Chapter 3 GPS Satellite Orbit

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Chapter 3 GPS Satellite Orbit

• Motion of Space Objects

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3.1a Motion of Space Objects

• 1473 -1543 Copernicus
• Heliocentric (sun in the center) Orbit
• 1546 1601 Tycho Brahe
• Before telescope followed the planets (acquired
  quality data)
• 1571 1630 Johannes Kepler (link)
• Discovered orbital path to be elliptical around
  focus point
• Keplers 3 laws of planetary motion
• 1642 1727 Sir Isaac Newton
• Physical Principals Universal law of
  Gravitation

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3.1b Keplers 3 (empirical) laws of Planetary
Motion

• First Law (elliptical orbit) link link2
• The orbital path of a planet takes the shape of
  an ellipse, with the Sun located at one of its
  focal points.
• Second Law (planet speed changes) link
• line connecting the Sun to any planet sweeps
  out equal areas of the orbital ellipse in equal
  time intervals
• Third Law (relationship of planet orbit periods)
• the ratio of the square of the planets orbital
  period and the cube of the mean distance from the
  Sun is constant

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3.1c Keplers 3 (empirical) laws of Planetary
Motion

• 1) Keplers three laws of planetary motion
• Apply to any orbiting object (Satellites)
• 2) GPS Satellites orbit the earth in an
  elliptical path
• 3) Earth becomes the focal points

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3.1c Geometry of an Ellipse

• Semi-major axis of the satellite orbit
• Eccentricity of the satellite orbit (deviation
  from a circle) link
• A satellite is closest to the earth at a point
  called Perigee
• A satellites farthest point from the earth is
  called apogee
• GPS orbital period of 12 hours based on
  Keplers third law corresponds to a satellite
  altitude of about 20,000km above the surface of
  the earth

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3.2a Types of Orbits

• Satellites orbits vary depending on
• 1) altitude 2) inclination 3) orbital period
• Three classes of Satellite orbits
• 1) Low Earth Orbit (LEO)
• up to 2,000km altitude
• remote sensing satellites, altimeter
  satellites, other
• 2) Medium Earth Orbit (MEO)
• altitudes between 5,000km 20,000km
• GPS satellites (12hr period twice a day)
• 3) Geostationary Earth Orbit (GEO) 24hr period
  appears fixed
• altitudes of 36,000km
• communication satellites

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3.2b Other Types of Orbits

• Inclined geosynchronous orbit (IGSO)
• ground tracking of a figure eight
• does not appear stationary
• Highly Elliptical
• perigee (closest point to the earth) 500km
• apogee (farthest point from the earth) 50,000km
• communication services at high latitudes
• Polar Orbits
• inclination of 90 degrees (perpendicular to
  equator)
• They are fixed in space
• Provides global coverage

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3.3 Ideal (Keplerian) Satellite Orbit
If satellites orbit motion obeys the 3 kepler
laws (ideal) This would be true only under
certain ideal conditions 1) all forces except
the Earths gravitation force are neglected 2)
the Earths gravitational field is radially
symmetric 3) no atmosphere 4) satellite mass is
negligibly small compared to Earths
mass Keplerian Elements link 1) Semi-major axis
of the satellite orbit (a) 2) Eccentricity of
the satellite orbit (e) 3) Right ascension of
the ascending node (?) 4) Argument of perigee
(?) 5) The Inclination (i) 6)True anomaly (f)
the only one that changes with time) eccentric
anomaly (E) and mean anomaly (M) mean anomaly
transmitted in navigation message

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3.4 Perturbed Satellite Orbit Higher the
satellite orbit is, the smaller the
perturbations and the smoother the orbit

1) Noncentral attraction of Earth (equatorial
bulge) 2) Gravitational attraction of Sun, moon,
and planets (third body) 3) Temporal variation
of gravity field due to tides (ocean earth) 4)
Solar radiation pressure (direct and albedo
effects) 5) Atmospheric drag effect (friction of
SV and particles) 6) Other factors including
magnetic forces and solar wind
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3.5a GPS Broadcast OrbitPredicted orbital
parameters

12 monitoring stations collect GPS data (May
2006) MCS runs the Kalmanlink filter to produce
orbital parameters GPS Navigation Message
(predicted orbital parameters) 16 parameters
needed to describe the perturbed orbit row 1
the ephemeris reference time rows 2 7 six
Keplerian elements rows 8 16 represent the
perturbation parameters Mean Motion - mean
angular satellite velocity, calc true
anomaly Argument of Latitude sum of the true
anomaly, argument of perigee
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3.5b GPS Broadcast OrbitPredicted orbital
parameters

After applying all of these corrections New
set of parameters are used to computer Satellite
coordinate at signal transmission time Satellite
Coordinates refer to WGS 84 system (World
Geodetic System of 1984) Ephemeris records are
updated every hour
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3.5c GPS Broadcast OrbitPredicted orbital
parameters

Issues with Broadcast Ephemeris IODC (issue of
data clocks) IODE (issue of data
ephemeris) See Ephemeris Chart page 38-39
El-Rabanny
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3.6a GPS AlmanacSubset of comprehensive
ephemeris data

Almanac contains Satellite coordinates Satellit
e clock correction parameters Transmitted as
part of the navigation message Less accurate
than the Ephemeris Updated every 6 days or less
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3.6b GPS AlmanacSubset of comprehensive
ephemeris data

A complete Almanac file helps Ground GPS
receiver rapidly acquire signal Used to predict
satellite visibility at a particular
location Mission planning software See chart
page 40
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3.7 Satellite VisibilityAt times there are only
4 or 5 SV visible

Number of Satellites Elevation of
Satellites Satellite geometry Urban Canopy
Forest areas (obstruction) Selecting suitable
observation times Based on user location
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3.7 Satellite VisibilityAt times there are only
4 or 5 SV visible

Sky Plot
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3.7 Satellite VisibilityAt times there are only
4 or 5 SV visible

Satellite Elevation
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3.7 Satellite VisibilityAt times there are only
4 or 5 SV visible

Satellites Azimuth
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3.7 Satellite VisibilityAt times there are only
4 or 5 SV visible

Satellites in View
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3.7 Satellite VisibilityAt times there are only
4 or 5 SV visible

Visible Periods
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3.7 Satellite VisibilityAt times there are only
4 or 5 SV visible

DOP Graph