BASIC ORBIT MECHANICS 1-1 Example Mission Requirements: Spatial and Temporal Scales of Hydrologic Processes 1.E+05 Lateral Redistribution 1.E+04 Year Evapotranspiration 1.E+03 Month 1.E+02 Week Percolation Streamflow Day 1.E+01 Time Scale (hours) Scale Time 1.E+00 Precipitation Runoff Intensity 1.E-01 Infiltration 1.E-02 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Length Scale (meters) 1-2 BASIC ORBITS • Circular Orbits – Used most often for earth orbiting remote sensing satellites – Nadir trace resembles a sinusoid on planet surface for general case – Geosynchronous orbit has a period equal to the siderial day – Geostationary orbits are equatorial geosynchronous orbits – Sun synchronous orbits provide constant node-to-sun angle • Elliptical Orbits: – Used most often for planetary remote sensing – Can also be used to increase observation time of certain region on Earth 1-3 CIRCULAR ORBITS • Circular orbits balance inward gravitational force and outward centrifugal force: R 2 F mg g s r mv2 F c r g R2 F F v s g c r 2r r T 2r 2 v gs R • The rate of change of the nodal longitude is approximated by: d 3 cos I J R3 g dt 2 2 s r 7 2 1-4 Orbital Velocities 9 8 7 6 5 Earth Moon 4 Mars 3 Linear Velocity in km/sec in Linear Velocity 2 1 0 200 400 600 800 1000 1200 1400 Orbit Altitude in km 1-5 Orbital Periods 300 250 200 Earth Moon Mars 150 Orbital Period in MinutesPeriodOrbitalin 100 50 200 400 600 800 1000 1200 1400 Orbit Altitude in km 1-6 ORBIT INCLINATION EQUATORIAL I PLANE EARTH ORBITAL PLANE 1-7 ORBITAL NODE LONGITUDE SUN ORBITAL PLANE EARTH VERNAL EQUINOX 1-8 SATELLITE ORBIT PRECESSION 1-9 CIRCULAR GEOSYNCHRONOUS ORBIT TRACE 1-10 ORBIT COVERAGE • The orbit step S is the longitudinal difference between two consecutive equatorial crossings • If S is such that N S 360 ; N, L integers L then the orbit is repetitive. S 1-11 PERIODIC COVERAGE PATTERNS FOR SUN-SYNCHRONOUS ORBITS 1-12 Example: 223 orbits in 16 days 1-13 Example: 225 orbits in 16 days 1-14 Example: 227 orbits in 16 days 1-15 Example: 233 orbits in 16 days (LandSat) 1-16 Example: 241 orbits in 16 days 1-17 Example: SRTM Orbit 1-18 QuikSCAT Orbit: 14 Orbits per day 1-19 QUIKSCAT Swaths 1-20 ELLIPTICAL ORBITS • The orbit is defined by: a1 e2 r 1 e cos a 3 T 2r 2 gs R r 2b 2a 1e2 2a 1-21 ELLIPTICAL GEOSYNCHRONOUS ORBIT TRACE 1-22 ELLIPTICAL ORBIT GROUND TRACE 1-23 ORBIT SELECTION Minimize Earth atmospheric drag --> h > 200 km Global coverage --> polar or near-polar orbit Constant illumination geometry --> sun-synchronous orbit Thermal inertia observations --> day and night pass over same area Minimize radar sensor power --> low altitude Minimize gravity anomalies perturbation --> high altitude Measure gravity anomalies --> low altitude Continuous monitoring --> geostationary or geosynchronous orbit 1-24.