Astronomical Institute, Academy of Sciences

Ondřejov Observatory,Czech Republic

&Geodetic Observatory,

Research Inst. for Geodesy, Topography and Cartography,

Zdiby&

CEDR Prague-Ondřejov

SATELLITE ORBIT GEOMETRY: DIVERSITY OF GROUND TRACKS,

APPLICATIONS FOR GRAVITY STUDIES, OCEANOGRAPHY, AND REMOTE SENSING

J. Klokočník, J. Kostelecký

LECTURE AT NRIAG HELWAN EGYPT November 2005

Definitions Geometry of Satellite Groundtrack Patterns is dictated by the orbit inclination, semimajor axis, and eccentricity

Fundamental interval Longitudinal spacing between sequential orbit traces at the equator Equals to the nodal period of satellite motiont times the difference between the inertial rotation of the Earth and precessional rate of the line of orbit nodes

S = o α/β Density of ground tracks Longitudinal spacing of adjacent tracks at equator

D = o/β [km] where o=40075km=2π R Density also depends on latitude which is not described by this equation

• Geodetic Mission• Exact Repeat (Oceanography) Mission• Orbit maneouvres in semimajor axis to tune orbit for specific application

Example of ground tracks for a satellite with given orbit inclination and semimajor axis,

ascending and descending tracks,

prograde vs retrograde orbits

crossover points, turning points

number of nodal revolutions per of synodic daysnumber of nodal revolutions per of synodic days

Ground tracks for EgyptSat1 initial elements I= 98. 1 deg a = 7046. 14 km resonant orbits (ExactRepeat Missions): Kozai’s semimajor axes a(44/3) = 7048.60 km a(191/13) = 7040.45 km

Examples of ground tracks density for EgyptSat1 theoretical orbit

• Density of ground tracks D =o/β [km], where o=40075km=2π R

• Geodetic Missions GM• Exact Repeat (Oceanography) Missions ERM• Orbit maneouvres in semimajor axis to tune orbit for specific application

Examples resonance β/α density of ground tracks [in km]---------------------------------------------------------------------------------------- 44/3 910 59/4 680 89/6 450 191/13 210 … 235/16 170 GM <20 **--------------------------------------------------------------------------------------

GRACE around 61/4 resonance

Conclusions

Orbit of a satellite can be tailored to the required application by a proper selection of orbital inclination and semimajor axis

(examples given for gravity missions and oceanography satellites)

Small changes of semimajor axis by the orbit maneouvre(s) (even without changing the other elements) result in different resonance regimes and in changes of the density of satellite ground tracks, and such changes may be dramatic

One satellite may offer several different orbits with diverse

density of ground tracks and thus may serve for different applications (different orbit scenarios)

(examples of orbit maneouvres of ERS 1,2, and also -- with another motivation -- semimajor axis increments for CHAMP)

To get a copy

• Anonymous ftp: sunkl.asu.cas.cz• pub/jklokocn

file: PPT_GEOMETRY_EGYPT05.ppt

• For more information: Web: www.asu.cas.cz/~jklokocn • e-mail: jklokocn@asu.cas.cz• kost@fsv.cvut.cz

The END