ECE 5233 Satellite Communications
Prepared by:
Dr. Ivica Kostanic
Lecture 5: Orbital perturbations, launch and
orbital effects
(Section 2.3-2.6)
Spring 2014
Outline
Orbital perturbations
Launches and launch vehicles
Placing a satellite in a geo-stationary orbit
Orbital effects
Examples
Important note: Slides present summary of the results. Detailed
derivations are given in notes.
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Sources of orbital perturbations
 Orbital perturbation – difference between real orbit and Keplerian orbit obtained
from two body equations of motion
 Major sources of orbital perturbations
o Perturbations due to non-ideal Earth
o Third body perturbations
o Atmospheric drag
o Solar radiation and solar wind
 Importance of perturbation source depends on the satellite altitude
 Modeling of the real satellite orbit
o Find “osculating orbit” at some time
o Assume orbit elements vary linearly with time
o Use measured data to determine rate of change for orbital parameters
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Effects of non-ideal Earth
 Earth is not a sphere
o Equatorial radius: ~ 6,378 km
o Polar radius: ~ 6,356 km (about 22km smaller)
o Equatorial radius not constant (small variations ~ 100m)
 Earth mass distribution
o Earth mass distribution not uniform
o Regions of mass concentrations: mascons
 Non-ideal Earth causes non-ideal gravitational field
 For LEO and MEO satellites this effect is not very significant
 GEO satellites are impacted the most
o GEO satellites drift towards mascons in the “east-west” direction
o Longitudes of two stable equilibrium points: 75°E and 252°E (or 108°W)
o Longitudes of two unstable equilibrium points: 162°E and 348°E (or 12°W)
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Third-body perturbation
 Motion of the satellite is not a “two-body” problem
 Satellite experiences gravitational pull from Sun
and Moon as well
 The orbital relationship is complex and time
dependent
 Gravitational forces from Sun and Moon tend to
move satellite out of the orbit
 Under these condition the orbit will precess and
its inclination will change (up to 1°/year)
 In practice:
o Some of these effects are planed
o Most of these effects are corrected using
the on-board fuel
o For GEO stationary satellite, the goal is to
keep its apparent position within 0.05
degree box
Orbital position of a satellite the
Earth, the Sun and the Moon
Note: Orbital parameters are continuously measured
and published as TLE data
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Atmospheric drag
 Significant for satellites below 1000km
Example: Consider ISS. From TLE data
 Drag reduces the velocity of the satellite
Mean motion: 15.72137770 rev/day
Derivative of MM/2: 0.00011353 rev/day2
o Semi-major axis is reduced
a/a0 (%)
 Approximate equation for change of semimajor axis
 n

a  a0 1  0 t  t0 
 n0

2 / 3
Semimajor axis change
o Eccentricity is reduced
100.00%
95.00%
90.00%
a/a0 (%)
85.00%
80.00%
0
where
a0 – semi-major axis at t0
n0 – mean motion (revs/day)
n‘0 – first derivative of mean motion (rev/day2)
500 1000 1500 2000
Elapsed time (days)
2500
Note: change is relatively small and it
is long term. In practice it can be
easily resolved through satellite
maneuvering.
Note: Derivative of mean motion is provided in TLE data
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Propagators
 Determine position of a satellite over time
 Three types:
o Analytic
o Semi-analytic
o Numerical
 Analytic – approximate motion of the
satellite through closed form equations
o TwoBody – considers only forces of
gravity from Earth, which is
modeled as a point mass
 Semi-analytic – combination of analytical
and numerical methods
o LOP – Long-term Orbital Predictor.
Uses same elements as analytic
propagators. Accurate over many
months.
o SGP4 for non LEO satellites
 Numerical – Solve complex sets of
differential equations. Accuracy is
obtained at the expense of computational
speed
o J2 Perturbation – models Earths
oblateness, solar and lunar
gravitational forces
o Astrogator – used for trajectory and
maneuver planning and includes
targeting capabilities
o J4 Perturbation – second order
improvements of J2 Perturbation
o HPOP – High Precision Orbital
Propagator. Uses the same orbital
elements as the analytic
propagators.
o SGP4 - Simplified General
Perturbations
Note: Propagators are included in commercial software packages
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Satellite launch
 Two categories of satellite launches
o
o
Expandable launch vehicles

Ariane (EU)

Atlas, Delta (US)

Soyuz (Russia)
Reusable launch vehicles

Space Shuttle (STS) – up to 2011

Dragon, Falcon 9 (Space X)

Buran? Orion?
 Launches are usually done in several stages
o
Launch vehicle is used to place satellite in one of the
transfer LEO orbits
o
Satellite is maneuvered from a transfer orbit into the final
orbit
 Due to Earth rotation – the launch is easiest from equator
o
Velocity boost from Earth rotation ~ 0.47km/sec
o
LEO orbits require velocities ~ 7.5km/sec
o
Launching from equator ~ 6% fuel savings
 Launches from sites that are not on the equator place satellites
in inclined orbits
o
Some of the most frequently used
launch sites
If the satellite is to be placed in GEO stationary orbit, the
correction of the orbit inclination needs to be performed
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Two typical GEO satellite launch approaches
Case 1: single
elliptical orbit
Case 2: two
transfer orbits
 Case 1: Launch vehicle puts the satellite into an elliptical transfer orbit
o
The orbit has high eccentricity with apogee at the geostationary (or geosynchronous) orbit
o
When the satellite passes through apogee, additional velocity is given to the satellite by Apogee Kick
Motor (AKM) and the satellite changes orbits
o
If the orbit is not GEO stationary, additional adjustments are required to correct for the orbit inclination
 Case 2: Lunch vehicle put the satellite into circular LEO orbit
o
Two maneuvers are required
o
Perigee maneuver to transform circular orbit into elliptical orbit, and
o
Apogee maneuver to transform elliptical orbit into GEO stationary orbit
Note: other launch approaches are possible
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Example of GEO launches: French Guyana and KSC
Launch from French
Guyana
Launch from Cape
Carnival, FL
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Orbital effects
 Motion of the satellite has significant impact on its
performance
 Some of the orbital effects to take into account
o Doppler shift
o Solar eclipse
o Sun transit outage
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Doppler shift
 Important in case of LEO and MEO satellites
 Negligible for GEO satellites
 Caused by relative motion between the satellite
and earth station
Example. Consider LEO satellite in circular polar
orbit with altitude of 1000km. Transmit frequency is
2.65GHz.
The velocity of satellite in orbit
T 2  4 2 re  h /   6306.94 sec
3
 The magnitude of Doppler shift is given by:
vs  2 re  h  / T  7.350km/sec
f R  fT f VT


fT
fT
c
Largest component of velocity between satellite and
Earth station occurs when the satellite is coming out
of horizon directly over the station
f  VT fT / c  VT / 
Where: fR – received frequency, fT – transmit
frequency, VT – velocity between satellite and
Earth station,  – wavelength, c – speed of light
vr max  vs cos   vs
re
 6.354km/sec
re  h
Maximum Doppler shift
f max  vr max fT / c  56.13kHz
Note: the shift becomes larger with
higher frequencies.
Geometry used for calculation of
maximum velocity
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Solar eclipse
 Eclipse – sunlight fails to reach satellite due to obstruction
from either Earth or Moon
 More common type of eclipse – eclipse due to satellite
coming in the shadow of the earth
 For geostationary satellite the solar eclipse occurs for about
82 days every year
 The eclipse times vary from day to day
Geometry of solar eclipse
 The longest eclipses are on equinox days (days when the
sun passes through equatorial plane) – Nominally: March 21st
and September 23st
 When the satellite passes through eclipse
o It loses its source of power (relies on battery power)
o It may need to shut off some of its transponders
o Experiences cooling down in temperature
o Transients due to switching of the equipment and
temperature variations may cause equipment failure
Duration of solar eclipse of a geo
stationary satellite relative to equinox time
Note: for non geostationary satellites
orbital study necessary to determine
eclipse times
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Sun transit outage
 Sun transit outage - occurs when the satellite
passes in front of the Sun
 Sun is a source of electromagnetic radiation
 Sun – noise source with equivalent temperature
of 6000K – 11000K
 In most cases this noise overcomes link design
margins
Geometry of sun transit eclipse
 During sun transit outage – communication lost
 Duration of the outage as much as 10 min/day
 For geo-stationary satellites outages occur
0.02% of the time
 Duration problematic since it usually occurs in a
traffic intensive part of the day
 Satellite providers try to re-route the traffic
through other satellites
Radiation spectrum of the Sun
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