Computation of Azimuth and Elevation George H. Born

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Computation of Azimuth and ElevationGeorge H.
Born
These slides describe how to convert a spacecraft
vector, , in ECEF or ECI coordinates to Azimuth
and Elevation given geocentric latitude, east
longitude, and height above the ellipsoid of a
tracking station. ECEF coordinates are
considered first.
is given
ECEF vector of spacecraft
Station location ( , , H)
ECEF frame
Geodetic latitude
East longitude
Height above ellipsoid
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Computation of Azimuth and Elevation
1) Compute in the ECEF ( , , ) frame
and are the equatorial radius and
flattening respectively of the reference ellipsoid
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Computation of Azimuth and Elevation
2) Compute in ECEF coordinates
3) Now convert to coordinates
To get replace with
the coordinates of .
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Computation of Azimuth and Elevation
4) Compute Azimuth, , and Elevation, .
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Computation of Azimuth and Elevation

• If the spacecraft vector is given in J2000 ECI
  coordinates (X, Y, Z) it is necessary to
  transform it into the ECEF frame. To be accurate
  this involves a series of five rotations to
  account for equatorial precession, nutation,
  Earth rotation, and polar motion. However, a
  close approximation can be obtained by only
  accounting for Earth rotation. This can be
  accomplished by computing the Greenwich sidereal
  time, , given by
• where is the rotation rate of the Earth,
  0.72921158553 x 10-4 rad/sec, is the angle
  between the ECI X-axis and the prime meridian
  measured in the equatorial plane, and is the
  value of at the reference time, . The
  spacecraft vector in the ECEF frame is given by

Now proceed with step 1.
Then
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Computation of Azimuth and Elevation
The value of at any UTC can be obtained by
inserting a satellite into a scenario in STK.
Set the orbit epoch and start time to the desired
UTC, set the longitude of the ascending node to
0.0 and click the apply button. Then choose
right ascention of the ascending node (RAAN).
This will be the value of for the chosen
time. Of course, one can also compute the
Azimuth and Elevation in STK.
For example, at universal time coordinated, UTC,
JAN 1, 2008, 0 h, 0 m, 0 sec,
.

• References
• Bate, Muller, and White, Fundamental of
  Astrodynamics, Dover, 1971,
• Chapter 2.
• Curtis, H. D., Orbital Mechanics for Engineering
  Students, Elsevier, 2005,
• Chapter 5.5.