Coordinates and Satellite Orbits

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2013/3/6WGS-84 ParametersJyh-Ching Juang, EE, NCKUDefining parametersSemimajor axis of ellipsoid, a = 6378137 m.Geometric flattening, f = 1/298.257223563Earth's geocentric gravitational constant, =GM= 3986004.418418×10 8 m 3 /sec 2Angular velocity of the Earth, = 7292115 ×10 -11 rad/secDerived geometric and physical constantsZonal harmonic coefficient of second degreeSemiminor axis, b = 6356752.3142 m.Square of major eccentricity,Normal gravitySpeed of light, c = 299792458 m/sec.15Orbital MechanismJyh-Ching Juang, EE, NCKUOrbital mechanics is concerned with the motion of natural orman-made celestial bodies under the influence of gravity and isgoverned by Newton's laws.Why do we have to know the GNSS orbits?An GNSS orbital error directly affect the positional error.GNSS orbital information can be obtained by either processing theGNSS broadcast message or from control/monitoring centers.Needs of satellite orbital informationPlanning the use of GNSS, satellite selectionSignal acquisitionGNSS broadcast information processingPoint position computation improvement168
2013/3/6Kepler’s LawJyh-Ching Juang, EE, NCKU1. The orbit of each planet is an ellipse with the sun at one of the foci.2. Each planet revolves so that the line joining it to the sun sweepsout equal areas in equal lengths of time regardless of the positionof the position of the planet in its orbit.3. The squares of the periods of any two planets are in the sameproportion as the cubes of their mean distances from the sun.3a 2bT periapsis(perigee)apoapsis(apogee)r ar paSemimajor axis17Newton’s LawJyh-Ching Juang, EE, NCKUAssume that two point masses M and m are separated by thedistance r. Applying Newtonian mechanics to the two-body systemyields the equation that governs the motion of m relative to M2( )dr r 0r r 02 3rdt r2d G M mdt2 3r : vector from M to mr r : distanceG: universal gravitational constant GM ( m)GMFor the two-body system, the following properties are valid.The center of mass of the two-body system is unaccelerated and thusmay serve as the origin of an inertial reference frame.The energy is conserved.The angular momentum of the system is constant; as a result, themotion is in a plane normal to the angular momentum vector.The masses M and m follow paths that are conic sections with theircenter of mass as one focus; thus, the possible orbits are a circle, anellipse, a parabola, or a hyperbola.189
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Page 16 and 17: 2013/3/6Matlab ExercisesJyh-Ching J
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Coordinates and Satellite Orbits

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