2. 1. Orbital Module1. Orbital Module
CharacteristicsCharacteristics
OR.A.SI - Orbit and Attitude Simulator
3. 1.1 Technical Features
4. Planetary and Moon Ephemeris
Moon’s orbital model – Charpnot ELP-2000/82 (Accuracy 2 arcsec)
Planetary orbital model – VSOP87
OR.A.SI - Orbit and Attitude Simulator
3. Earth Gravity Model
GEM10B
Order and degree of approximation defined by the user.
Capability to upgrade the model by changing the geopotential coefficients.
1. Numerical Integrator
Continuous embedded 6th
stage Runge-Kutta-Fehelberg method RKF4(5)
Continuous embedded 13th
stage Runge-Kutta method RKF8(7)-13
2. Internal step size adaptation according to the steepness of the problem
Control of the local truncation error in order for each step to contribute uniformly to
the total integration error.
(code capable of accurately solving any kind of orbit: LEO – GEO - Interplanetary).).
4. OR.A.SI - Orbit and Attitude Simulator
1.2 Capabilities – Orbital features
1. Forward and backward propagation by taking account an indefinite
number
of orbital maneuvers
Three degrees of freedom maneuver (radial, tangential and normal velocity components).
Ability to execute both impulsive and continuous thrusts (ionic propulsion).
3. E/W station keeping maneuver computation
Functional for every geographical longitude.
Supports tilted circle collocation strategy (eccentricity separation).
Radial and tangential effects of the upcoming N/S maneuver are taken into account.
2. N/S station keeping maneuver computation
Supports tilted circle collocation strategy (inclination separation).
4. Maneuver calibration
5. State vector transformations
Transformation from Keplerian to synchronous elements and vice versa.
Transformation between reference frames (B1950, J2000, Mean of Date , True of Date)
6. Mean value of a state vector
5. OR.A.SI - Orbit and Attitude Simulator
1.3 Capabilities: Earth-Spacecraft Geometry Calculations
1. Antenna Pointing Data
Topocentric horizon polar (range, azimuth, elevation) and Cartesian coordinates
(x,y,z) with respect to whatever Earth station in the satellite geographical coverage.
Tropospheric range and elevation correction as functions of local temperature,
relative humidity and barometric pressure (Hopfield model for radio frequencies).
Doppler shift calculation.
2. Calculation of Sun outage for GEO satellites and whatever Earth station in
the relevant coverage.
Calculation of the first and the last day of Sun outage for both Vernal and Autumnal
periods for all the satellite coverage area.
Entrance and exit times of a parabolic antenna main lobe from the solar disk
according to the downlink frequency and the diameter of the antenna.
Angular separation between the bore sight of the antenna and the centre of the solar
disk during the phenomenon.
Percentage of the main lobe obscuration by the solar disk during the phenomenon.
6. OR.A.SI - Orbit and Attitude Simulator
1.4 Capabilities: Earth-Spacecraft Geometry Calculations
3. Calculation of Sun eclipse by the Earth for a GEO spacecraft.
5. IRES Blinding for GEO spacecraft.
6. Earth station – Satellite geometry calculations and transformations.
Transformation from topocentric horizon (range, azimuth elevation) to geographical
(geocentric distance, longitude, latitude) and vice versa.
Antenna biases and weather conditions are taken account (local temperature,
relative humidity and barometric pressure ).
7. Geographical antenna coverage for whatever Earth satellite.
4. Calculation of Sun eclipse by the Moon for a GEO spacecraft.
7. OR.A.SI - Orbit and Attitude Simulator
1.5 Calendrical Calculations and Conversions
Conversion between JD, MJD, UTC and Gregorian Date.
Calculation of J50, ET, GMST, GAST, JDE and TAI.
Calculation of the UTC corresponding to a specific GMST and date.
8. OR.A.SI - Orbit and Attitude Simulator
1.6 Capabilities: Mission Analysis for GEO spacecrafts
1. Mission analysis module characteristics
Fully autonomous calculation of the necessary optimal N/S and E/W maneuvers with
simultaneous orbit propagation and maneuver execution.
Mission analysis for both inclination and eccentricity separation strategies.
Functional for every geographical longitude.
Flexibility to change the duration of the station keeping cycle duration.
2. Data entry for mission analysis
Spacecraft characteristics : i) initial mass ii) SRP
Duration of mission analysis (Start and end date).
Station keeping cycle duration.
Station longitude.
Station keeping window dimensions.
Inclination separation strategy (centre of the solar ellipse).
Correction of periodic solar perturbation correction for inclination control.
Eccentricity separation strategy (centre of the eccentricity ellipse).
Eccentricity constrains: i) maximum eccentricity ii) eccentricity tolerance
9. One Year Mission Analysis – Eccentricity Evolution
Scenario: Inclination and Eccentricity Separation for 39o
East
10. One Year Mission Analysis – Inclination Evolution
Scenario: Inclination and Eccentricity Separation for 39o
East
11. One Year Mission Analysis – True and Mean Longitude Evolution
Scenario: Inclination and Eccentricity Separation for 39o
East
12. One Year Mission Analysis – True and Mean Longitude Evolution
Scenario: Station Keeping at 129o
East (Negative longitudinal acceleration)
18. OR.A.SI - Orbit and Attitude Simulator
2.1 Technical Features (1/3)
1. Numerical Integrator
Continuous embedded 6th
stage Runge-Kutta-Fehelberg method RKF4(5)
Quaternions used as generalized coordinates (no problem with singular points and
instability cases).
2. Code capable of simulating the following rotational dynamic cases :
Free rigid body rotation.
Rotation of a rigid body under the influence of impulsive torques (thrusts).
Rotation of a rigid body under the influence of continuous torques (perturbing
torques).
3. Motion description with respect to three different coordinate systems :
Quasi inertial reference frame MGSD – Mean Geocentric System of Date.
Body axis reference frame (sensors readings).
Local orbital frame.
4. Flexibility to initialize the rotational state of the spacecraft by defining :
The angular velocity vector with respect to any of the predefined coordinate systems.
The angular momentum vector with respect to any of the predefined coordinate systems.
The vector components form (Cartesian or Polar).
19. OR.A.SI - Orbit and Attitude Simulator
2.1 Technical Features (2/3)
5. Flexibility to describe the dynamical properties of the system to be
simulated :
Definition of the mass distribution by choosing the principal moments of inertia
Ixx , Iyy and Izz.
Addition of inertial wheels of whatever orientation by defining the respective
vector components of their angular momentum Lx, Ly and Lz with respect to the
body frame.
Model the behavior of a dual-spin satellite by identifying the platform with an
inertial wheel and the rotor with the rigid body.
6. Simultaneous description of the rotational motion by using four
different types of generalized coordinates :
Euler angles φ, θ and ψ (z-x-z convention).
Tait-Bryan angles (roll, pitch, yaw).
Directional cosines of the body axes with respect either to inertial or local frame.
Quaternions.
20. 2.1 Technical Features (3/3)
7. Computation of two successive torques needed to dump the precessional
motion of the spacecraft (Nutation dumping) :
Initialization of any kind of rotational state.
Computation of the epoch for the second impulsive torque when the corresponding
epoch for the first one is given.
Computation of the two impulsive torque components with respect to both the inertial
and the body axis frame.
OR.A.SI - Orbit and Attitude Simulator
First Pulse
∆ 1
∆H2
T1
2
Momentum
Precession
Roll
H
T
Second Pulse
Yaw
21. OR.A.SI - Orbit and Attitude Simulator
Output
UTC – Universal Time Coordinated
dd/mm/yyyy hh:mm:ss - Gregorian Date
GAST - Greenwich Apparent Sidereal Time
Euler angles – φ,θ,ψ
Τait-Bryan angles – roll, pitch, yaw
Quaternions – qo, q1, q2, q3
Angular velocity with respect to the
inertial frame – ωx, ωy and ωz
Angular velocity ω with respect to the
body frame – Gyro readings.
Angular momentum vector with respect to
inertial frame – Lx, Ly, Lz
Angular momentum vector with respect to
the body frame.
Angular momentum vector with respect to
the local orbital frame.
Directional cosines of the body axes with
respect to the inertial frame.
Directional cosines of the body axes with
respect to the local orbital frame.
Angle between the x,z and y body axes and
the angular momentum vector.
Angle between the angular velocity vector
and the angular momentum vector.
LIASS unbalance angle.
LIASS pitch angle.
22. 3. OR.A.SI utilization for3. OR.A.SI utilization for
modeling realisticmodeling realistic
attitude problemsattitude problems
OR.A.SI - Orbit and Attitude Simulator
23. OR.A.SI - Orbit and Attitude Simulator
3.1 Precession dumping with two successive impulses (1/3)
Geometry and dynamics of the simulation
wheel
xbody
zbody-ybody
xinertial
yinertial
zinertial
9.47o
L
ylocal
zlocal
-ylocal
xlocal
xbody
zbody
-ybody
7.36o
L
Body and Inertial Frame Body and Local Orbital Frame
24. OR.A.SI - Orbit and Attitude Simulator
3.1 Precession dumping with two successive impulses (2/3)
Final State
xbody
zbody
-ybody
wheel
xinertial
yinertial
zinertial
L
Ixx = 16669.631 Kg m2
Iyy = 2714.554 Kg m2
Izz = 16216.076 Kg m2
Roll = 6o
Pitch = 0o
Yaw = 0o
• Wheel angular momentum : 45 Nms
• Total angular momentum L : 45.3942 Nms
• Precession period : 38.3455 min
• Precession radius : 7.364o
• Angle between angular momentum and z-inertial axis: 9.47o
• Angle between angular momentum and y-body axis: 7.36o
Initial State
25. 3.1 Precession dumping with two successive impulses (3/3)
OR.A.SI - Orbit and Attitude Simulator
Torque Impulses computed by OR.A.SI:
Date of the first impulse : 01/01/2008 12:00:00 (Defined by the user)
Date of the second impulse : 01/01/2008 12:19:1
Torque impulses [N m sec] with respect to the inertial frame
***************************************************
DLx1 = 6.132987 DLy1 = -1.578041 DLz1 = 0.423591
DLx2 = 0.414507 DLy2 = -2.030013 DLz2 = -0.000010
Torque impulses [N m sec] with respect to the body frame
**************************************************
DLx1 = 1.424230 DLy1 = -0.168105 DLz1 = 6.182757
DLx2 = 2.050461 DLy2 = -0.000034 DLz2 = 0.297288
32. 4. Current Utilization of4. Current Utilization of
OR.A.SI to EnhanceOR.A.SI to Enhance
Hellas Sat’s FD OperationsHellas Sat’s FD Operations
OR.A.SI - Orbit and Attitude Simulator
33. OR.A.SI - Orbit and Attitude Simulator
4.1 Current utilization of OR.A.SI to enhance FD operations
Training.
Verification of the chosen station keeping strategy optimality by computing the
expected optimal ΔV increment corresponding to the desired time period.
Computation of the expected future ergol consumption by executing long term
mission analysis.
Assessment of the number and the epochs of the anticipated West maneuvers.
SED – Satellite Ephemeris Data (Cartesian Ephemeris with respect to Earth
Centered Fixed reference frame) provision to the customers with DVB-RCS platforms
Enhance Flight Dynamics operations safety with the ability to execute the
necessary orbital calculations even while away from office.
34. 5. Future Plans for Further5. Future Plans for Further
Code DevelopmentCode Development
OR.A.SI - Orbit and Attitude Simulator
35. Incorporation of Long Term Inclination Control Strategy.
Addition of Orbit Determination Module.
Enhancement of Mission Analysis with automatic calculation of plasmic thrusts.
Implementation of platform depented characteristics (Maneuver Implementation).
Description of a realistic model for the atmosphere up to the height of 1000 Km in
order to take account the air drug perurbation for LEO calculations.
Implementation of control laws for solar arrays, and wheel.
Code enhancement with multi threading characteristics in order to interact with
the program “on the run”.
Code optimization to decrease the necessary run time.
Addition of a Windows GUI.
OR.A.SI - Orbit and Attitude Simulator
5.1 Future Plans for Further Code Development
38. Comparison with an analytic solution
Utilization of a “steep” problem in order to challenge the integrator’s
capability to adapt its step size.
(the problem doesn’t ought to be physically realizable)
Highly eccentric Keplerian (non-perturbed) orbit with the following characteristics :
a = 65127 Km
e = 0.987
i = 0o
perigee radius = 894.45 Km (Earth’s radius = 6378 Km)
apogee radius = 129407.372 Km
maximum orbital velocity = 28.92 Km/sec (Escape velocity : 11 Km/sec)
OR.A.SI - Orbit and Attitude Simulator
40. OR.A.SI - Orbit and Attitude Simulator
Relative Accuracy With Respect to the Analytic Solution
41. OR.A.SI Planetary and Earth ModelOR.A.SI Planetary and Earth Model
EvaluationEvaluation
OR.A.SI - Orbit and Attitude Simulator
42. Comparison with COSMIC
Utilization of a series of realistic station keeping maneuvers actually executed for Hellas
Sat II between 16-12-05 and 13-02-06 :
All perturbations taken account.
Total of 7 consecutive maneuvers.
4 South maneuvers coupled with 3 East maneuvers.
OR.A.SI - Orbit and Attitude Simulator
1) How accurate is the orbit prediction ?
2) How accurate are the antenna pointing data ?
43. OR.A.SI - Orbit and Attitude Simulator
True and Mean Longitude Evolution
44. OR.A.SI - Orbit and Attitude Simulator
Inclination Evolution
45. OR.A.SI - Orbit and Attitude Simulator
Osculating and Mean Major Semi Axis Evolution
46. OR.A.SI - Orbit and Attitude Simulator
ey Eccentricity Component Evolution
47. OR.A.SI - Orbit and Attitude Simulator
Output - Osculating Elements (1/2)
UTC – Universal Time Coordinated
MJD – Modified Julian Day
dd/mm/yyyy hh:mm:ss - Gregorian Date
GAST - Greenwich Apparent Sidereal Time
LST – Local Sidereal Time
a – major semi axis
e – eccentricity
i – inclination
Ω – Right Ascension of the Ascending node
ω – Argument of the perigee
M – Mean anomaly
v – True anomaly
λ – True longitude
λο – Mean longitude
φ – Sub satellite point latitude
(ex , ey) – Eccentricity vector
(ix , iy ) – Inclination vector
D – Longitude drift rate (deg/day)
R – Geocentric distance (height)
S – Slant distance
(X,Y,Z) – Cartesian Coordinates with respect
to ECI.
(Vx, Vy, Vz) – Velocity vector with respect
to ECI.
(X,Y,Z)Earth - Cartesian Coordinates with
respect to ECF.
48. OR.A.SI - Orbit and Attitude Simulator
Output - Osculating Elements (2/2)
(Vx, Vy, Vz)Earth – Velocity vector with respect to ECF.
(X,Y,Z)topocentric - Topocentric Horizon Cartesian Coordinates.
Azimuth and Elevation - Antenna tracking angles (Tropospheric refraction taken account).
Doppler shift – Δf/f.
Sun’s RA – Sun’s Right Ascension.
Sun’s Dec – Sun’s Declination.
Step size – Evolution of the adaptive step size used by the differential equations integrator.
49. Output - Mean Elements
OR.A.SI - Orbit and Attitude Simulator
UTC – Universal Time Coordinated
MJD – Modified Julian Day
dd/mm/yyyy hh:mm:ss - Gregorian Date
GAST - Greenwich Apparent Sidereal Time
LST – Local Sidereal Time
a – Major semi axis
e – Eccentricity
i – Inclination
Ω + ω – Right Ascension of the Ascending node plus argument of the perigee
λo – Mean longitude
(ix , iy) – Inclination vector
(ex , ey) – Eccentricity vector
50. OR.A.SI - Orbit and Attitude Simulator
Elevation Evolution for Earth Station at φ = 22.6859ο
and λ = 38.822ο
51. OR.A.SI - Orbit and Attitude Simulator
Azimuth Evolution for Earth Station at φ = 22.6859ο
and λ = 38.822ο
52. OR.A.SI - Orbit and Attitude Simulator
Slant Distance Evolution for Earth Station at φ = 22.6859ο
and λ = 38.822ο
