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8/19/2019 Orbital Mechanics 2
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8/19/2019 Orbital Mechanics 2
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• Orbit transfer
• Change of orbital plane• Orbit Rendezvous• Orbit maintenance• De-orbit
Orbitmaneuvering
• Low-altitude Earth orbit• Medium-altitude Earth oribt• High-altitude Earth orbit
Type of orbits
• The orbit desing process• Orbits during the space mission lifetime• Earth coverage
Orbit design
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ORBIT MANEUVERING
• Most satellites must change their OE during their lifetime:• Examples:
1. Transfer from initial parking orbit to final orbit2. Correct orbits from perturbation
3. Intercept a target4. De-orbit
• To change the orbit of a satellite: to change the satellitesvelocity vector in magnitude or direction using a thruster
V=Vneed -Vcurrent• The position does not change significantly during
impulsive burns.
8/19/2019 Orbital Mechanics 2
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ORBIT MANEUVERING
• The most common type of orbit maneuvering: change sizeand energy of the orbit remaining in the same orbital plane
• There exists different transfer
orbits depending of the missionrequirements:
• Smallest amount of energy•
Minimum transfer time
Coplanar orbit transfers
8/19/2019 Orbital Mechanics 2
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ORBIT MANEUVERING
• Walter Hohmann (1880-1945)german engineer.
• Hohmann transfer orbit consists in
a elliptical orbit tangent to both theinitial and final circular orbits at thetransfer’s orbit perigee and apogee,respectively.
• Velocity vectors are collinear at theintersecction points
• Represents the most fuel-efficienttransfer between two coplanarcircular orbits
Hohmann transfer orbit
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ORBIT MANEUVERING
Hohmann transfer orbit
8/19/2019 Orbital Mechanics 2
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ORBIT MANEUVERING
Hohmann transfer orbit
8/19/2019 Orbital Mechanics 2
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ORBIT MANEUVERING
Hohmann transfer orbit
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ORBIT MANEUVERING
Hohmann transfer orbit formulation
Parking orbit
r A= 6567 kmGeostationary orbit
r B= 42160 km
Orbital velocity of the parking orbitV A= 7.79 km/s
Orbital velocity of the GOV B= 3.08 km/s
Semimajor axis of the transfer orbita T= 0.5( r A+r B)=24364 km
Btransf B A Atransf B A V V V V V V V ,,
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ORBIT MANEUVERING
Hohmann transfer orbit formulation
Transfer velocity at perigee V TA= 10.25 km/s
Transfer velocity at apogee V TB= 1.49 km/s
Change velocity at perigee V A=2.46 km/s
Change velocity at apogee V B=1.49 km/s
Total velocity change V =3.95 km/s
Time of transfer, P/2 T=5 hr 15 min
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ORBIT MANEUVERING
• Hohmann transfer is efficient in energy terms, but notin transfer time
• The time of transfer can be calculated with the 3rdKepler’s law
• Paradox: we have increase the velocity in two burns,but the final velocity is slower than originally
Hohmann transfer orbit discussion
1/ 23transf
flight
aT
GM
8/19/2019 Orbital Mechanics 2
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ORBIT MANEUVERING
• Sometimes we need totransfer a satellite in lesstime than that required for
a Hohmann transfer• In the one-tangent burn
the transfer orbit istangential to the initial
orbit• The transfer orbit
intersects the final orbitwith an angle equal to theflight-path-angle
One-tangent-burn transfer
8/19/2019 Orbital Mechanics 2
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ORBIT MANEUVERING
Variable Hohmann Transfer One-tangent-burn
rA 6570 km 6570 km
rB 42200 km 42200 km
a tx 24385 km 28633 km
VT 3.935 km/s 4.699 km/s
TOF 5.256 h 3.457 h
• Comparison of coplanar orbit transfers from LEO toGeosynchronous orbit
Comparison
8/19/2019 Orbital Mechanics 2
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ORBIT MANEUVERING
• Another option for changing the size of the orbit is to usea constant low-thrust burn (ionic engines)
• The resulting transfer orbit is a spiral orbit.• We can approximate the velocity change for this type of
orbits by
• For the previous example, the total change of velocitywould be 4.71 km/s
Constant low-thrust burn
A B V V V
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ORBIT MANEUVERING
Smart-1
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ORBIT MANEUVERING
• To change the orbital plane we must change the direction of the velocity vector
• For a simple plane change, the required change in velocity is
• Plane changes are very expensive and requires an important
fuel consumption
Orbit plane changes
2sin2 iV V
8/19/2019 Orbital Mechanics 2
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ORBIT MANEUVERING
• An example:• Change in velocity required to transfer from a low-
altitude (h=185 km) inclined (i=28 deg) orbit to an
equatorial orbit (i=0) at the same altitute:r=6563 km V=7.79 km/s V=3.77 km/s
• For a i=60 deg, the required change in velocity equalsthe current velocity.
Orbit plane changes
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ORBIT MANEUVERING
Orbit plane changes
Describe a 3-burn orbitalchange from an
inclined low-altitude
circular orbit to a high-altitude equatorial
circular orbit.
THINK
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ORBIT MANEUVERING
• Objective: to rendezvous with or intercept another object inspace, eg:
• A probes send to a planet, a comet, an asteroid.• Shuttle send to the ISS• A communication satellite in a geosynchronous orbit
Orbit Rendezvous
Phasing orbit : Hohmann transfer orbit which the interceptormust arrive at the rendezvous point at the same time asthe target
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ORBIT MANEUVERING
Orbit Rendezvous
f is the phase angle needed forrendezvous
i is the initial phase angle
k is the number of rendezvousopportunities
int is the angular velocity of theinterceptor
tgt is the angular velocity of thetarget
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ORBIT MANEUVERING
• Wait time : the interceptor remains in the initial orbit untilinterceptor and target achive the desired geometry forrendezvous
• The lead angle is calculated by:
• And the phase angle
• The total time
Orbit Rendezvous
)/()2( int tgt f iwait k T
L tg flight T
180º f L
flight wait total T T T
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ORBIT MANEUVERING
Orbit Rendezvous
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ORBIT MANEUVERING
• After the mission is complete we must to think “what todo with the satellite ”
• Low-altitude orbits: allow to decay and reenter the
atmosphere• Boost satellites into benign orbits to reduce the
probability of collision• Sometimes the deorbit must be controlled: used for the
recovery of the payload (eg. Manned mission)
Deorbit
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TYPE OF ORBITS
Classifications• Heliocentric orbit• Geocentric orbit
1 Centricclassifications
• Low Earth orbit• Medium Earth orbit• High Earth orbit
2 Altitudeclassifications
• Polar orbit• Inclined orbit• Equatorial orbit
3 Inclinationclassifications
• Circular orbit• Elliptic orbit• Parabolic orbit• Hyperbolic orbit
4 Eccentricityclassifications
• Geosynchronous orbit• Geostationary orbit• Semi-syncrhonousorbit• Heliosynchronous
5 Synchronousclassifications
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TYPE OF ORBITS
• Earth observation satellites• Manned spaceflight• Aid remote sensing satellites
LEO, Low-altitudeEarth Orbit (160-
2000 km)
• Global positioning (GPS, GLONASS andGalileo)
MEO, Medium-altitude Earth
Orbit
• Geostationary orbit for communication• Geostationary orbit for meteorology
HEO, High-altitute Earth
Orbit
Altitude classification
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TYPE OF ORBITS
PROS:• Below the inner Van Allen radiation belt
(reduction to exposed radiation in mannedspaceflight)
• Good resolution for Earth observation• Low energetic requirements for communication
CONS:• Bad Earth coverage. Several groundsation
needed.• Space debris. LEO orbit congested.
LEO
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TYPE OF ORBITS
MEO
PROS:• Good Earth visibility and coverage• Low apparent motion of the
satellite
CONS:
• High energetic requirement forcommunication. (Earth laptop onlyin reception mode)
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TYPE OF ORBITS
HEO
PROS:• Possibility that the satellite remains at rest in the
sky• Large Earth coverage
CONS:• Very high energy requirements for
communication. (Exclusive groundsatation, largesolar panels)
• Communication latency becomes important• Affected by cosmic radiation and solar wind
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• The orbit selection process is complex
• The orbit typically defines:• Space mission lifetime•
Cost• Environment• Viewing geometry• Payload performance
ORBIT DESIGN
The orbit design process
Gold rule: to meet the largest number of mission
requirements at the least possible cost
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ORBIT DESIGN
Orbits during the space mission lifetime
Parking orbit: for spacecraft checkoutor storage
Transfer orbit: to move thespacecraft between orbit
Injection orbit: where the spacecraftsepareted from the launch vehicle
Operational orbit: orbit/s for missionactivities
Disposal orbit: where the spacecraftwill do minimum damage
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ORBIT DESIGN
Footprint Area (FOV): area that aspecific instrument or antenna
can see at any instant.
Instantaneous Access Area (IAA):all the area that the instrumentcould potentially see
Area Coverage Rate (ACR): therate at which the instrument issensing new land
Area Access Rate (AAR): the rateat which new land is coming intothe SC’s access area.
Earth coverage
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ORBIT DESIGN
• The fraction of the orbitover which the point Pis in view is
• Where
• 2 max is called theswath width
oview F 180/
cos/coscos max
Earth coverage geometry
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• Launch windows: to determine the appropiate time tolaunch from the Earth surface into the desired orbitaltime
ORBIT DESIGN
Launch windows
• No launch windows exist if L>i for direct orbit or L>180deg- i for retrograde orbit
• One launch window exists if L=i or L=180 deg –i • Two launch windows exist if L<i or L<180 deg - i
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ORBIT DESIGN
• An example: interplanetary probe send to Mars
Launch windows