ iLo = Loi - Cv cδu oc∆uocvr = vor + vtv o rvof = vor + vcϕ ovdiv dcδu dcv trv t c = vt i - vcδuorr∆udrvcroc roiL iϕ rqdivcqdfr drqoc - πv cr of r orv orLof = Lo + Cϕ iLoδu drq oi - πq orq of∆u orCr oc q dcqdir ic∆u dcL dv div tir cv trr rro r horizonr o f horizonv i = v di + v tiFigure 20. Tether Capture/Release Operations.21