Fun With the HP 42S

Fun With the HP 42S

Previous Links:

HP 42S Programming Part I:  Matrix Column Sum, GCD, Error Function:  http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-i-matrix-column.html

HP 42S Programming Part II:  Dew Point, Ellipse Area and Eccentricity, Easy Transverse:
http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-ii-dew-point.html

HP 42S Programming Part III: Numerical Derivative, Recurring Sequences, Fractions:
http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-iii-numerical.html

HP 42S Julian Date

Given month, day, year, and university time (Greenwich), the Julian date is calculated.  For January 1, 2000 at 12:00 AM, the date is 2,451,545.5.

00 {141-Byte Prgm}

01 LBL “JULDATE”

02 “MONTH”

03 PROMPT

04 STO 01

05 “DAY”

06 PROMPT

07 STO 02

08 “4 DIGIT YEAR”

09 PROMPT

10 STO 03

11 “UT TIME”

12 PROMPT

13 STO 04

14 367

15 RCL* 03

16 STO 00

17 9

18 RCL+ 01

19 12

20 ÷

21 IP

22 RCL+ 03

23 4

24 ÷

25 7

26 *

27 IP

28 STO -00

29 RCL 01

30 9

31 –

32 7

33 ÷

34 RCL+ 03

35 100

36 ÷

37 IP

38 3

39 *

40 4

41 ÷

42 IP

43 STO- 00

44 275

45 RCL* 01

46 9

47 ÷

48 IP

49 STO+ 00

50 RCL 02

51 STO+ 00

52 1721028.5

53 STO+ 00

54 RCL 04

55 24

56 ÷

57 STO+ 00

58 RCL 00

59 END

Example:

Input:  May 8, 2017, 03:00 UT.  Result:  2457881.6250

HP 42S Sun Approximate Declination, Altitude, and Azimuth

Original Post:  http://edspi31415.blogspot.com/2013/06/hp-35s-sun-altitude-azimuth-solar-pond.html

Input:  Days after the vernal equinox (typically March 21), Earth’s latitude (north/south), number of hours after local noon (example:  for 7 AM, enter -5.  For 7 PM, enter 7).

00 { 147-Byte Prgm }

01 LBL “SUNAA”

02 DEG

03 “DAYS AFTER EQ.”

04 PROMPT

05 STO 00

06 “LATTITUDE”

07 PROMPT

08 STO 01

09 “HRS AFTER NOON”

10 PROMPT

11 STO 02

12 0.9856

13 RCL* 00

14 SIN

15 23.45

16 *

17 STO 04

18 COS

19 RCL 01

20 COS

21 *

22 15

23 RCL* 02

24 COS

25 *

26 RCL 01

27 SIN

28 RCL 04

29 SIN

30 *

31 +

32 ASIN

33 STO 05

34 SIN

35 RCL 01

36 SIN

37 *

38 RCL 04

39 SIN

40 –

41 RCL 05

42 COS

43 RCL 01

44 COS

45 *

46 ÷

47 ACOS

48 STO 06

49 RCL 04

50 “DECLINATION”

51 AVIEW

52 STOP

53 RCL 05

54 “ALTITUDE”

55 AVIEW

56 STOP

57 RCL 06

58 “AZIMUTH”

59 AVIEW

60 END

Example:

Input:  100 days after the vernal equinox, 43.72° N, about 12 noon (T = 0)

Results:  Declination ≈ 23.1888°, Altitude:  69.4688°, Azimuth: 0.0002°

 HP 42S Chebyshev Polynomial

The trigonometric definition is used to calculate T_n(x):

For |x| > 1, cosh (n * acosh x)

For |x| ≤ 1, cos (n * acos x)

00 {42-Byte Prgm}

01 LBL “CHEBY”

02 “N”

03 PROMPT

04 STO 00

05 “X”

06 PROMPT

07 STO 01

08 ABS

09 1

10 X≥Y?

11 GTO 00

12 RCL 01

13 ACOSH

14 RCL* 00

15 COSH

16 GTO 01

17 LBL 00

18 RCL 01

19 ACOS

20 RCL* 00

21 COS

22 LBL 01

23 END

Examples:

T_4(2) (n = 4, x = 2).  Result:  97

T_4(0.5)  (n = 4, x = 0.5)  Result:  -0.5

HP 42S Pulley

There are two weights in a pulley system, held by a rope has a negligible contribution.  The program uses SI units (kg, m, s, with g = 9.80665 m/s^2).  The simultaneous equations solve for acceleration (m/s^2) and tensions:

T – m1 * a = m1 * g

T + m2 * a = m2 * g

Source:  HP 22S Science Student Applications.  Edition 1.  Corvallis, Oregon.  May 1988

00 {161-Byte Prgm}

01 LBL “PULLEY”

02 “MASS 1 (KG)”

03 PROMPT

04 STO 01

05 “MASS 2 (KG)”

06 PROMPT

07 STO 02

08 9.80665

09 STO 00

10 2

11 ENTER

12 2

13 DIM “MAT1”

14 INDEX “MAT1”

15 1

16 STOEL

17 J+

18 RCL 01

19 +/-

20 STOEL

21 2

22 ENTER

23 1

24 STOIJ

25 1

26 STOEL

27 J+

28 RCL 02

29 STOEL

30 2

31 ENTER

32 1

33 DIM “MAT2”

34 INDEX “MAT2”

35 RCL 00

36 RCL* 01

37 STOEL

38 I+

39 RCL 00

40 RCL* 02

41 STOEL

42 RCL “MAT1”

43 INVRT

44 RCL “MAT2”

45 *

46 STO “MAT3”

47 INDEX “MAT3”

48 RCLEL

49 “T”

50 AVIEW

51 STOP

52 I+

53 RCLEL

54 “a”

55 AVIEW

56 END

Example:  m1 = 32 kg, m2 = 56 kg

Result:  tension = 399.3981, a = 2.6745 m/s^2

 HP 42S Rotation Matrix

R = [[ cos θ, -sin θ ],[ sin θ, cos θ ]]

00 {138-Byte Prgm}

01 LBL “ROTATE2”

02 DEG

03 “ANGLE °”

04 PROMPT

05 STO 00

06 1

07 ENTER

08 2

09 DIM “MAT1”

10 INDEX “MAT1”

11 “X0”

12 PROMPT

13 STOEL

14 J+

15 “Y0”

16 PROMPT

17 STOEL

18 2

19 ENTER

20 2

21 DIM “MAT2”

22 INDEX “MAT2”

23 RCL 00

24 COS

25 STOEL

26 J+

27 RCL 00

28 SIN

29 +/-

30 STOEL

31 2

32 ENTER

33 1

34 STOIJ

35 RCL 00

36 SIN

37 STOEL

38 J+

39 RCL 00

40 COS

41 STOEL

42 RCL “MAT1”

43 RCL “MAT2”

44 *

45 STO “MAT3”

46 INDEX “MAT3”

47 RCLEL

48 “X1”

49 AVIEW

50 STOP

51 J+

52 RCLEL

53 “Y1”

54 AVIEW

55 END

Example:

Input:  [3, -2], at an angle θ = 40°

Result:  [ 1.0126, -3.4605 ]

 Always fun working with the classic HP 42S!

Eddie

This blog is property of Edward Shore

HP Prime, TI-84 Plus, Casio Prizm: Julian Day Shortcut Formulas

Julian Day Shortcut Formulas

Here are a couple of formulas that can be used to quickly get the Julian Day.  (I haven't figured how to include the time yet).


HP Prime (Rev. 7820):

yyyy:  four digit year, mm:  two digit month, dd: two digit day.  The international date format is used.

From December 31, 1899:

JD = DDAYS(1899.1231,yyyy.mmdd) + 2415020

Alternatively, from November 16, 1858:

JD = DDAYS(1858.1116, yyyy.mmdd) + 2.4E6


TI-84 (and BA II  Plus to that extent):

Dates are good from January 1, 1950 to December 31, 2049:

JD = dbd(1.0150, mm.ddyy) + 2433283

The days between dates function (dbd) is accessed by pressing [ APPS ], [ 1 ], [ALPHA], [ x^-1] (D).  

Casio Prizm and fx-Graphing calculators:

Dates are good from January 1, 1901 to December 31, 2099:

JD = Days_Prd(1,1,1901,mm,dd,yyyy) + 2415386

Where to find Days_Prd:  [ OPTN ], ( > ) (until you see the FINANCE sub menu), (FINANCE), ( > ), (DAYS), (PRD)

Hope you find this helpful.

Source:
"Julian Day"  http://en.wikipedia.org/wiki/Julian_day   Retrieved May 28, 2015


Eddie


This blog is property of Edward Shore.  2015.

HP Prime, HP 42S, HP 12C: Julian Date

The following program calculates the Julian Date given:

M = month
D = day
Y = year, four digits
UT = Universal Time.  The universal time is notated by 0:00 to 24:00, as the current time at the Greenwich Mean Time.  Depending on where you live, it may be necessary to adjust the current time in your time zone to get Greenwich Mean Time.  For example, add 8 hours to the Pacific Standard Time, and add 7 hours to the Pacific Daylight Savings time, to get the equivalent Greenwich Mean Time for the Pacific Time Zone.  You may have to adjust the day number by 1 (either way) as a consequence. 

Formula for the Julian Date:

j:=367*Y-IP(7*(Y+IP((M+9)/12))/4)
-IP(3*(IP((Y+(M-9)/7)/100)+1)/4)

+IP(275*M/9)+D+1721028.5+H/24

where IP is the integer function.  The integer function is also symbolized by INT, INTG, and iPart.  This is the most complete formula, as there are shortcut formulas for Julian Date.

Source for formula:  http://scienceworld.wolfram.com/astronomy/JulianDate.html 

Here are the programs for Julian Date for three different HP calculators:  HP Prime, HP 42S, and HP 12C.

My thanks to Jason Foose who traded with me, I now have a 42S.  He asked to trade me for my one of my 50g's.  

Julian Date:  HP Prime

EXPORT JULIAN(M,D,Y,H)
BEGIN
// wolfram.com
// 2015-02-08
// H UT time
// +8 PST +7 PDT
LOCAL j;
j:=367*Y-IP(7*(Y+IP((M+9)/12))/4)
-IP(3*(IP((Y+(M-9)/7)/100)+1)/4)
+IP(275*M/9)+D+1721028.5+H/24;
RETURN j;

END;

Julian Date:  HP 42S

Before running the program "JD", store the following:
Month (M) to Memory 01
Day (D) to Memory 02
Year (Y) to Memory 03
Universal Time (H) to  Memory 04

The Julian Date is stored in Memory 00.
(edited 2/13/2015 - thanks Mike)

00   { 102-Byte Prgm }
01   LBL "JD"
02   367
03   RCLx 03
04   STO 00
05   9
06   RCL+ 01
07   12
08   ÷
09   IP
10   RCL+ 03
11   7
12   x
13   4
14   ÷

15   IP
16   STO- 00
17   -9
18   RCL+ 01
19   7
20   ÷

21   RCL+ 03
22   100
23    ÷

24    IP
25    1
26    +
27    0.75
28    x
29    IP
30    STO- 00
31    275
32    RCLx 01
33    9
34    ÷

35   IP
36   STO+ 00
37   RCL 00
38   RCL+ 02
39   1721028.5
40   +
41   RCL 04
42   24
43   ÷
44    +
45   STO 00
46   RCL 00
47  .END.

Examples:

January 7, 2015;  12:35 UT
M = 1, D = 7, Y = 2015,  H = 12.58333333

Result:  JD = 2,457,030.02431

December 17, 2230;  18:30 UT
M = 12, D = 17, Y = 2230, H = 18.5

Result:  JD = 2,535,901.27083


Julian Date:  HP 12C

This program uses the ΔDYS function.  Universal time is assumed to be 12:00.  

Step    Key    Key Code
01       1         1
02       .          48
03       0         0
04       1         1 
05       2         2
06       x<>y   34
07       ΔDYS 43 26
08       2         2 
09       4         4
10       5         5
11       1         1
12       5         5
13       4         4
14       5         5
15       +        40

Examples:

June 30, 2016;   JD = 2,457,570

October 31, 2111:  JD = 2,492,390

Hopefully this program will be helpful.  Until next time,

Eddie



This blog is property of Edward Shore.  2015

HP15C: Julian Date from Gregorian Date

Thanks to the University of Texas at San Antonio Computer Science Department. The explanation and formulas can be found by clicking on this link.

Note: This program only works for dates on or after October 15, 1582. Thank you Dieter.


Calculator
HP 15C (can be adopted with any RPN keystroke calculator)

Input
Preload the following information into these registers:
R1 = month (1 for January, 12 for December)
R2 = date
R3 = year in four digits (example: 2013)

Output
R0 = Julian Date

Temporary
R4 = a = integer((14-month)/12)
R5 = y = year + 4800 - a

Formulas
(See link above)
a = integer((14-month)/12)
y = year + 4800 - a
m = month + 12a - 3
Julian Date = day + integer((153m+2)/5) + 365y + integer(y/4) - integer(y/100) + integer(y/400) - 32045

Assumptions: 12:00 PM Universal Time is assumed (that's 7:00 AM in Pacific Standard Time or 8:00 AM in Pacific Daylight Savings Time)

Program
LBL A
1
4
RCL - 1
1
2
÷
INT
STO 4
4
8
0
0
RCL + 3
RCL - 4
STO 5
RCL 2
STO 0
1
2
RCL × 4
RCL + 1
3
-
1
5
3
×
2
+
5
÷
INT
STO + 0
3
6
5
RCL × 5
STO + 0
RCL 5
4
÷
INT
STO + 0
RCL 5
1
%
CHS
INT
STO + 0
RCL 5
4
÷
1
%
INT
STO + 0
RCL 0
3
2
0
4
5
-
STO 0
RTN


In HP RPN calculators, a number followed by 1, %, divides said number by 100.

Example:

March 14, 1977 has a Julian Date of 2,443,217
April 28, 2012 has a Julian Date of 2,456,046
December 31, 2015 has a Julian Date of 2,457,388

This blog is property of Edward Shore. 2013