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 2r r T   2r 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:

a1  e2  r  1  e cos a 3 T  2r 2 gs R

r

 2b  2a 1e2

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