**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**

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