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Group Report 1964-45
Haystack Pointing System: Moon
H. E. Frachtman
10 September
Lincoln Laboratory kCHUSET TUTE OF
Le ssachus
•
The work reported in this document was performed at Lincoln Laboratory, a center for research operated by Massachusetts Institute of Technology, with the support of the U.S. Air Force under Contract AF 19(628)-500.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LINCOLN LABORATORY
HAYSTACK POINTING SYSTEM: MOON
H. E. FRACHTMAN
Group 62
GROUP REPORT 1964-45
10 SEPTEMBER 1964
56
LEXINGTON MASSACHUSETTS
ABSTRACT
This report describes the procedure used by the Haystack pointing computer
program for obtaining the celestial coordinates of the Moon at any time.
Accepted for the Air Force Franklin C. Hudson, Deputy Chief
Air Force Lincoln Laboratory Office
in
I. INTRODUCTION
MOONTRACK is a program in the Haystack Univac 490 pointing system whose
output is the celestial coordinates of the Moon at a given time. The program computes
the coordinates by 4th difference interpolation in the tables of the apparent right
ascension, declination, and radius vector of the Moon published in The American
Ephemeris. The rates of change of the three quantities are computed by numerical
differentiation.
II. INPUTS TO PROGRAM
A. Inputs Furnished by Core Memory
The program uses the registers listed in Table I for input information. The year
and day are used to select the appropriate entries from the ephemeris. The coordin-
ates of the Moon are interpolated for the time which is the sum of the times in CEL-
TIME and DELTATEE.
B. Inputs Furnished by Magnetic Tape
The tape format of the Moon Ephemeris, which has been edited and recorded on
tape by a 7094 program described in Reference (1), is shown in Fig. 1. Each block
of 192 words covers a period of one day. The ephemeris for each day required 8
words for each of 24 hours. The program does not make use of the hour-year-month-
day words in the block. The tape mast be on Unit 1 (normally Servo B) of the Univac
490.
III. PROGRAM OUTPUTS
A. Outputs Left in Core Memory
The apparent celestial coordinates of the Moon, corresponding to the time in
the register CELTIME, together with their numerical derivatives, are stored in
the appropriate registers, as illustrated in Table II.
Register
W(CELTIME)
W(DELTATEE)
U(YEARMONTH)
L(YEARMONTH)
L(DAY)
W(EQUATOR)
Contents and Scaling
Days B28
Days B28
Year B15 (4 decimal digits)
Month BO
Day of Year BO
Equatorial radius of Earth B17
TABLE I
Core Memory Inputs to MOONTRACK Program
NOTE: Notation "B28" means
that the binary point is to the
right of bit 28.
3-62-3003
14 0
I. D. 13d Conventional Day Number
19 14 8 4 0
All Zero Hour Year Month Day
Right Ascension B26 Radians
First Difference Right Ascension B26 Radians
Declination B26 Radians
First Difference Declination B26 Radians
Radius Vector B22 Earth Equatorial Radii
First Difference Radius Vector B22 Earth Equatorial Radii
Fig. 1. Magnetic Tape Format for Moon Ephemeris
Register
W(RA)
W(DEC)
W(RADIUS)
W(RADOT)
W( DECDOT)
W(RADIUSDOT)
Contents and Scaling
Apparent Right Ascension B27 in revolu- tions
Apparent Declination B27 in revolutions
Distance from center of Earth to center of Moon, B22 Earth Equatorial radii
Numerical Derivative of Right Ascension B37 radians/sec
Numerical Derivative of Declination B37 radians/sec
Numerical Derivative of Radius Vector B24 nautical miles/sec
TABLE II
Core Memory Outputs of MOONTRACK Program
B. Typewriter Outputs
During initialization the MOONTRACK program will type, using the INTERCOM
subroutine, certain information concerning the Moon. Items printed are:
1. Julian Day corresponding to values in YEARMONTH, DAY, and CELTIME
(7 digits).
2. Apparent Right Ascension of the Moon (Hours, Minutes, Seconds to
hundredths).
3. Apparent Declination of the Moon (Degrees, Minutes, Seconds to
hundredths).
4. Day of Year corresponding to values in YEARMONTH and DAY (up to
3 digits).
5. Universal Time for which the coordinates are interpolated. It is the
time in CELTIME at initialization (Hours, Minutes, Seconds to hundredths).
6. The distance between the centers of the Earth and the Moon (Earth's
Equatorial radii to millionths).
7. The words "OBJECT MOON".
If, after a search through 12 files on Unit 1 (or the finding of an end of tape mark),
the moon ephemerides are not found, the program will type "MOON EPHEMERIS FOR
X/Y NOT AMONG FIRST 12 FILES" and will exit to the master control program error
return. "X" and "Y" indicate the current month and year, respectively.
If there is a tape servo malfunction during search, the program will type "IIIC
STATUS SI ZZ" and will exit to the master control program error return. The two
digit octal number "ZZ" comes from the tape status word and indicates the error
condition.
IV. ASTRONOMICAL SIGNIFICANCE
The apparent right ascension and declination of the Moon in the emphemerides
are referred to the true equinox and equator of date and are corrected for planetary
aberration. They are geocentric apparent quantities; the parallax correction is made
by the coordinate conversion program (COCON) in the Haystack system. The values
in the tables are computed for Ephemeris Time as argument. The equation
ET = UT + AT
is used to convert from Universal Time to Ephemeris Time. The constant AT,
represented by the number in the register DELTA TEE is approximately 35 seconds.
The values for the radius vector and first difference of the radius vector which
appear on the ephemeris tape (Figure 1) are computed from the Moon's horizontal
parallax which occurs in the source data. The formula
D = l
sin h
is used by the tape preparation program (Reference 1) to compute the distance D, in
units of Earth's equatorial radii, from the geocentric equatorial horizontal parallax
h. The register EQUATOR contains a number which represents the Earth's equa-
torial radius in nautical miles.
V. PROGRAM DETAILS
The MOONTRACK program is a subroutine of the Haystack Univac 490 pointing
program. The initialization section begins at MOONINIT, the working section at
MOONCONT. There are several closed subroutines within MOONTRACK. These
are: DAYFIND, STATUSCK, INTERPOL, LEFRNDOFF, and MOONTIME. A listing
of the program is given in Appendix I.
A. Initialization
The program, upon initialization, stores an RIL instruction in the tape channel
internal interrupt register and an RJP STATUSCK instruction in the external interrupt
register. The area in core into which the tape data will be read is cleared, together
with some additional registers. This is done to make diagnosis easier in case of
malfunction.
The daily Moon ephemeris entries are serially numbered by the program which
generates the magnetic tape (Reference 1). These serial numbers are called "Con-
ventional Day Numbers" (CDN). An arbitrary decision was made to produce and use
tapes such that the CDN for 25 April 1963 is zero. The tape search process looks
at the first word in each block, therefore, the MOONTRACK, program must compute
the CDN of the block containing the entry for the required hour.
Using as inputs the year, day of year, and the effect of integral and half-integral
values of CELTIME, the program computes the Julian Day number for the typewriter.
The ephemerides start and run continuously from 25 April 1963, which has a Julian
Day Number of 2438144. 5; this number is subtracted from the computed Julian Day
number and appears on tape as the Conventional Day Number. The first CDN in a
block is stored in SAFE and TAPEBLOCK and the Moon identification number is added
to generate a tape search comparison word.
Six blocks of Moon cphemcrides are read to provide sufficient data for 4th
difference Bessel interpolation for a four day period.
If the six block search and read operations are successful control is regained
at NORMAL and the tape is rewound without interrupt or interlock.
The MOONTIME subroutine is entered to select and store the addresses of the
ephemeris entries corresponding to the hour of the day and to compute the interpola-
tion argument P. The register TIME2 contains a number representing the integral
number of hours in the sum of CELTIME and DELTATEE.
Besselian interpolation of right ascension is done by the INTERPOL subroutine
and the interpolated result is converted to hours, minutes, and seconds and stored
for type out. Declination and distance are then interpolated and stored for type out.
The other quantities which are to be typed out by INTERCOM are set up. Control is
transferred to INTERCOM 7 times for the seven line type out, which completes oper-
ation of the initialization section of MOONTRACK.
B. Working Section
The MOONTRACK working section begins at MOONCONT. Control is transferred
to the subroutine MOONTIME which selects the ephemeris entry corresponding to
the current hour, stores the addresses of the table entries, and computes the inter-
polation argument P from the given value of CELTIME. The INTERPOL subroutine
is then entered three times for the interpolation of right ascension, declination, radius
and their time rates. All values are converted, scaled and stored properly in core
memory and control is transferred to the master control program.
C. Subroutines
The initialization section of the MOONTRACK program makes use of the INTERPOL,
DAYFIND, STATUSCK, LEFRND3FF, and MOONTIME subroutines. The working
section uses all except STATUSCK.
1. INTERPOL
The MOONTRACK interpolation subroutine uses Bessel's interpolation formula for
(Reference 3) 4th difference interpolation of the Moon's ephemeris. The formula is
f =f +P6f1/9 + ^5-^ [62f +62f.] p o 1/2 4 o 1
P(P-l)(P-l/2) 3 (P+l)P(P-l)(P-2) 4 4 + g o iy2 t- 4g ^° I0^° V
The quantities in the formula are associated with computer registers as follows:
a. The address of f is in index register 4.
b. The interpolation argument P is in register P.
c. <5fi/9 is in register GAMMA.
d. P(P-l) is in register PSQMP. 2 2
e. 6 f +6 f. is in register DMINB.
f. P(P-l) is in register PSQMP6.
g. 6 f 1/2 is in register DMIN2CPLB.
h. (64f + <54f ) is in register EP2BM2DMA.
i. fp is in the A register at the finish.
The subroutine also performs numerical differentiation using the following formula
(Reference 3):
hf,P = 6h/2+^r: i*\ + 6\*
3P2 - 3P + 1/2 .3. + 6 6 fl/2
At the completion of the subroutine, hf' is stored in the register NUMDERIV.
Wnen the subroutine is entered, Index Register 4 contains the address of f
and the register SETINTAD contains the address of 6f, ,„ of the quantity to be inter-
polated. Index register 3 is used to acquire the other two first difference registers.
2. DAYFIND
The DAYFIND subroutine computes the Julian Day number and CDN correspond-
ing to the current day.
3. STATUSCK
The STATUSCK subroutine is entered from the external interrupt register asso-
ciated with the tape channel when the interrupt occurs. Examination of the status
code generates four possible outcomes:
a. If the code indicates a normal completion, control is returned to
the program at the interrupted point.
b. If the code indicates that an end of tape mark was sensed, the tape
is rewound and a message indicating failure to find the ephemeris is printed by the
typewriter. The message is described in Section III B. Control is passed to the
error return of the master control program.
c. If the code indicates that an end of file mark was sensed, the register
IMPERIAL is indexed and tested for the value 12. When less than 12 an end of tape
condition is assumed and the action is as described in (b) above.
d. If the code indicates anything but end of file, end of tape, or normal
completion, a tape error has occurred. The message described in Section III B,
indicating the type of error, is printed by the typewriter and control is passed to the
error return of the master control program.
4. LEFRNDOFF
The LEFRNDOFF subroutine left shifts the AQ register the number of places
indicated by the contents of index register 5 and rounds the A register.
5. MQQNTIME
The MOONTIME subroutine computes the integral value of the current ephemeris
hour and stores the addresses of the quantities to be interpolated. It computes the
value of the interpolation argument P.
VI. PROGRAM LISTING
The next 23 pages show a APURT output of the MOONTRACK program in 3 parts:
Pp. 10-26
Pp. 27-29
Pp. 30-32
Printout of MOONTRACK program.
Alphabetic list of program symbols.
Numerical list of program symbols.
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32
REFERENCES
1. "Haystack Pointing System Ephemeris Tape Program", M.I. T. Lincoln Laboratory, Publication 1964-41. (In preparation)
2. Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (Her Majesty's Stationery Office, London, vmy.
3. R. Butler and E. Kerr, An Introduction to Numerical Methods (Sir Isaac Pitman and Sons, Ltd. , London).
33
DISTRIBUTION LIST
W. B. Davenport G. P. Dinneen H. G. Weiss J. W. Meyer
Group 31
J. S. Arthur J. R. Burdette C. A. Clark C. T. Frerichs R. F. Gagne G. M. Hyde R. P. Ingals M. L. Meeks J. E. Morriello V. C. Pineo W. Rutkowski P. B. Sebring M. L. Stone S. Weinreb
Group 62
P. Rosen F. E. Heart W. R. Crowther J. D. Drinan H. E. Frachtman D. M. Hafford A. A. Mathiasen F. Nagy S. B. Russell R. J. Saliga P. D. Smith P. Stylos R. Teoste S. J. White Group 62 Office (5)
Group 76
A. O. Kuhnel
34
UNCIASSTFTPD Security Classification
DOCUMENT CONTROL DATA - R&D (Security classification ot title, body ot abstract and indexing annotation must be entered when the overall report it c lessitied)
I. ORIGINATING ACTIVITY (Corporate author)
Lincoln Labs., Lexington, Mass.
2a. REPORT SECURITY C L AISI FIC A TION
UNCLASSIFIED 2b GROUP
-H/A- 3 REPORT TITLE
Haystack Pointing Systems Moon
4 DESCRIPTIVE NOTES (Type ot report and inclusive dates)
Group Report 5. AUTHORfSJ (Last name, tint name. Initial)
Frachtman, H.£.
6 REPORT DATE
oep 64
7a- TOTAL NO. OF PASES
J£_ 7b NO. OF REFS
8a. CONTRACT OR GRANT NO.
AF19(628)500 b. PROJECT NO.
d.
9a. ORIGINATOR'S REPORT NUMBERfSJ
GR-1964-45 9b. OTHER REPORT MO(S) (A ny other number* that may be assigned
this report)
ESD-TDR-64-371 10. AVAILABILITY/LIMITATION NOTICES
Qualified Requesters May Obtain Copies Frew. DDC.
11. SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY
ESI), L.G. Hanscor. Field, Bedford, Mass.
13. ABSTRACT
This report describes the procedure used by the Haystack pointing computer program for obtaining the celestial coordinates of the Moon at any time.
DD .5251 1473 Security Classification
UNCLASSIFIED Security Classification
14. KEY WORDS
LINK A LINK B
ROLE
LINK C
Haystack Moontrack Program Inputs Program Outputs Astronomical Significance
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Secunty^JraSSrncation
