ece 5233 - lecture 5
TRANSCRIPT
ECE 5233 Satellite Communications Prepared by:
Dr. Ivica Kostanic
Lecture 5: Orbital perturbations, launch and orbital effects
(Section 2.3-2.6)
Spring 2014
Florida Institute of technologies
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Orbital perturbationsLaunches and launch vehiclesPlacing a satellite in a geo-stationary orbitOrbital effectsExamples
Outline
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 perturbationso Perturbations due to non-ideal Eartho Third body perturbationso Atmospheric drago 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 timeo Use measured data to determine rate of change for orbital parameters
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Effects of non-ideal Earth
Earth is not a sphereo Equatorial radius: ~ 6,378 kmo Polar radius: ~ 6,356 km (about 22km smaller) o Equatorial radius not constant (small variations ~ 100m)
Earth mass distributiono 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” directiono 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 planedo Most of these effects are corrected using
the on-board fuelo For GEO stationary satellite, the goal is to
keep its apparent position within 0.05 degree box
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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 Drag reduces the velocity of the satellite
o Semi-major axis is reducedo Eccentricity is reduced
Approximate equation for change of semi-major axis
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3/2
00
00 1
ttnnaa
where
a0 – semi-major axis at t0
n0 – mean motion (revs/day)
n‘0 – first derivative of mean motion (rev/day2)
Example: Consider ISS. From TLE data
Mean motion: 15.72137770 rev/day
Derivative of MM/2: 0.00011353 rev/day2
0 500 1000 1500 2000 250080.00%
85.00%
90.00%
95.00%
100.00%
a/a0 (%)
a/a0 (%)
Elapsed time (days)
Sem
imaj
or a
xis
chan
geNote: 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-analytico 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
o J2 Perturbation – models Earths oblateness, solar and lunar gravitational forces
o J4 Perturbation – second order improvements of J2 Perturbation
o SGP4 - Simplified General Perturbations
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Note: Propagators are included in commercial software packages
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 Astrogator – used for trajectory and maneuver planning and includes targeting capabilities
o HPOP – High Precision Orbital Propagator. Uses the same orbital elements as the analytic propagators.
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Satellite launch Two categories of satellite launches
o Expandable launch vehicles Ariane (EU) Atlas, Delta (US) Soyuz (Russia)
o 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 orbitso 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/seco LEO orbits require velocities ~ 7.5km/seco Launching from equator ~ 6% fuel savings
Launches from sites that are not on the equator place satellites in inclined orbits
o 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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Some of the most frequently used launch sites
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Two typical GEO satellite launch approaches
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Case 1: Launch vehicle puts the satellite into an elliptical transfer orbito The orbit has high eccentricity with apogee at the geostationary (or geosynchronous) orbito When the satellite passes through apogee, additional velocity is given to the satellite by Apogee Kick
Motor (AKM) and the satellite changes orbitso 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 orbito Two maneuvers are requiredo Perigee maneuver to transform circular orbit into elliptical orbit, ando Apogee maneuver to transform elliptical orbit into GEO stationary orbit
Case 1: single elliptical orbit
Case 2: two transfer orbits
Note: other launch approaches are possible
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Example of GEO launches: French Guyana and KSC
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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 accounto Doppler shifto Solar eclipseo 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 The magnitude of Doppler shift is given by:
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cV
ff
fff T
TT
TR
// TTT VcfVf
Where: fR – received frequency, fT – transmit frequency, VT – velocity between satellite and Earth station, – wavelength, c – speed of light
Example. Consider LEO satellite in circular polar orbit with altitude of 1000km. Transmit frequency is 2.65GHz.
The velocity of satellite in orbit
sec94.6306/4 322 hrT e
km/sec350.7/2 Thrv es Largest component of velocity between satellite and Earth station occurs when the satellite is coming out of horizon directly over the station
km/sec354.6cosmax
hr
rvvve
essr
Maximum Doppler shift
kHz13.56/maxmax cfvf Tr
Geometry used for calculation of maximum velocity
Note: the shift becomes larger with higher frequencies.
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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 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 eclipseo It loses its source of power (relies on battery power)o It may need to shut off some of its transponderso Experiences cooling down in temperature o Transients due to switching of the equipment and
temperature variations may cause equipment failure
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Geometry of solar eclipse
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 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
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Radiation spectrum of the Sun
Geometry of sun transit eclipse