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
Time Scale (hours)
1.E+03
Month
1.E+02
1.E+01
Week Percolation
Streamflow
Day
1.E+00
Precipitation
Intensity
Runoff
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:
2
Fg  mgs
Fc 
R 
r 
mv 2
r
Fg  Fc  v 
T
•
g s R2
r
2 r
r
 2r
v
gs R 2
The rate of change of the nodal longitude is approximated by:
d
3
cos I
  J2 R 3 gs 7 2
dt
2
r
1-4
Orbital Velocities
9
8
Linear Velocity in km/sec
7
6
5
Earth
Moon
Mars
4
3
2
1
0
200
400
600
800
1000
1200
1400
Orbit Altitude in km
1-5
Orbital Periods
300
Orbital Period in Minutes
250
200
Earth
Moon
Mars
150
100
50
200
400
600
800
1000
1200
1400
Orbit Altitude in km
1-6
ORBIT INCLINATION
I
EQUATORIAL
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
S  360
N
;
L
N, L
integers
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:
r
a1  e
2

1  e cos 
T  2 r
a3
gs R 2
r

2b  2a 1 e 2
2a
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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
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