# hp41programs

binarystar Binary Stars for the HP-41

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: /

-Lines 52 to 66 solve Kepler's equation.
-The iterations stop when the difference between 2 successive approximations is smaller than 0.001°  ( line 64 )

 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   53  RCL 09   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  )

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:

[1]  Jean Meeus , "Astronomical Algorithms" - Willmann-Bell  -  ISBN 0-943396-61-1
[2]  Washington Double Star Catalogue.