Hybrid Ion and Chemical GEO Stationkeeping Maneuver Planning Software

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Hybrid (Ion and Chemical) GEO Stationkeeping
Maneuver Planning Software

• J. K. Skipper, D. Racicot, S. Li, R.
  Provencherand J. Palimaka
• Telesat Canada, Ottawa, Ontario, Canada

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareAbstract

• GEO Stationkeeping Flight Dynamics System a
  suite of software applications to perform
  Prediction, State Estimation and Maneuver
  Planning functions
• Telesat Canadas FDS used since 1976 to support
  mission and S/K operations of over 40 satellites
  from 5 S/C manufacturers
• Orbit control (firing of thrusters to offset
  perturbing effects of earth triaxiality, solar
  radiation force and gravitational effects of sun
  and moon) has historically used chemical
  propellants to provide high thrust at relatively
  low specific impulse (propellant efficiency)
• Some new satellite designs use ion-electric
  thrusters to generate much higher specific
  impulses at lower thrust levels, resulting in
  reduced propellant masses at launch and longer
  propellant lifetimes
• Depending on spacecraft design, orbit control may
  use only ion thrusters or a combination of ion
  and chemical propulsion systems
• Telesats OnOrbit FDS includes Hybrid maneuver
  planning function to simultaneously plan ion and
  chemical maneuvers

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareIntroduction 1

• GEO orbit does not remain geostationary due to
  perturbations
• Luni-solar gravity precesses orbit plane
  (direction and magnitude is influenced by a
  6-month term in solar gravitational effect and a
  18.6 year term due to the motion of the moons
  ascending node)
• Earth oblateness (equatorial bulge) acts with
  luni-solar gravity to precess orbit plane
• Triaxiality (longitudinal harmonics in
  geopotential) causes satellite to accelerate east
  or west toward longitude nulls (105.3W and
  75.1E)
• Solar radiation affects orbit eccentricity
  (circularity) mean eccentricity vector
  naturally traces out a near-circular path once
  per year
• Perturbations are offset by performing maneuvers
  (thruster firings) to adjust orbit velocity
• North-South maneuvers apply delta-velocity in
  north or south direction to adjust orbit plane
  (inclination)
• East-West maneuvers apply positive or negative
  change in spacecraft velocity to correct
  eccentricity and longitude drift

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareIntroduction 2

• For all-chemical propulsion systems, North-South
  and East-West maneuvers are largely uncoupled
  (independent), and are typically performed once
  every 1 or 2 weeks
• With ion-electric systems, ion thrusters are
  usually positioned and oriented to provide
  north-south and nadir (earth-directed) components
  of delta-velocity (thrust vector nominally
  through CM)
• Nadir delta-v causes shift in mean longitude with
  each maneuver, and can be used to control
  eccentricity
• Mean longitude shift is offset by increasing
  nominal orbit altitude
• Low thrust of ion thrusters requires much more
  frequent maneuvers than chemical e.g. two burns
  (one north, one south) 12 hours apart every day
• Ion maneuvers may be supplemented with chemical
  maneuvers to provide drift-only or drift and
  eccentricity control frequency of chemical
  burns may range from twice per day to once every
  2 weeks, depending on satellite design and ion
  thruster firing strategy

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareNon-Singular Orbital Elements

• The satellite orbit may be represented by 6
  non-singular orbital elements
• Mean longitude drift rate (/day E)
• Mean right ascension of the satellite ( mean
  longitude Greenwich Hour Angle) (E)
• h1 e sin (??)
• k1 e cos (??)
• h2 sin i sin ? ? i sin ?
• k2 sin i cos ? ? i cos ?
• where
• e is the orbit eccentricity
• i is the orbit inclination (in radians)
• ? is the argument of perigee
• ? is the right ascension of the ascending node

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareManeuver Planning 1

• When a thruster is fired at satellite right
  ascension a, changes in non-singular orbital
  elements are determined by radial, tangential and
  normal components of delta-velocity vector (DVR,
  DVT, DVN)

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareManeuver Planning 2

• When inclination is close to zero, luni-solar
  perturbations precess inclination vector (k2, h2)
  primarily in h2 direction hence inclination
  maneuvers are performed close to a 90 or 270
• Nadir (negative radial) component of DV at 90 or
  270 results in change to k1 ? k1 component of
  eccentricity may be controlled by choosing
  relative sizes of north and south maneuvers
• Shifting maneuver right ascensions away from 90
  and 270 (i.e. toward 0 or 180) produces change
  in h1 proportional to sum of nadir DVs
• Possible ion-thruster planning strategies
  include
• Inclination only (chemical drift and eccentricity
  control)
• Inclination k1 (chemical drift and h1 control)
• Inclination eccentricity (chemical drift
  control)
• Can also define firing profiles in which ion
  thrusters are not fired every day (e.g. 6 days
  on, 1 day off in 7-day cycles)
• For selected strategy and firing profile, daily
  required changes in (k1, h1) and (k2, h2) are
  determined and burn DVs and right ascensions are
  computed

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareManeuver Planning 3

• Daily normal (N/S) component of ion burn ?Vs
  and right ascension offsets
  from (90, 270) can be determined by
  solving the following equations
• where
  (CN CS are the north and south ion-thruster
  cant angles), and

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareManeuver Planning 4

• The solution is
• Burn durations are computed from ?Vs
• where
• M is the satellite mass
• is the normal component of ?V
• F is the ion-thruster thrust
• C is the ion-thruster cant angle
• is the earth rotation rate

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareManeuver Planning 5

• Nadir component of DV from each ion maneuver
  (-DVR) results in an eastward shift in mean
  longitude
• Average daily normal component of ion ?V is ?VN
  ?i Vsyn, where ?i is the average daily change in
  inclination in radians
• Average daily radial component of ?V from ion
  maneuvers is
• ?VR - ?VN tan C - ?i Vsyn tan C
• To offset average daily longitude shift due to
  ion radial ?V, define nominal westward drift
  target dN as
• dN - ?l - 2 ?i tan C
• where dN (lt 0) is in deg/day East if ?i is
  expressed in degrees
• Note that dN does not depend on number of firing
  days in cycle, only on average daily change in
  inclination due to perturbations

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareManeuver Planning 6

• If chemical maneuvers are used to control one or
  both components of eccentricity vector, classical
  method of single- or double-burn drift ecc.
  maneuvers performed once per cycle (e.g. every 7
  or 14 days) may be used
• If ion maneuvers fully control eccentricity, it
  may be desirable to perform chemical drift
  maneuvers in conjunction with ion maneuvers (i.e.
  daily) two equal DV burns 12 hours apart change
  drift without affecting eccentricity
• In theory, if S/C is at correct longitude with
  drift dN at start of cycle, daily drift maneuvers
  are required only to offset drift change due to
  triaxiality effect in practice, there may be
  errors in longitude and drift at start of cycle
• Errors are corrected over 2 cycles by defining an
  intermediate drift target dint at end of first
  cycle, and daily drift targets based on the
  selected firing profile
• Intermediate drift target is chosen such that the
  time integral of drift relative to the nominal
  drift target dN over 2 cycles equals the required
  longitude change to correct the initial longitude
  error
• Daily drift targets are chosen to achieve dint at
  the end of the first cycle and dN at the end of
  the second cycle, such that drift corrections are
  constant for each firing day of each cycle

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareManeuver Planning 7

• Sample drift profile over two 7-day cycles with
  drift maneuvers (2 per day) performed on days 1,
  2, 5 and 6 of each cycle
• Each firing day of first cycle adjusts drift by
  Dd1, each firing day of second cycle adjusts
  drift by Dd2

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareOnOrbit FDS 1

• Telesat Canadas OnOrbit FDS includes Hybrid
  maneuver planning application
• Plans combined daily ion and bi-propellant
  (chemical) stationkeeping maneuvers to control
  inclination, eccentricity and drift/longitude for
  stationkeeping cycles of up to 28 days
• Eccentricity control may be done entirely with
  ion thrusters, entirely with chemical thrusters,
  or split between ion and bi-prop
• Generates OnOrbit FDS events representing planned
  maneuvers for the stationkeeping cycle
• Generates maneuver messages / maneuver tables for
  the planned maneuvers
• Generates plots of predicted orbit dynamics
  during the stationkeeping cycle

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareOnOrbit FDS 2

• Main window and planning input dialogs

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareOnOrbit FDS 3

• Typical 7-day cycle simulation

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Hybrid GEO Stationkeeping Maneuver Planning
SoftwareSummary

• A technique for simultaneously planning daily ion
  and chemical maneuvers to control the orbital
  effects of perturbations on Geostationary
  satellites equipped with both ion-electric and
  chemical propulsion systems has been developed
  and implemented in Telesat Canadas OnOrbit FDS
  Flight Dynamics System
• The implementation allows for 3 possible
  ion-thruster planning strategies
• Inclination only (chemical drift and eccentricity
  control)
• Inclination k1 (chemical drift and h1 control)
• Inclination eccentricity (chemical drift
  control)
• and supports user-specified firing profiles for
  cycles of up to 28 days
• Release 1.0 of the OnOrbit FDS has been delivered
  to L-3 Storm Control Systems, Inc. Release 1.1
  is scheduled for delivery in 2Q 2004 and will be
  used operationally to control Shin Satellites
  iPSTAR-1 spacecraft