Deliverable Notification
for the MOMS Contract
To:
Robert DeFazio, MOMS Task Monitor
From:
Dave Hooshmand, Task Manager
CC:
Roger Werking, FDSS Project Manager
Greg Dell, FDSS Deputy Project Manager
Jeffrey Dibble, Task Technical Lead
Subject:
SDO Flight Dynamics – Sun Transit Product Definition
Date:
08/23/2005
This memorandum is to inform you that the design specifications for Sun Transit Product
have been completed by FDSS, as requested under the MOMS contract, Task Order #085
(SDO Flight Dynamics).
Attached is the technical memorandum presenting the proposed definition of the transit
product including derivations of the reference coordinate frame. Also included is the
proposed format for the product.
We will contact you by 08/25/2005 to ensure you have received this deliverable and to
answer any questions that may arise. Feel free to contact us at 301-306-1756 (x177) or
Jeff Dibble at (x153) beforehand, as needed.
Sincerely,
David Hooshmand
Task Manager
a.i. solutions, Inc.
FDF-85-006
Mission Operations and Mission Services
Flight Dynamics (FD)
Task Order 85
TECHNICAL MEMORANDUM
Solar Dynamics Observatory (SDO)
Sun Transit Product Definition
Issue Date: August 23, 2005
Submitted by:
Jeffrey Dibble
Task Technical Lead
a.i. solutions, Inc.
and
Joseph Hashmall
Task Member
a.i. solutions, Inc.
TECHNICAL MEMORANDUM
Solar Dynamics Observatory (SDO)
Sun Transit Product Definition
I Introduction
This memorandum presents the results of an analysis conducted by a.i. solutions, Inc. in support
of the Flight Dynamics Analysis Branch (FDAB) at Goddard Space Flight Center (GSFC). This
analysis was performed to provide a definition of a new product requested by the Helioseismic
and Magnetic Imager (HMI) science team. The product will provide planet and/or moon
position information in a Sun-centered coordinate frame during times of transit across the solar
disk. This product will assist the HMI team to calibrate their science cameras.
II Product Definition
The HMI team has requested a product containing the position of a planet or the Earth’s Moon
(an object of interest) relative to the center of the solar disk versus time during periods when the
object of interest traverses the solar disk, as viewed by SDO. Figure 1 depicts the geometry
involved during a transit period.
Figure 1 Sun Transit Geometry
Page 1 of 4
FDF-85-006
Using the definitions listed in Table 1 below, the positions of the center of objects of interest
with respect to the Sun are calculated and reported as follows:
Table 1 Symbol Definitions
Ŝ J 2000
A unit vector from SDO to the Sun center in the J2000 GCI coordinate frame
P̂J 2000
A unit vector from SDO to an object of interest (planet, moon) in the J2000 GCI
coordinate frame
A unit vector from SDO to an object of interest (planet, moon) in the Solar coordinate
frame
P̂S
x, y, and z
N̂ J 2000
U

The x, y, and z components of
P̂S
The unit vector of the Solar North Pole in the J2000 GCI coordinate frame.
 0.1223535 


Nominally - 0.4230721 or right ascension, 286.1300°, declination 63.8700°


 0.8977971 
A function that normalizes a vector
Rotation Angle about SDO to Sun vector, from Solar coordinate frame X-axis to
P̂J 2000

Separation Angle between
x
Separation angle from
Ŝ J 2000 and P̂J 2000
Ŝ J 2000 to P̂J 2000 in a direction parallel to the Solar
coordinate frame x-axis
y
Separation angle from
Ŝ J 2000 to P̂J 2000 in a direction parallel to the Solar
coordinate frame y-axis
First we define a rotation from J2000 to the Solar Frame as:

A  U Nˆ J 2000  Sˆ J 2000
 U Sˆ
J 2000

 Nˆ J 2000  Sˆ J 2000

Sˆ J 2000

(1)
The matrix A defines the axes of the Solar frame in terms of J2000 GCI directions. It converts
vectors in the Solar frame to vectors in the J2000 frame. The transpose of A (i.e., AT) converts
vectors in the opposite direction. The unit vector from SDO to the object of interest in the Solar
coordinate frame is then:
PˆS  AT PˆJ 2000
(2)
The position of the object of interest, relative to the Sun will be reported in two ways: (, ) pairs
and (x,y) pairs. They are defined as follows:
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FDF-85-006
y
x
1
  cos z 
(3)
x
z.
y
 y  tan 1  
z
(4)
  tan 1  
and
 x  tan 1  
 and  will be reported in degrees and x and y in arcseconds.
III Operations Concept
The positions will be tabulated at 1 second intervals. Because only a few hours each year will
include these events, an efficient strategy to produce the product is needed. This is a plan for
such a strategy.
The limiting factor in determining an event is the apparent rate of motion of the object of
interest. The fastest motion is that of the moon which moves slightly more than a degree each
hour.
The position of each possible object of interest with respect to the Sun will be computed at 0.5
hour intervals throughout the reporting period. The apparent angular radius of the object and of
the Sun will also be calculated. If the angle between the Sun and the object ( ) is never less than
twice the sum of the object’s angular radius and the Sun’s angular radius during the report
period, then there are no events for this object during the report period. If there are times at
which  is less than twice the sum of the object’s angular radius and the Sun’s angular radius,
separations are recalculated every 1 second starting 0.5 hours before the first reported event time
and ending 0.5 hours after the last reported event time. Only the values where  is less than
twice the sum of the object’s angular radius and the Sun’s angular radius will be reported.
IV Product Sample
A proposed sample format for the new product is presented in Figure 2. In addition to the object
of interest’s position relative to the Sun, the distance from SDO to the object and the object’s
angular radius as viewed from SDO are provided.
Page 3 of 4
FDF-85-006
07 Aug 2005 12:00:00
Sun Disk Transits
Requested Time Period(s):
Start Time
Stop Time
--------------------------2008277.000000
2008312.000000
Object Name
----------Venus
Venus
Venus
Venus
Object Name
----------Moon
Moon
Moon
Moon
Time (YYYYDDD)
-------------2008301.005004
2008301.005005
2008301.005006
.
.
.
2008301.021001
Time (YYYYDDD)
-------------2008278.005004
2008278.005005
2008278.005006
.
.
.
2008278.021001
-------- Sun Frame Position
Lambda
Phi
x
(deg)
(deg)
(arcsec)
------- ------------200.522
0.164
-24.2136
200.654
0.162
-24.3483
200.795
0.160
-24.7562
-------y
(arcsec)
--------22.7189
-21.9635
-21.5671
S/C to Object
Distance (km)
------------235222211.966
235223251.341
235224517.365
Object
Angular
Radius
(deg)
------0.00147
0.00147
0.00147
331.722
-22.7189
235226611.901
0.00147
0.164
16.2136
-------- Sun Frame Position
Lambda
Phi
x
(deg)
(deg)
(arcsec)
------- ------------200.522
0.164
-24.2136
200.654
0.162
-24.3483
200.795
0.160
-24.7562
-------y
(arcsec)
--------22.7189
-21.9635
-21.5671
S/C to Object
Distance (km)
------------337532.969
337652.706
337773.079
Object
Angular
Radius
(deg)
------0.29505
0.29495
0.29484
331.722
-22.7189
391421.512
0.25443
0.164
16.2136
Figure 2 Sample Product Format
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FDF-85-006