Corso di Missioni e Sistemi Spaziali Prof. Luciano Iess A.A. 2014-‐2015 Prova di ammissione all’esame in modalità facilitata z" ! D ! v0 y" Radar)B" ! g ! r0 x" Radar)A" A mass is following a ballistic trajectory after launch from an unknown site at t0 = 0 sec. A few seconds after launch two radar stations start tracking the object, generating range and range-‐ rate measurements. Both radars are fixed and their coordinates relative to the reference system origin are: Radar A Radar B x 0 m 1720 m y 0 m 2457 m z 0 m 0 m Radar A provides range-‐rate measurements accurate to 1mm/s and range measurements accurate to 2 m. Radar B provides range measurements accurate to 4 m. You find the observable quantities in the files trackA.txt and trackB.txt, whose structure is: File: TrackA.txt TrackB.txt 1st column: observation time (s) observation time (s) nd 2 column: range in (m) range in (m) rd 3 column: range-‐rate (m/s) -‐ Assuming that: • Motion is in 3D space and the ground is flat and non-‐rotating • The (constant) gravity acceleration is 9.81 m/s2 • Drag is not negligible and the object ballistic coefficient is Bc • The (constant) atmospheric density is 1.2 kg/m3 • First guess initial condition are: Launch a-‐priori value a-‐priori uncertainty (1-‐sigma) site: x0 9893 m ± 10000 m y0 830 ± 10000 m z0 301 ± 5000 m Object: a-‐priori value a-‐priori uncertainty (1-‐sigma) vx0 -‐259 m/s ± 100 m/s vy0 -‐68 m/s ± 100 m/s vz0 222 m/s ± 50 m/s 2 Bc 7999 kg/m ± 3000 kg/m2 1) Estimate the launch site coordinates, the projectile initial velocity, and the ballistic coefficient Bc with Radar-‐A range-‐rate and Radar-‐B range measurements. 2) Repeat the estimate of point 1 using the Radar-‐A range measurements in place of range-‐ rate. 3) Compare and comment the estimates in point 1 and 2. 4) Are the provided measurements accuracies correct? 5) Compute an estimate (value and uncertainty) of the distance covered by the object and its maximum height from solutions of point 1 and 2.
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