The Museum of HP Calculators
The Museum of HP Calculators
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.
-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 = 36.9°
T = 2005.13
i = 148.0°
omega = 256.5°
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.
Go back to the HP-41 software library
Go back to the general software library
Go
back to the main exhibit hall