SDO ACS Coordinate Systems

464-ACS-ICD-0067 Revision D

DRAFT D-3

Solar Dynamics Observatory (SDO) Attitude Control System (ACS) Coordinate System Document

Effective Date: 25 January 2007

Expiration Date:

Prepared By: Kristin Bourkland/595

National Aeronautics and Goddard Space Flight Center Space Administration Greenbelt, Maryland

CHECK THE SDO MIS AT https://sdomis.gsfc.nasa.gov TO VERIFY THAT THIS IS THE CORRECT VERSION PRIOR TO USE. CM FOREWORD

This document is Solar Dynamics Observatory Project controlled document. Changes to this document require prior approval of the SDO Project CCB Chairperson. Proposed changes shall be submitted to the SDO Project Configuration Management Office (CMO), along with supportive material justifying the proposed change.

Questions or comments concerning this document should be addressed to:

SDO Configuration Management Office Mail Stop 464 Goddard Space Flight Center Greenbelt, Maryland 20771

Release Date – 25 January 2007 ii Signature Page

Prepared by: Contributors:

Alice Liu / 595 ______Kristin Bourkland / 595 Kristin Bourkland Date Paul Mason / 595 SDO ACS Analyst Melissa Vess / 595 595 Scott Starin / 595

Reviewed by:

______ Date Date

Concurred by:

______ Date Date

Release Date – 25 January 2007 iii Solar Dynamics Observatory Attitude Control System Coordinate System Document

DOCUMENT CHANGE RECORD Sheet: 1 of 1 REV/ APPROVED DATE VER DESCRIPTION OF CHANGE BY APPROVED LEVEL A Initial Release B Add description of “A” and “B” CSS sensor locations. Correction in CSS rotation description. Addition of Thruster diagrams. Replace sensor and actuator diagram. Alter HGA diagrams to match naming convention. Change HGA description to include elevation and azimuth. Change CSS diagrams. Include Guide Telescope transformation matrix. Add documentation to GT diagram. Remove thruster diagrams. Fix IRU diagram to match naming convention. Fix IRU GyroA matrix. Change IRU A, B, C to IRU 1, 2, 3. Change IRU software numbering. Alter CSS diagrams. Change ST rotations. Change ST description to accommodate chosen sensor. Fix typo in RWA diagram labeling. Change HGA section to include a comparison of all gimbal naming conventions. Fix typo in CSS rotation matrix. Change ST rotation matrix to incorporate new rotation angles. Define difference in ST1 and ST2. Redefine ST axis descriptions. Updated ST axis descriptions and added additional “clocking” rotation. Fixed spelling error Replaced dimensional diagram with newer version Add star tracker location and orientation picture Add DSS orientation picture

Release Date – 25 January 2007 iv C Change IRU picture to one provided by Paul Mason. Add line of description to IRU transformation. Updated ST alignments to match new configuration. Replace spacecraft pictures with current configuration. Change IRU drawing from ABC to 123. Delete mass property table in thruster section. Update picture in Figure 4.

D Change description of DSS alignment to account for rotation of DSS mount. Add mapping of RT address and A-STR serial number to ST section. Add solar array serial numbers to solar array section. Add table of CSS serial numbers. Correct signs in HGA figure 9. Correct DSS directions in Figure 13. Update thruster location table to correct for the switch of A and B thrusters.

Release Date – 25 January 2007 v Table of Contents

1.0 PURPOSE OF DOCUMENT...... 1-1 2.0 COORDINATE FRAME DEFINTIONS...... 2-1 2.1 Geocentric Inertial Frame (GCI)...... 2-1 2.2 Solar North Referenced Frame (SNR)...... 2-1 2.3 Spacecraft Body Coordinate System (BCS)...... 2-3 3.0 HARDWARE COMPONENTS...... 3-1 3.1 Deployables...... 3-1 3.1.1 Solar Arrays...... 3-1 3.1.2 High Gain Antennas...... 3-2 3.2 Sensors...... 3-5 3.2.1 Coarse Sun Sensors...... 3-5 3.2.2 Digital Sun Sensors...... 3-7 3.2.3 Star Trackers...... 3-9 3.2.4 Inertial Reference Units...... 3-12 3.2.5 Guide Telescope...... 3-15 3.3 Actuators...... 3-17 3.3.1 Reaction Wheels...... 3-17 3.3.2 Thrusters...... 3-19 4.0 REFERENCES...... 4-1

Release Date – 25 January 2007 vi List of Figures

Figure 1. SDO Spacecraft...... 1-1 Figure 2. SDO Stowed Configuration...... 1-2 Figure 3. SDO Deployed Configuration...... 1-3 Figure 4. SDO Commanded Axes and Target Sun...... 1-4 Figure 5. SNR Coordinate Frame Definition...... 2-2 Figure 6. SDO's Sensors and Actuators...... 3-1 Figure 7. High Gain Antenna Local Frames...... 3-2 Figure 8. Stowed Configuration: Spacecraft and HGA dishes (not to scale)...... 3-3 Figure 9. Deployed Configuration: Spacecraft and HGA dishes (not to scale)...... 3-3 Figure 10. SDO CSS Locations...... 3-5 Figure 11. "A" and "B" CSS Sensors...... 3-6 Figure 12: DSS coordinate system and sun angles6...... 3-8 Figure 13: DSS orientation on spacecraft...... 3-9 Figure 14: Star Tracker location and orientation...... 3-11 Figure 15. SDO IRU—Kearfott TARA 1T...... 3-12 Figure 16. SDO IRU System with Coordinate Systems...... 3-13 Figure 17. SDO IRU System Location...... 3-14 Figure 18. Guide Telescope Coordinate System and Sun Vector Measurement...... 3-16 Figure 19. Guide Telescope Numbering5...... 3-17 Figure 20. SDO RW Numbering and Locations...... 3-18 Figure 21. SDO RW Pyramidal Configuration. Positive spin matches RWA vendor’s definition of positive axes...... 3-18 Figure 22. Thruster Positions and Spacecraft Coordinate Frame...... 3-19

Release Date – 25 January 2007 vii List of Tables

Table 1: CSS Serial Numbers...... 3-6 Table 2. CSS Boresight Vectors...... 3-7 Table 3. SDO IRU Channel Axes, Spacecraft Axes, and Software Numbering...... 3-15 Table 4. SDO IRU Prime and Redundant...... 3-15 Table 5. RWA Spin Axes in the Spacecraft Body Frame...... 3-18 Table 6. Nominal Thruster Location and Performance...... 3-20

Release Date – 25 January 2007 viii 1.0 PURPOSE OF DOCUMENT

This document gives an overview of the Solar Dynamics Observatory (SDO) coordinate reference frames and their relation to the spacecraft and geocentric inertial reference frames. In addition, this document defines the coordinate transformations between the SDO Attitude Control System (ACS) hardware components and the spacecraft coordinate system.

A three-view drawing of the SDO spacecraft is shown in Figure 1.

Figure 1. SDO Spacecraft

Release Date – 25 January 2007 1 Figure 2 shows the stowed configuration of the spacecraft, where the solar arrays and High Gain Antennas (HGAs) have not yet been deployed. The various spacecraft modules are labeled in the diagram.

INSTRUMENT MODULE (IM)

SPACECRAFT BUS (SB) X Y

Z PROPULSION MODULE (PM) Internal to SB Figure 2. SDO Stowed Configuration

Release Date – 25 January 2007 2 The deployed spacecraft configuration is shown in Figure 3, with the main instruments and hardware labeled. AI A

EV E Instrument Module (IM)

Solar Arrays Star Trackers SADS (2) X HMI Y

Z HGADS (2) Spacecraft Bus (SB) High Gain Antenna Booms Propulsion Module (PM)

Figure 3. SDO Deployed Configuration

Release Date – 25 January 2007 3 Figure 4 shows the commanded configuration of the spacecraft. In the default science attitude, the spacecraft x-axis points towards the Sun, and the z-axis aligns the HGAs and Solar North.

Solar North

+z (aligns with HGAs and Solar North)

+x (toward Sun)

+y (aligns with solar arrays)

Figure 4. SDO Commanded Axes and Target Sun

Release Date – 25 January 2007 4 2.0 COORDINATE FRAME DEFINTIONS

Three right-handed, orthogonal coordinate systems are used for SDO. All vectors referred to below are unit length vectors.

2.1 GEOCENTRIC INERTIAL FRAME (GCI)

The Geocentric Inertial frame (GCI) is an Earth-centered frame in which the xGCI axis points to the vernal equinox, the zGCI axis points to the North Celestial Pole (parallel to the Earth's spin axis), and the yGCI axis is the cross product yGCI = zGCI  xGCI. This frame is mean of J2000.

2.2 SOLAR NORTH REFERENCED FRAME (SNR)

The Solar North Referenced frame (SNR) is a body-centered frame in which the vector to the Sun is always [1 0 0]. This frame represents the desired body attitude, or commanded attitude. The SNR frame rotates in the GCI frame at approximately 1/day. The xSNR axis points from the spacecraft to the Sun, and the ySNR axis is defined as the cross product of the solar north pole, zH, and xSNR , or ySNR = zH  xSNR. The zSNR axis completes the orthogonal frame: zSNR = xSNR  ySNR. See Figure 5 for a pictorial representation.

Release Date – 25 January 2007 1 Figure 5. SNR Coordinate Frame Definition

The Solar North Reference Frame is defined by:

rSun / Earth  rSDO / Earth xˆ SNR   rˆSun / SDO  sˆ rSun / Earth  rSDO / Earth

zˆ H  xˆ SNR yˆ SNR  zˆ H  xˆ SNR

xˆ SNR  yˆ SNR zˆ SNR  xˆ SNR  yˆ SNR

where rSun / Earth is the vector from the Earth to the Sun, rSDO / Earth is the vector from the Earth to the Spacecraft, and rˆSun / SDO is the unit vector in the direction from the spacecraft to the Sun.

The Sun’s spin axis in the direction of the Sun's north pole, zˆ H , (also known as the Solar North Pole unit vector), can be described in the Geocentric Inertial (GCI) frame using the following equation: cos()cos( ) ˆ   z H  sin()cos( )  sin( )  where  and  are right ascension and declination, respectively. From the inclination of the

Release Date – 25 January 2007 2 Sun and the longitude of the ascending node, the position of the Sun north pole is1

 = 286.1300 deg,  = 63.8700 deg  0.12235  ˆ   z H  - 0.42307 .  0.89780 

2.3 SPACECRAFT BODY COORDINATE SYSTEM (BCS)

The body coordinate system (BCS) is centered at the spacecraft center of mass. The xBCS axis is parallel to the spacecraft centerline, and is directed from the propulsion module to the instruments. The zBCS axis is parallel to the High Gain Antenna booms, directed from the centerline to the star tracker mounting location. The yBCS axis completes the triad yBCS = zBCS  xBCS and is pointed along the solar arrays. (See Figure 3.)

Release Date – 25 January 2007 3 3.0 HARDWARE COMPONENTS

The hardware components fall into three categories: deployables, sensors, and actuators. A detailed display of the locations of the actuators and sensors can be found in Figure 6.

RWA IRU

Star Tracker X Y Z

8 ACS Thrusters Main Engine Figure 6. SDO's Sensors and Actuators

3.1 DEPLOYABLES

3.1.1 Solar Arrays

SDO has two solar arrays that will be deployed after separation. After deployment, these arrays will remain in a fixed position.

The solar arrays have attach points on the +y and –y faces of the spacecraft. While in the stowed position, the tips of the arrays are pointed in the –x direction, with the panel faces pointing in +y and –y. Upon deployment, the panels are positioned with their tips pointing towards +y and –y, and with their faces in the +x direction. See Figure 1 and Figure 2.

The +y solar array has a serial number of 2062540-002, and the –y solar array has a serial number of 2062540-001.

Release Date – 25 January 2007 1 3.1.2 High Gain Antennas

SDO has two High Gain Antennas (HGA) located on the +z and –z face of the spacecraft bus. These will be referred to as the (+) and (-) antennas, and parameters referring to them will appear with a (+) or (-) superscript to indicate to which antenna the parameters apply. Where no (+) or (-) symbol is used, the reference applies to both antennas. The two HGAs are defined to have identical local dish frames, denoted by subscript “D”, as shown in Figure 7. The local zD-axis points along the HGA boom and away from the spacecraft bus, the local xD-axis points along the boresight of the dish, and the local yD-axis completes the triad. The dish frame is fixed to the antenna dish but rotates with respect to the spacecraft.

+ - +zD +z D

+ - +y D +y D

+ +x - +x D D

HGA Dish

HGA Boom Figure 7. High Gain Antenna Local Frames

Schematics of spacecraft plus HGA assemblies for the stowed and deployed configurations are shown in Figure 8 and Figure 9, respectively. The subscript “B” denotes the spacecraft body frame in these figures. An additional gimbal reference frame (GR) is introduced in the deployed configuration. The gimbaled reference frame (GR) is fixed with respect to the body frame and co-aligns with the antenna dish frame (D) when the HGA booms are first deployed.

Release Date – 25 January 2007 2 + +z - +zD D - +yD + +xD - +xD +xBCS + +yD +yBCS

Figure 8. Stowed Configuration: Spacecraft and HGA dishes (not to scale)

+x BCS

+y BCS +z BCS

+z + + +y - - GR ,D GR ,D +z - - GR ,D +y + + GR ,D +x + + +x - - GR ,D GR ,D Figure 9. Deployed Configuration: Spacecraft and HGA dishes (not to scale)

The rotation matrix from body to +z GR frame is given by X  1 0 0X       Y    0 1 0Y  Z   0 0 1Z    GR    BCS whereas the rotation matrix from body to –z GR is X  1 0 0 X       Y    0 1 0 Y  Z   0 0 1Z    GR    BCS While the GR frames remain fixed with respect to the spacecraft body frame, the dish frames move with the antennas. Each of the antennas is articulated by two gimbals – the inner, or azimuth, gimbal rotates about the spacecraft z-axis; the outer, or elevation, gimbals are attached to the antennas and rotate about the spacecraft y-axis if the inner gimbal rotations are zero. Consequently, the rotation of the dish frame with respect to the GR frame can be described by

Release Date – 25 January 2007 3 two sequential Euler rotations about the 3 and then 2 axis. The rotation matrix that transforms from GR to antenna dish frame can then be computed as

X  cos  0  sin    cos sin 0X         Y    0 1 0   sin cos 0Y  Z  sin  0 cos    0 0 1Z    D      GR cos  cos cos  sin  sin  X        sin cos 0 Y  sin  cos sin  sin cos  Z     GR where  is the inner gimbal angle, and  is the outer gimbal angle. When these two angles are at their zero positions, the GR frames coincide with the antenna dish frames. Note that the above rotation matrix from GR to the dish frame is the same for both +z and –z face HGAs, but there are two sets of gimbal angles that can be changed, one for each HGA. We will use (++) and ( – –) to indicate the gimbal angles for +z and –z face HGAs, respectively. The rotation matrices from spacecraft body to the two antenna dish frames are computed below:

D D   GR D D   GR RBCS  RGR ( ,  )RBCS RBCS  RGR ( ,  )RBCS

X   cos   cos   cos   sin   sin   X         Y   sin  cos 0 Y  Z   sin   cos   sin   sin  cos   Z    D    BCS

X   cos   cos  cos   sin  sin   X         Y   sin cos 0 Y  Z   sin   cos  sin   sin   cos   Z    D    BCS

For hardware testing purposes, a positive  + command should appear as rotating the +z HGA dish about the spacecraft body +zBCS-axis when the antennas are deployed. However, a positive –  command would appear to rotate the –z HGA dish about the -zBCS-axis. On the other hand, a +   – positive  command rotates the +z HGA dish about the -yBCS-axis, and a positive  command rotates the –z face HGA dish about the +yBCS-axis. The ACS will provide appropriate commands to point the HGA boresight to the ground station with specified accuracy.

There are several conventions for naming the HGAS gimbals. Their relationships are summarized below.

+ = +Z HGA inner gimbal = +Z HGA azimuth gimbal + = +Z HGA outer gimbal = +Z HGA elevation gimbal + = -Z HGA inner gimbal = -Z HGA azimuth gimbal + = -Z HGA outer gimbal = -Z HGA elevation gimbal

Release Date – 25 January 2007 4 3.2 SENSORS

In SDO’s complement of sensors are two Star Trackers (STs), eight pairs of Coarse Sun Sensors (CSSs), a Digital Sun Sensor (DSS), and three Inertial Reference Units (IRUs). All sensor data will be processed for internal use and for telemetry. In addition, the Guide Telescope will be used for fine science pointing.

3.2.1 Coarse Sun Sensors

There are sixteen coarse sun sensors (CSS) on SDO consisting of two sets of eight each; they are mounted in pairs for redundancy. The sensors are mounted on the outer tip corners of the solar panels on the +x and –x sides. The locations of the eight CSS pairs are shown Figure 10, with sensors on the –x side of the spacecraft shown in parentheses.

Figure 10. SDO CSS Locations

There are two sets of CSSs at each location of the spacecraft, with one set tied to ACE A, and the other to ACE B. The ‘A’ set of sensors is on the outboard side of the mounting bracket, and the ‘B’ set is on the inboard side, as shown in Figure 11.

Release Date – 25 January 2007 5 Set A

CSS 3B CSS 3A

CSS 7B y CSS 7A z Set B Figure 11. "A" and "B" CSS Sensors

The serial numbers of the CSSs are listed in Table 1.

Table 1: CSS Serial Numbers Sensor A Set B Set Serial Number Serial Number CSS1 007 001 CSS2 009 011 CSS3 015 003 CSS4 016 013 CSS5 005 002 CSS6 004 006 CSS7 017 012 CSS8 008 014 (Spare) (010)

The currents from the CSSs pass through the Attitude Control Electronics (ACE) where they are normalized. These normalized currents are used in the flight software to determine the Sun vector in the spacecraft frame.

The four +x CSS sensor boresights are each first rotated (beginning at the y-axis) around the z- axis in elevation by -45. The second rotation for each of the four is an azimuth rotation about the x-axis through the angles –45, 45, 135, and -135 respectively. For the four –x CSSs, the first rotation is 45 about the z-axis, and the second rotation is through the same four azimuth angles as the +x sensors. The CSS boresight unit vectors are listed in Table 2.

Table 2. CSS Boresight Vectors CSS X Y Z

Release Date – 25 January 2007 6 1 (A) 0.7071 0.5 -0.5 2 (B) 0.7071 0.5 0.5 3 (C) 0.7071 -0.5 0.5 4 (D) 0.7071 -0.5 -0.5 5 (E) -0.7071 0.5 -0.5 6 (F) -0.7071 0.5 0.5 7 (G) -0.7071 -0.5 0.5 8 (H) -0.7071 -0.5 -0.5

The transformation matrix between the body coordinate frame and the CSSs is listed below.

 A  G  0.7071 0.5  0.5 X  B  H  0.7071 0.5 0.5      Y  C  E  0.7071  0.5 0.5   Z       BCS D  F CSS 0.7071  0.5  0.5

The transformation from CSSs to body coordinate frame is determined using a pseudoinverse and is listed below.

 A  G  X 0.3536 0.3536 0.3536 0.3536 B  H  Y   0.5 0.5  0.5  0.5      C  E  Z   0.5 0.5 0.5  0.5    BCS    D  F  CSS

3.2.2 Digital Sun Sensors

SDO has one Digital Sun Sensor (DSS) mounted on the +x face of the spacecraft. The Digital Sun Sensor is a medium accuracy sensor used to determine the sun unit vector with respect to the sensor. It consists of a single sensor optical head with two sensor slits which are used to sense the sun angle about two orthogonal axes. Its nominal field of view is +/- 31.5 degrees. For each measurement axis, the DSS outputs a 14 bit binary word that is used in a sensor transfer function to calculate the sun angles,  and . The DSS sun unit vector will be used in a six state extended Kalman Filter to update the spacecraft attitude and gyro drift bias.

3.2.2.1 Sun Angle Measurement

The relationship between Sun angles output by the DSS and the sensor head coordinate system are shown in Figure 12.

Release Date – 25 January 2007 7 Y AXIS

X AXIS

Z AXIS Figure 12: DSS coordinate system and sun angles6

The DSS is used to determine the Sun vector in the spacecraft body frame. The Sun vector is determined in the DSS frame by using the transformations between the DSS head output and the DSS coordinate system:

 tan    2 2 X  tan   tan   tan  1 1  tan   Y   tan        2 2    2 2  Z  tan   tan  1  1  tan   tan  1   DSS    1    2 2  tan   tan  1 where  and  are the azimuth and elevation angles measured relative to the DSS boresight.

3.2.2.2 Orientation on the Spacecraft

The DSS head has a 31.5 degree half square FOV. The DSS boresight (zDSS) is aligned with the +xBCS. The yDSS is in the same direction as zBCS, and the xDSS is in the direction of yBCS. The rotation from BCS to DSS is as follows:

X  0 1 0X       Y   0 0 1Y  Z  1 0 0Z    DSS    BCS

Release Date – 25 January 2007 8 The DSS orientation is shown in Figure 13.

-Y DSS

Figure 13: DSS orientation on spacecraft

3.2.3 Star Trackers

The Star Trackers (STs) are made by Galileo Avionica and are mounted on the +z face of the instrument module. Data from the STs will be used in a six state extended Kalman Filter to update the spacecraft attitude and gyro drift bias. The ST is an electro-optic device capable of acquiring and tracking multiple stars in its field of view. The on board catalogue is generated starting from the position and proper motion provided in the Hipparcos catalogue.7 The sensor output to be used on SDO is the quaternion describing the orientation of the sensor coordinate system (utilizing the boresight vector as one axis) in the GCI coordinate frame. The STs, when provided with the spacecraft rate, will correct for velocity aberration. In addition, the STs will output spacecraft rate.

3.2.3.1 ST Coordinate System

Release Date – 25 January 2007 9 The ST coordinate frame to which the attitude output pertains is a functional coordinate system tied to the CCD and the optics. The output of the star tracker is in the International Celestial Reference Frame (ICRF), in which the Hipparcos and Tycho catalogue positions and proper motion are given. This frame is consistent with the conventional equatorial system for the mean equator and equinox of J2000, previously realized by the FK5 Catalogue, and therefore the ICRF and GCI frames can be considered equal.

3.2.3.2 Orientation on spacecraft

The tracker boresight is defined as the zST-axis, with yST in the direction from the mounting slot to the mounting hole, and the xST axis is orthogonal. ST1 has an A_STR serial number of SN025, is located at 1553 RT address 8, and is defined as the tracker with the boresight towards the +yBCS- axis. ST2 has an A_STR serial number of SN026, is located at 1553 RT address 11, and has the boresight towards the –yBCS-axis. The star tracker locations and orientations are shown in Figure 14.

ST2 y ST1 ST2 z ST1 x ST1 x ST2 z ST2

X BCS Y BCS

Figure 14: Star Tracker location and orientation

Release Date – 25 January 2007 10 The rotation from the body to ST1 is represented by a 3-2-1 Euler angle sequence. The rotation of ST1 is calculated by a “3” rotation of -90, followed by “2” rotation of -26 followed by a “1” rotation of 0.

The direction cosine matrix (DCM) from ST1 to the spacecraft reference frame is:

X   0 1.0 0 X       Y    0.89879405 0 0.43837115Y  Z   0.43837115 0 0.89879405Z    BCS   ST1 and the DCM from the spacecraft reference frame to ST1 is:

X   0  0.89879405 0.43837115X       Y   1.0 0 0 Y  Z   0 0.43837115 0.89879405Z   ST1    BCS

The rotation from the body to ST2 is represented by a 3-1-2 Euler angle sequence. The rotation of ST2 is calculated by a “3” rotation of 180, a “1” rotation of -26 followed by a “2” rotation of 0.

The DCM from ST2 to the spacecraft coordinate frame is:

X  1.0 0 0 X       Y    0  0.89879405  0.43837115Y  Z   0  0.43837115 0.89879405 Z    BCS   ST 2 and the DCM from the spacecraft reference frame to ST2 is:

X  1.0 0 0 X       Y    0  0.89879405  0.43837115Y  Z   0  0.43837115 0.89879405 Z   ST 2    BCS

3.2.4 Inertial Reference Units The SDO Inertial Reference Unit (IRU) system is located inside the spacecraft module structure, on the +y side of the spacecraft. The IRU system is used for determining spacecraft rates. It has three individual inertial reference units, each with two axes of information, thereby providing redundancy. The SDO baseline Kearfott TARA 1T IRU is shown in Figure 15 and the SDO IRU coordinate system is shown in Figure 14. Figure 15 defines the location of the IRU system within the spacecraft.

Release Date – 25 January 2007 11 X Y

Figure 15. SDO IRU—Kearfott TARA 1T

XMech3 3C

YMech3 B2

2 ch YMe YgCIRU2 XBcs XgCIRU3 XMech2

XgBIRU2 YgBIRU3 A1

Mech1 XIRU_sysIRU X ZBcs

YMech1 YSDOBcs XgAIRU1 ZIRUIRU_sys YIRUsIRU YgAIRU1

Figure 16. SDO IRU System with Coordinate Systems

Release Date – 25 January 2007 12 System

Figure 17. SDO IRU System Location

The transformation from each individual IRU box (1, 2, 3) coordinate frame to the IRU system coordinate frame is provided below:

The transformation from each individual IRU mechanical frame to the IRU system frame is currently the same as the individual IRU box frame to the IRU system frame. The gyro channels are mapped to spacecraft axes in the same way as they are mapped to the IRU coordinate frame in the perfect alignment case. Table 2 provides the relationship of each of the frames to the individual IRU boxes.

Table 3. SDO IRU Channel Axes, Spacecraft Axes, and Software Numbering IRU 1 IRU 2 IRU 3 IRU Box X Y X Y X Y IRU System -X Y Z X Z Y Spacecraft -X Y Z X Z Y SW # 1 2 3 4 5 6

The primary and redundant gyro channels are listed below:

Release Date – 25 January 2007 13 Table 4. SDO IRU Prime and Redundant S/C Axis X Y Z Primary 1 6 3 Redundant 4 2 5

There is no harnessing inversion, which yields an identity transformation matrix from IRU-to- body:

3.2.5 Guide Telescope

The Guide Telescope coordinate system, GT, shown in Figure 18, is defined by the GT objective lens and the GT photodiodes. A GT photodiode assembly mounts the four photodiodes at 90° intervals around the circumference of a circle within a plane. The origin of the GT coordinate system is located at the center of the GT objective lens. The xGT axis connects the centers of the GT photodiode circle and the GT objective lens and is nominally parallel to the GT optical axis. The +xGT vector points toward the aperture of the GT. The yGT axis and zGT axis are aligned such that their projection on the GT photodiode plane points toward two of the photodiodes. The four photodiodes are identified by the labels +Y, –Y, +Z, –Z. The yGT axis is parallel to the line which connects the centers of Photodiode –Y and Photodiode +Y. The zGT axis completes the orthogonal triad according to the right-hand rule.

Figure 18. Guide Telescope Coordinate System and Sun Vector Measurement

Release Date – 25 January 2007 14 3.2.5.1 Guide Telescope Orientation with respect to the SDO Observatory

XGT, yGT and zGT are nominally parallel to the corresponding Observatory body coordinate system, xBCS, yBCS and zBCS respectively. When AIA is mounted to the Observatory Instrument module (IM), zGT points into the IM. During flight, the Observatory X (roll) attitude will nominally be held so zGT aligns with the zSNR (Solar North Reference frame) as defined in the ACS Requirements2.

The Guide Telescope alignment requirements shall be as defined in the SDO Pointing, Jitter and Alignment Budget3.

3.2.5.2 Guide Telescope Identification

For purposes of labeling each GT uniquely, and to associate that unique identifier with a physical location, the guide telescopes are numbered 1 through 4 as shown in the Figure 19.

Figure 19. Guide Telescope Numbering5

The transformation from the GTn frame to BCS frame for each telescope is

X  1 0 0X       Y   0 1 0Y  Z  0 0 1Z    BCS    GTn

Release Date – 25 January 2007 15 where n designates Guide Telescopes 1 through 4.

3.3 ACTUATORS

The SDO actuators are four reaction wheel assemblies (RWA), each consisting of a reaction wheel and its electronics, and 9 ACS thrusters used for momentum unloading and orbit adjustment. Raw tachometer data shall be processed from each wheel.

3.3.1 Reaction Wheels

A reaction wheel assembly consists of a reaction wheel and its electronics. There are four RWAs on SDO, which are located on four panels of the spacecraft module (+y, -y, +z, -z) shown in Figure 20. The four RWAs are oriented in a pyramidal configuration as shown in Figure 21, with the top of the pyramid along the +x-axis of the spacecraft.

+X RWA#1 = [-0.5, 0, -0.866]

RWA#4 = [-0.5, -0.866, 0]

RWA#2= [-0.5, 0.866, 0] +Y

RWA#3= [-0.5, 0, 0.866]

-Z Figure 20. SDO RW Numbering and Locations

Figure 21. SDO RW Pyramidal Configuration. Positive spin matches RWA vendor’s definition of positive axes.

Release Date – 25 January 2007 16 For each wheel, a positive rotation (which is defined using the right-hand rule) produces a momentum vector pointing inward towards the spacecraft –x-axis. This positive spin matches the hardware definition. The transformation from the body to RWA for SDO’s four-wheel configuration is:

Table 5. RWA Spin Axes in the Spacecraft Body Frame RWA X Y Z 1 -sin() cos()*sin(0°) -cos()*cos(0°) 2 -sin() cos()*sin(90°) -cos()*cos(90°) 3 -sin() cos()*sin(180°) -cos()*cos(180°) 4 -sin() cos()*sin(270°) -cos()*cos(270°) where the angle the spin axis makes with the spacecraft yz-plane, , is 30. The DCM for the RWA spin axes in the spacecraft frame is:

1 X    0.5  0.5  0.5  0.5  2 Y    0 0.8660 0  0.8660     3 Z   0.8660 0 0.8660 0    BCS    4 RWA where RWA represents the spin axes for each reaction wheel. The inverse of the above matrix is the spacecraft to wheel DCM:

1  0.5 0  0.5774 X  2  0.5 0.5774 0      Y  3  0.5 0 0.5774   Z       BCS 4 RWA  0.5  0.5774 0 

3.3.2 Thrusters

There are eight Attitude Control System (ACS) thrusters on the SDO spacecraft plus one main engine (see Figure 22). All thrusters are canted 10 degrees from the spacecraft +x axis. There is a side A and B associated with this configuration.

Release Date – 25 January 2007 17 Y

22N Thrusters Canted 10o off X-axis

4A 4B 1B 1A X Z Main Engine ME

3A 3B 2B 2A

Figure 22. Thruster Positions and Spacecraft Coordinate Frame

This diagram indicates the general location and numbering for the SDO thrusters. Numbering of the 8 ACS thrusters starts in the +y, +z quadrant and proceeds clockwise (+x) around the perimeter of the bus. The outside set of 4 thrusters are designated set A, and the inside 4 are designated set B. The ACS thrusters are 22.24N class engines and ME (Main Engine) thruster is a 490N class engine.

The locations and unit force vector for each thruster is listed in Table 6, along with the thruster numbering used in the flight software. The location of each thruster is relative to the spacecraft mechanical reference frame. The force unit vector is also relative to the spacecraft reference frame. The unit torque vector is the torque due to a unit force, relative to a center of mass. Please note that the following values are for reference only. Check the Propulsion System Mechanical Interface Document4 for current values.

Table 6. Nominal Thruster Location and Performance

Location (m) Force Unit Vector (unit) REA SW# x y Z x y z T1A 1 -0.078 0.831 0.927 0.985 0.174 0.000 T2A 2 -0.078 -0.831 0.927 0.985 -0.174 0.000 T3A 3 -0.078 -0.831 -0.927 0.985 -0.174 0.000 T4A 4 -0.078 0.831 -0.927 0.985 0.174 0.000 T1B 5 -0.078 0.831 0.837 0.985 0.174 0.000 T2B 6 -0.078 -0.831 0.837 0.985 -0.174 0.000 T3B 7 -0.078 -0.831 -0.837 0.985 -0.174 0.000 T4B 8 -0.078 0.831 -0.837 0.985 0.174 0.000 ME ME 0.00 0.00 0.00 1 0 0

Release Date – 25 January 2007 18 4.0 REFERENCES

1. Explanatory Supplement to the Astronomical Almanac, 1992 ed. 2. SDO ACS Requirements Document, 464-ACS-REQ-0024. 3. SDO Pointing, Jitter and Alignment Budget, 464-SYS-SPEC-0009. 4. SDO Propulsion System Mechanical Interface Document, 464-PROP-ICD-0063. 5. AIA ICD, 464-AIA-ICD-0011, Section 8 – GN&C. 6. System Description / User Manual, Digital Sun Sensor (DSS), Solar Dynamics Observatory (SDO), Adcole Corporation, Document QD48068. 7. “The Hipparcos and Tycho Catalogues”, Introduction and guide to the data” SP-1200 Vol.1, Appendix A

Release Date – 25 January 2007 1