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Chapter 3 GPS Satellite Orbit

3.1a Motion of Space Objects. 1473 -1543 CopernicusHeliocentric (sun in the center) Orbit1546 ? 1601 Tycho BraheBefore telescope followed the planets (acquired quality data)1571 ? 1630 Johannes Kepler (link)Discovered orbital path to be elliptical around focus pointKeplers 3 laws of planetary motion1642 ? 1727 Sir Isaac NewtonPhysical Principals ? Universal law of Gravitation.

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Chapter 3 GPS Satellite Orbit

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    1. Chapter 3 GPS Satellite Orbit Motion of Space Objects

    2. 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 http://galileo.rice.edu/ Galileo 1560-1640 (introduced the telescope 1610) http://galileo.rice.edu/chron/galileo.html http://galileo.rice.edu/sci/theories/copernican_system.html http://galileo.rice.edu/sci/brahe.html http://galileo.rice.edu/sci/kepler.html (naked eye observations) http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Kepler.html http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Kepler.html Neither was Kepler's approach to the problem of causes of motion in any mathematical sense an anticipation of the work of Newton (despite the views of some previous commentators); it was, by contrast, governed by his background in the Aristotelian tradition. Though this Aristotelian 'physics' was becoming outdated even in Kepler's day, people still believed that an object would not move unless there was a 'force' or cause of motion to make it do so. Also, this 'force' had to act by contact; and, the object would then move only in the direction of the 'force', while the amount of 'force' was responsible for the amount of motion produced. Kepler could never have supposed that the Sun could exert an attractive force because that concept did not exist in Aristotelian terms. http://galileo.rice.edu/ Galileo 1560-1640 (introduced the telescope 1610) http://galileo.rice.edu/chron/galileo.html http://galileo.rice.edu/sci/theories/copernican_system.html http://galileo.rice.edu/sci/brahe.html http://galileo.rice.edu/sci/kepler.html (naked eye observations) http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Kepler.html http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Kepler.html Neither was Kepler's approach to the problem of causes of motion in any mathematical sense an anticipation of the work of Newton (despite the views of some previous commentators); it was, by contrast, governed by his background in the Aristotelian tradition. Though this Aristotelian 'physics' was becoming outdated even in Kepler's day, people still believed that an object would not move unless there was a 'force' or cause of motion to make it do so. Also, this 'force' had to act by contact; and, the object would then move only in the direction of the 'force', while the amount of 'force' was responsible for the amount of motion produced. Kepler could never have supposed that the Sun could exert an attractive force because that concept did not exist in Aristotelian terms.

    3. 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 planet’s orbital period and the cube of the mean distance from the Sun is constant”

    4. 3.1c Keplers 3 (empirical) laws of Planetary Motion 1) Kepler’s 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 link http://astro.unl.edu/naap/pos/pos_background1.html http://astro.unl.edu/naap/pos/animations/ellipsedemo.swf http://astro.unl.edu/naap/pos/pos_background1.html http://astro.unl.edu/naap/pos/animations/ellipsedemo.swf

    5. 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 Kepler’s third law corresponds to a satellite altitude of about 20,000km above the surface of the earth” http://www.wolffdata.se/gps/gpshtml/anomalies.html http://www.wolffdata.se/gps/gpshtml/anomalies.html

    6. 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

    7. 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

    8. 3.3 Ideal (Keplerian) Satellite Orbit

    9. 3.4 Perturbed Satellite Orbit Higher the satellite orbit is, the smaller the perturbations and the smoother the orbit

    10. 3.5a GPS Broadcast Orbit Predicted orbital parameters

    11. 3.5b GPS Broadcast Orbit Predicted orbital parameters

    12. 3.5c GPS Broadcast Orbit Predicted orbital parameters

    13. 3.6a GPS Almanac Subset of comprehensive ephemeris data

    14. 3.6b GPS Almanac Subset of comprehensive ephemeris data

    15. 3.7 Satellite Visibility At times there are only 4 or 5 SV visible

    16. 3.7 Satellite Visibility At times there are only 4 or 5 SV visible

    17. 3.7 Satellite Visibility At times there are only 4 or 5 SV visible

    18. 3.7 Satellite Visibility At times there are only 4 or 5 SV visible

    19. 3.7 Satellite Visibility At times there are only 4 or 5 SV visible

    20. 3.7 Satellite Visibility At times there are only 4 or 5 SV visible

    21. 3.7 Satellite Visibility At times there are only 4 or 5 SV visible

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