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Homework 3 will include a Helmert Transformation

Homework 3 will include a Helmert Transformation Estimation problem. Specifically interested in scale. Started on January 29, 2010. Message: different systems are based on different “rulers”. Back to ECI to ECEF. Precession & Nutation.

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Homework 3 will include a Helmert Transformation

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  1. Homework 3 will include a Helmert Transformation Estimation problem. Specifically interested in scale. Started on January 29, 2010

  2. Message: different systems are based on different “rulers”

  3. Back to ECI to ECEF

  4. Precession & Nutation • Precession caused by the gravitational attraction of the Sun and Moon on the non-spherical Earth (period 26,000 yrs). • Nutation: small "nodding" motion (largest period of 18.6 yrs, Moon). • A spherical Earth with homogeneous density distribution would neither precess nor nutate. • CU physics prof. John Wahr created the international theory for nutations as part of his PhD thesis! • Nutation theory has since been improved - especially due to VLBI measurements.

  5. Polar motion • Axisymmetrical body, moments of inertial I and I’, and no forcing rotates about the axis of symmetry at a constant rate comparable to (I’-I)/I’ • Based on flattening factor, “free-nutation” of the Earth was predicted by Euler in 1755 to have period of 355 days. • Actual Chandler period is ~433 days. Discrepancy is due to anelasticity of the Earth. • Polar motion cannot be predicted; it must be measured.

  6. At the equator, an arc second is 30.87 meters Polar Motion ~16 meters

  7. Length of day, aka earth rotation data

  8. Where can I find precise Earth Orientation data? IERS Bulletin A IERS Bulletin B OCT 26 54399 0.06157 0.19014 -0.208079 -33.208079 -65.6 -5.1 OCT 31 54404 0.04779 0.19100 -0.212423 -33.212423 -64.6 -4.9 NOV 5 54409 0.03593 0.19258 -0.216363 -33.216363 -63.8 -4.2 NOV 10 54414 0.02530 0.19346 -0.220665 -33.220665 -63.4 -4.4 NOV 15 54419 0.01111 0.19549 -0.225243 -33.225243 -62.5 -4.3 NOV 20 54424 -0.00423 0.19944 -0.230923 -33.230923 -62.1 -4.1 NOV 25 54429 -0.01814 0.20487 -0.237795 -33.237795 -61.9 -4.0 NOV 30 54434 -0.02865 0.20954 -0.244205 -33.244205 -61.0 -3.6 DEC 5 54439 -0.03673 0.21721 -0.250380 -33.250380 -61.3 -3.1 Values of x,y, UT1R-UTC, UT1R-TAI, dPsi,dEpsilon http://www.iers.org/

  9. These data are (mostly) available from the IGS

  10. Example of IGS polar motion quality http://igscb.jpl.nasa.gov/components/prods.html

  11. Lecture starting February 1, 2010 Talk about truncation/fprintf http://www.colorado.edu/ASEN/asen6090/orbit_practical2.html (what happens if you don’t do all this stuff) For comparison, Venus is 1E-10

  12. In ASEN 5090, orbits are a forward model calculation. In ASEN 6519, orbits are a interpolation problem. But what do the real GPS people do?

  13. Solar Pressure • Effect of sun on the satellite • Need to know how much area is normal to sun-direction. • How reflective are the surfaces • Distance and luminosity of the sun

  14. Design constraints • Antenna boresight points at the geocenter. Why? • Solar panels are oriented to point continually at the sun • Y-axis is perpendicular to z and p. • How well do we know attitude? EPS = Earth-probe-sun

  15. SRP model parameters • Reflectivity - proportion of radiation incident on a surface that is reflected • Specularity - how much of the reflection is “specular” • Y-bias - force acting along the spacecraft BFS (body-fixed-system) and believed to derive from NCF effects.

  16. Another view of the spacecraft

  17. What about eclipsing GPS satellites? • SRP goes to zero - but it takes a while for the spacecraft to cool down. • Attitude control system loses its bearings. • Before 1994, it would yaw wildly. Yaw bias now applied by DoD. • Satellites in eclipse season are more poorly modelled than other satellites. Many analysis centers remove the data entirely.

  18. We know that “precise” IGS orbits are precise How do you test their accuracy? - Satellite Laser Ranging (SLR) tracking. People have even talked about tracking GPS signals from VLBI systems.

  19. Davis and Trask, 2007

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