Presentation for the 16th EUROSTAR Users Conference June 2008

OR.A.SIOR.A.SIOrbit and AttitudeOrbit and Attitude

SimulatorSimulator

Antonios Arkas Flight Dynamics Engineer

1. Orbital Module 1. Orbital Module CharacteristicsCharacteristics

OR.A.SI - Orbit and Attitude Simulator

1.1 Technical Features

4. Planetary and Moon Ephemeris Moon’s orbital model – Charpnot ELP-2000/82 (Accuracy 2 arcsec) Planetary orbital model – VSOP87


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).).


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


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.


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.


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.


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

One Year Mission Analysis – Eccentricity Evolution

Scenario: Inclination and Eccentricity Separation for 39o East

One Year Mission Analysis – Inclination Evolution


One Year Mission Analysis – True and Mean Longitude Evolution


One Year Mission Analysis – True and Mean Longitude Evolution

Scenario: Station Keeping at 129o East (Negative longitudinal acceleration)

Lifetime Mission Analysis for Hellas Sat II – Eccentricity Evolution

Lifetime Mission Analysis for Hellas Sat II – Inclination Evolution

Lifetime Mission Analysis for Hellas Sat II – True and Mean Longitude Evolution

Lifetime Mission Analysis for Hellas Sat II – Latitude versus Longitude Evolution

2. Attitude Module 2. Attitude Module CharacteristicsCharacteristics



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).



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.


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.


First Pulse

1

H2

T1

2

MomentumPrecession

Roll

H

TSecond Pulse Yaw


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.

3. OR.A.SI utilization for 3. OR.A.SI utilization for modeling realistic modeling realistic attitude problems attitude problems



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



Final State

xbody

zbody

-ybody

wheel

xinertial

yinertial

zinertial

LIxx = 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



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

4. Current Utilization of 4. Current Utilization of OR.A.SI to Enhance OR.A.SI to Enhance

Hellas Sat’s FD OperationsHellas Sat’s FD Operations



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.

5. Future Plans for Further 5. Future Plans for Further Code DevelopmentCode Development


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.


5.1 Future Plans for Further Code Development

THANK YOU FOR ATTENDING MY PRESENTATION

OR.A.SI Integrator EvaluationOR.A.SI Integrator Evaluation


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)


Step Size Control


Relative Accuracy With Respect to the Analytic Solution

OR.A.SI Planetary and Earth Model OR.A.SI Planetary and Earth Model EvaluationEvaluation


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.


1) How accurate is the orbit prediction ?

2) How accurate are the antenna pointing data ?


True and Mean Longitude Evolution


Inclination Evolution


Osculating and Mean Major Semi Axis Evolution


ey Eccentricity Component Evolution


Output - Osculating Elements (1/2)


MJD – Modified Julian Day



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.


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.

Output - Mean Elements



MJD – Modified Julian Day



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


Elevation Evolution for Earth Station at φ = 22.6859ο and λ = 38.822ο


Azimuth Evolution for Earth Station at φ = 22.6859ο and λ = 38.822ο


Slant Distance Evolution for Earth Station at φ = 22.6859ο and λ = 38.822ο


Doppler Evolution

State Form Transformation Module Output

Satellite position, earth station position and antenna charachteristics ***********************************************************

Satellite's longitude : 39.000000 degrees East Satellite's azimuth : 154.955357 deg Satellite's elevation : 41.961143 deg Earth station longitude : 22.685968 degrees East Earth station latitude : 38.822452 degrees Antenna diameter : 31.000000 m Downlink frequency : 6.000000 GHz Antenna HPBW : 0.112824 deg

First day of Vernal outage: 26/02/2008 Last day of Vernal outage: 11/04/2008

Vernal outage for year 2008 ************************

4/3/2008 9:26 Angular separation : 0.314282 deg Obscuration : 9.510246% 4/3/2008 9:27 Angular separation : 0.161102 deg Obscuration : 100.000000% 4/3/2008 9:28 Angular separation : 0.277018 deg Obscuration : 42.538741% 5/3/2008 9:26 Angular separation : 0.312228 deg Obscuration : 11.330798% 5/3/2008 9:27 Angular separation : 0.229455 deg Obscuration : 84.695338%

First day of Autumnal outage: 30/08/2008 Last day of Autumnal outage: 15/10/2008

Autumnal outage for year 2008 ***************************

8/10/2008 9:1 Angular separation : 0.225690 deg Obscuration : 88.032401% 8/10/2008 9:2 Angular separation : 0.102622 deg Obscuration : 100.000000% 8/10/2008 9:3 Angular separation : 0.149870 deg Obscuration : 100.000000% 8/10/2008 9:4 Angular separation : 0.273488 deg Obscuration : 45.667732%

Penumbra vernal eclipse for 2008 and longitude 39 degrees East *******************************************************

Enter Exit Duration

26/02/2008 21:27:43 26/02/2008 21:45:43 18 min27/02/2008 21:23:02 27/02/2008 21:50:02 27 min28/02/2008 21:19:48 28/02/2008 21:52:55 33.12 min29/02/2008 21:16:55 29/02/2008 21:55:26 38.52 min01/03/2008 21:14:24 01/03/2008 21:57:36 43.2 min02/03/2008 21:12:14 02/03/2008 21:59:24 47.16 min03/03/2008 21:10:26 03/03/2008 22:00:50 50.4 min04/03/2008 21:08:38 04/03/2008 22:01:55 53.28 min05/03/2008 21:07:12 05/03/2008 22:03:00 55.8 min06/03/2008 21:05:45 06/03/2008 22:04:04 58.32 min07/03/2008 21:04:19 07/03/2008 22:04:48 60.48 min08/03/2008 21:03:14 08/03/2008 22:05:31 62.28 min09/03/2008 21:02:09 09/03/2008 22:06:14 64.08 min10/03/2008 21:01:04 10/03/2008 22:06:36 65.52 min11/03/2008 21:00:21 11/03/2008 22:06:57 66.6 min12/03/2008 20:59:16 12/03/2008 22:07:19 68.04 min13/03/2008 20:58:33 13/03/2008 22:07:19 68.76 min14/03/2008 20:57:50 14/03/2008 22:07:40 69.84 min15/03/2008 20:57:07 15/03/2008 22:07:40 70.56 min16/03/2008 20:56:45 16/03/2008 22:07:40 70.92 min17/03/2008 20:56:02 17/03/2008 22:07:40 71.64 min18/03/2008 20:55:40 18/03/2008 22:07:19 71.64 min19/03/2008 20:55:19 19/03/2008 22:07:19 72 min20/03/2008 20:55:19 20/03/2008 22:06:57 71.64 min21/03/2008 20:54:57 21/03/2008 22:06:36 71.64 min22/03/2008 20:54:36 22/03/2008 22:05:52 71.28 min23/03/2008 20:54:36 23/03/2008 22:05:31 70.92 min24/03/2008 20:54:36 24/03/2008 22:04:48 70.2 min25/03/2008 20:54:36 25/03/2008 22:04:04 69.48 min26/03/2008 20:54:57 26/03/2008 22:03:21 68.4 min

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Hellas Sat's Vernal Eclipse for 2008

Penumbra duration Umbra Duration

dura

tion

[min

]

UTC [days]

Start date: 01/01/2008 0:0:0 End date: 31/12/2008 23:59:59 Ephemeris: Center-of-box Window center : 39.000000 deg East

Start: 06/02/2008 22:39:00 0.765697 % Maximum : 06/02/2008 22:53:00 37.468716 % End: 06/02/2008 23:07:00 0.399627 %

Start: 07/02/2008 12:16:00 0.137689 % Maximum: 07/02/2008 12:51:00 58.648095 % End: 07/02/2008 13:28:00 0.039556 %

Start: 27/12/2008 19:10:00 0.329664 % Maximum: 27/12/2008 19:18:00 4.690416 % End: 27/12/2008 19:26:00 0.241870 %

Sun Eclipse by the Moon for 2008 and Orbital Position 39o East

Start date: 1/6/2008 0:0:0 End date: 30/6/2008 0:0:0 Ephemeris: Center-of-box Window center: 39.000000 deg East Moon phase threshold : 40.000000% Error margin: 0.100000 deg

10/06/2008 02:14:00 BOLOMETER 2 : START 44.602096 %10/06/2008 04:42:00 BOLOMETER 2 : END 45.675974 %




IRES Blinding by the Moon for June 2008 and Orbital Position 39o East

Geographical-Topocentric Horizon Transformation

Presentation for the 16th EUROSTAR Users Conference June 2008

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Transcript of Presentation for the 16th EUROSTAR Users Conference June 2008