The Museum of HP Calculators

# Binary Stars for the HP-41

This program is Copyright © 2005 by Jean-Marc Baillard and is used here by permission.

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

## Overview

-This program calculates the polar coordinates ( r ; µ ) of a binary star  ( S1 ; S2 )
and the eccentricity e' of the apparent orbit, as seen from the Earth.

North
|
S2       |
\        |
\  µ  |
r  \    |                                     r  =  the angular distance = S1S2
\  |                                     µ  =  the position angle = ( S1N ; S2N )
\|
S1

Program Listing

Data Registers:       When the program stops,   R00 = e' =  eccentricity of the apparent orbit

-Registers R08 & R09 are used for temporary data storage.          Registers R01 thru R07 are to be initialized before executing "BSTAR"

•   R01 = P = period of revolution ( expressed in years )
•   R02 = T = time of perihelion passage ( given as a year and decimals )
•   R03 = e = eccentricity
•   R04 = a = semimajor axis ( in arcseconds )
•   R05 = i  = inclination of the orbit
•   R06 = OMEGA = position angle of the ascending node
•   R07 = omega = longitude of the periastron.

Flags: /
Subroutines: /

01  LBL "BSTAR"
02  DEG
03  STO 00
04  RCL 03
05  RCL 07
06  COS
07  *
08  X^2
09  STO 08
10  RCL 05
11  COS
12  X^2
13  ST* Y
14  -
15  X<> 08
16  RCL 03
17  X^2
18  -
19  1
20  +
21  RCL 05
22  COS
23  RCL 07
24  RCL 03
25  P-R
26  *
27  *
28  ST+ X
29  X^2
30  RCL 08
31  ST- Z
32  R^
33  +
34  X^2
35  +
36  SQRT
37  ENTER^
38  ST+ Y
39  R^
40  +
41  /
42  SQRT
43  X<> 00
44  RCL 02
45  -
46  360
47  *
48  RCL 01
49  /
50  STO 08
51  STO 09
52  LBL 01                      lines 52 to 66 solve Kepler's equation
53  RCL 09                     the iterations stop when the difference between 2 successive approximations is smaller than 0.001°  ( line 64 )
54  ENTER^
55  SIN
56  RCL 03
57  R-D
58  *
59  RCL 08
60  +
61  STO 09
62  -
63  ABS
64   E-3
65  X<=Y?
66  GTO 01
67  RCL 09
68  2
69  /
70  1
71  RCL 03
72  ST+ Y
73  ASIN
74  COS
75  /
76  P-R
77  LASTX
78  /
79  R-P
80  X<>Y
81  ST+ X
82  RCL 07
83  +
84  1
85  P-R
86  STO 08
87  X<>Y
88  RCL 05
89  COS
90  *
91  X<>Y
92  R-P
93  CLX
94  RCL 06
95  +
96  1
97  RCL 09
98  COS
99  RCL 03
100  *
101  -
102  RCL 04
103  *
104  RCL 08
105  *
106  RCL Y
107  RCL 06
108  -
109  COS
110  /
111  END

( 135 bytes / SIZE 010 )

 STACK INPUTS OUTPUTS Y / µ X YYYY.yy r

Example:   The elements of  Gamma Virginis are:         P = 168.68 years              a = 3.697"             OMEGA =  36.
T = 2005.13                      i = 148.0°                 omega = 256.
e = 0.885

-Calculate  r  and  µ  for the epoch  2010.25    ( ~ 2010/04/01 )

-Store these 7 numbers in registers R01 thru R07  ( in the order  P ,  T ,  e  ,  a  ,  i  ,  OMEGA  ,  omega  )

-Then,     2010.25  XEQ "BSTAR"  >>>>  r =  1.544"         ( in 33 seconds )
X<>Y   µ =  19.66°         ( and the apparent eccentricity  e' = 0.844 in R00 )

Notes:    -If you don't need to compute the apparent eccentricity e' , delete lines 03 to 43.
-Execution time may tend to infinity as e tends to 1.

-Here are the elements of a few binary stars. Right Ascensions and declinations are referred to J2000
-m1 & m2 are the magnitudes.

 STARS Right Asc Decl m1 m2 P T e a i OMEGA omega eta Cas 0h49m05s +57°49'00" 3.7 7.5 480.0 1889.6 0.497 11.994 34.8 278.4 268.6 alpha Psc 2h02m03s +2°45'49" 4.3 5.3 933.050 2098.643 0.696 4.000 120.9 23.3 225.4 alpha For 3h12m04s -28°59'21" 3.8 7.0 269.0 1947.0 0.730 4.000 81.0 117.0 43.0 Sirius 6h45m09s -16°42'58" -1.4 8.4 50.090 1894.130 0.592 7.500 136.5 44.6 147.3 Castor 7h34m36s +31°53'19" 2.0 2.9 467.000 1958.000 0.343 6.805 114.5 41.3 249.5 Procyon 7h39m18s +5°13'39" 0.4 10.8 40.650 1927.600 0.400 4.548 35.7 284.3 269.8 gamma Leo 10h19m58s +19°50'31" 2.6 3.8 618.557 1743.320 0.843 2.505 36.4 143.2 162.5 xi Uma 11h18m11s +31°31'45" 4.3 4.8 59.840 1995.050 0.412 2.533 121.2 100.9 126.8 gamma Vir 12h41m40s -1°26'58" 3.6 3.7 168.680 2005.130 0.885 3.697 148.0 36.9 256.5 zeta Uma 13h23m55s +54°55'31" 1.6 2.1 36.5 1994.8 0.6 0.80 93.0 32.0 287.0 xi  Boo 14h51m24s +19°06'02" 4.8 6.9 151.505 1909.361 0.512 4.904 140.0 168.1 23.9 eta CrB 15h23m12s +30°17'18" 5.0 5.3 41.585 1933.721 0.262 0.868 59.0 203.2 38.4 sigma CrB 16h14m42s +33°51'31" 5.7 6.7 888.989 1826.949 0.761 5.927 31.8 16.9 72.2 zeta Her 16h41m17s +31°36'07" 2.8 5.5 34.45 1967.7 0.46 1.33 131.0 50.0 111.0 70 Oph 18h05m27s +2°30'09" 4.3 6.0 88.38 1895.94 0.499 4.554 121.2 302.1 14.0 gamma CrA 19h06m25s -37°03'46" 4.2 4.3 121.760 2000.640 0.320 1.896 149.6 50.3 349.0 beta Cyg 19h30m43s +27°57'35" 3.2 5.3 96.840 2010.270 0.719 0.586 118.0 98.8 77.2 61 Cyg 21h06m54s +38°44'58" 5.6 6.3 722.000 1689.700 0.401 24.650 51.8 172.3 158.0 zeta Aqr 22h28m50s -0°01'12" 3.7 3.9 587.18 1973.39 0.396 3.847 138.2 129.8 255.9

References:        Jean Meeus , "Astronomical Algorithms" - Willmann-Bell  -  ISBN 0-943396-35-2
Washington Double Star Catalogue.