1. Day-of-Year 16 950 +85 2006-203 17 1000 +23 2006-250 18 960 +71 2006-266 19 980 +61 2006-282 20 1030 +8 2006-298 21 1000 +44 2006-346 23 1000 +31 2007-013 25 1000 +31 2007-053 26 980 +32 2007-069 27 1010 +41 2007-085 28 990 +51 2007-100 29 980 +59 2007-116 30 960 +69 2007-132 32 950 +84 2007-164 36 975 -60 2007-275 37 1000 -22 2007-323 39 970 -70 2007-354 40 1010 -12 2008-005 41 1000 -34 2008-053 42 1000 -27 2008-085 43 1000 +17 2008-133 A. TitanAtmospheric DensityModel
2. 900 1100 1300 1500 1700 1900 2100 2300 2500 2700
3. Figure4. Titan Density vs. Altitude. Variation of Titan atmosphere density with Titan-relative altitude (in a semi-logplot). unit vector uV. TheareaofthespacecraftprojectedontoaplanethatisperpendiculartothevectoruVisdenotedby AProjected(in m2). Sincethespacecraftmightbeslewedduringtheflybytoachievescienceobjectives,theprojected area will change continuously with time. The variation of the projected area with respect to the changing azimuth and elevation angles (between uVand the spacecraft's body frame) is given in the simulation testbed. One convenient way to do this is to use a two-dimensional look-up table. The displacement vectors, from the origin of the spacecraft coordinate frame to the spacecraft's center of mass and center of pressure (in m) are denoted by rCMand rCP, respectively. Note that rCMis a constant vector while the rCPis a time-varying vector. Another look-up table is used to provide value of rCPwith respect to the azimuth and elevation angles. Finally, the dimensionless quantity CDis the drag coefficient associated with the free molecular flowof Titan atmospheric constituentspassed the body of theCassini spacecraft. Thedragcoefficient CDcanbeestimatedusingformulaegiveninReferences10-12. Inourwork,weuseCD=2.2.
4. Here, μTitanis the product of the universal gravitational constant and the mass of Titan (≈ 8.9782×103km3/s2). The set [i, j, k] represents unit vectors along the spacecraft's axes. URistheunitvectorfromTitan'scenterofmass to the spacecraft's center of mass, and d(t) (in km) is time-varying distance between the two centers of mass. The symbol "•" in equation (3) denotes the scalar product of two vectors. The moments of inertia (in kg-m2) of the spacecraft about the [X, Y, Z] axes are denoted by IXX, IYY, and IZZ, respectively. Representative value of gravity gradienttorqueis on theorderof0.001Nm, about1-2orderof magnitudesmaller than the atmospheric torque.