(35) Locating the Moon

[SlideRule]

An algorithm from the article Using the HP 35 to Locate the Moon, Locating the Moon (Eimac).

The following procedure is a technique for using the Hewlett-Packard HP-35 hand held calculator for determining the moon's AZIMUTH in relation to true north, and the ELEVATION with respect to the local horizon for the geographical location in question.

BEST!
SlideRule

[Thomas Klemm]

This program is for the HP-42S:

Code:

00 { 32-Byte Prgm }
01▸LBL "MOON"
02 R↓
03 -
04 X<>Y
05 R↑
06 1
07 →REC
08 R↑
09 X<>Y
10 →REC
11 X<>Y
12 R↓
13 →POL
14 R↓
15 X<>Y
16 -
17 R↑
18 →REC
19 R↓
20 →POL
21 R↑
22 X<>Y
23 →POL
24 R↓
25 END

Example:




37.33 ENTER
122.13 ENTER
80.85 ENTER
23.36 XEQ "MOON"

y: 99.6580
x: 52.0939

It works also for most other HP calculator models that provide polar-rectangular coordinate transformations.
Of course it's not restricted to locate the moon but any celestial body.

I wasn't aware of moonbounce.
Does anyone here has experience with it?

Cheers
Thomas

[pier4r]

Quote:I wasn't aware of moonbounce.
Does anyone here has experience with it?

Listening to the computer history museum podcast (If I am not mistaken), there is the quest of discovering the radar capabilities of the soviets. The problem: you cannot fly an airplane with electronics and detectors deep in the soviet airspace, so it is rather complicated.

They started to realize that they can pick up reflected signals from missiles going up and directly from the moon. I suspect the arecibo radar telescope was used for that too. ( https://en.wikipedia.org/wiki/Arecibo_Observatory )

[PedroLeiva]

I have modifie this HP-42S program to be use in HP-67, also change the input data procedure to labels A to D for LAT, LONG, GHA and DECL. But I have doubths about the LAT and LOG sings to use. Usually N of equator and E of Greendwich are (+), and (-) for the opposite locations. Is this apply here?
Your opinion will be highly appreciated
Pedro

[Thomas Klemm]

(02-08-2019 11:31 AM)PedroLeiva Wrote:  But I have doubts about the LAT and LOG sings to use. Usually N of equator and E of Greenwich are (+), and (-) for the opposite locations. Is this apply here?

Yes. But I had to look up the definitions of GHA and azimuth:

The hour angle may be expressed as negative east of the meridian plane and positive west of the meridian plane.

Azimuth is defined as a horizontal angle measured clockwise from a north base line or meridian.

From looking at the 2 examples on page 6 I assume that the longitude of my example is meant to be in the west as well. Thus we should rather use -122.13.
And since the azimuth is measured clockwise we have to change a sign as well.

This leads to this corrected program:

Code:

00 { 33-Byte Prgm }
01▸LBL "MOON"
02 R↓
03 +
04 X<>Y
05 R↑
06 1
07 →REC
08 R↑
09 X<>Y
10 →REC
11 X<>Y
12 +/-
13 R↓
14 →POL
15 R↓
16 X<>Y
17 -
18 R↑
19 →REC
20 R↓
21 →POL
22 R↑
23 X<>Y
24 →POL
25 R↓
26 END

Line 03 was changed and line 12 was inserted.

Examples:

37.33 ENTER
-122.13 ENTER
80.85 ENTER
23.36 XEQ "MOON"

y: 99.6580
x: 52.0939

---

36 ENTER
-122 ENTER
71 ENTER
2 XEQ "MOON"

y: 113.7316
x: 31.9605

---

36 ENTER
-122 ENTER
181 ENTER
-2 XEQ "MOON"

y: -111.1134
x: 23.3226

I hope that's correct now.

Cheers
Thomas

[PedroLeiva]

(02-08-2019 05:05 PM)Thomas Klemm Wrote:  

(02-08-2019 11:31 AM)PedroLeiva Wrote:  But I have doubts about the LAT and LOG sings to use. Usually N of equator and E of Greenwich are (+), and (-) for the opposite locations. Is this apply here?

Yes. But I had to look up the definitions of GHA and azimuth:

The hour angle may be expressed as negative east of the meridian plane and positive west of the meridian plane.

Azimuth is defined as a horizontal angle measured clockwise from a north base line or meridian.

From looking at the 2 examples on page 6 I assume that the longitude of my example is meant to be in the west as well. Thus we should rather use -122.13.
And since the azimuth is measured clockwise we have to change a sign as well

Same results as yours. Thank you
Pedro

[PedroLeiva]

[/quote]
This is a program for HP-67. Some chanches were made: the input information of LAT, LONG, GHA, DECLIN by pressing [A], [B], [C] and [D], the output pressing [E] and [x<>y]

Code:


*LBL A:
001:  31 25 11   LBL A
002:  33 11      STO A
003:  35 22      RTN

     *LBL B:
004:  31 25 12   LBL B
005:  33 12      STO B
006:  35 22      RTN

     *LBL C:
007:  31 25 13   LBL C
008:  33 13      STO C
009:  35 22      RTN

     *LBL D:
010:  31 25 14   LBL D
011:  33 14      STO D
012:  35 22      RTN

     *LBL E:
013:  31 25 15   LBL E
014:  34 11      RCL A
015:  34 12      RCL B
016:  34 13      RCL C
017:  34 14      RCL D
018:  35 53      R↓
019:  61         +
020:  35 52      x≷y
021:  35 54      R↑
022:  01         1
023:  31 72      P➝R
024:  35 54      R↑
025:  35 52      x≷y
026:  31 72      P➝R
027:  35 52      x≷y
028:  42         CHS
029:  35 53      R↓
030:  32 72      R➝P
031:  35 53      R↓
032:  35 52      x≷y
033:  51         -
034:  35 54      R↑
035:  31 72      P➝R
036:  35 53      R↓
037:  32 72      R➝P
038:  35 54      R↑
039:  35 52      x≷y
040:  32 72      R➝P
041:  35 53      R↓
042:  35 22      RTN

Example1: angles in degrees
Data
A-LATITUDE: 37.33 DEG
B-LONGITUDE: -122.13 DEG
Convention: N of equator and E of Greenwich are (+), opposite position (-)

C-GHA: 80.85 DEG
Greenwich Hour Angle
(June 2, 1973 at 19:00 GTM)
Convention to get Azimuth from true N:
1- If the GHA is east of your longitude 
A= Azimuth
2- If the GHA is west of your longitude 
360 - A= Azimuth

D-DECLINATION: +23.36 DEG
(June 2, 1973 at 19:00 GTM)
Convention: N (+), S (-)

Results
ELEVATION: 52.0939 DEG
AZIMUTH: 99.6580 DEG

INSTRUCTIONS
Input
37.33 [A]
-122.13 [B]
80.85 [C]
23.36 [D]

Output
[E]
x: 52.0939
[x<>y]
y: 99.6580

Example2:
Data
36 [A]
-122 [B]
71 [C]
2 [D]

Solution
[E]
x= 21.9605 DEG
[x<>y]
y= 113.7316 DEG

Example3:
Data
36 [A]
-122 [B]
181 [C]
-2 [D]

Solution
[E]
x= 23.3226 DEG
[x<>y]
y= -111.1134 DEG
[quote]

[Thomas Klemm]

(02-09-2019 02:08 AM)PedroLeiva Wrote:  Some changes were made: the input information of LAT, LONG, GHA, DECLIN by pressing [A], [Β], [C] and [D]

We can slightly improve the program E when the input is in registers A - D:

Code:

013:  31 25 15   LBL E
014:  34 12      RCL B
015:  34 13      RCL C
016:  61         +
017:  34 11      RCL A
018:  34 14      RCL D
019:  01         1
020:  31 72      P➝R
021:  35 54      R↑
022:  35 52      x≷y
023:  31 72      P➝R
024:  35 52      x≷y
025:  42         CHS
026:  35 53      R↓
027:  32 72      R➝P
028:  35 53      R↓
029:  35 52      x≷y
030:  51         -
031:  35 54      R↑
032:  31 72      P➝R
033:  35 53      R↓
034:  32 72      R➝P
035:  35 54      R↑
036:  35 52      x≷y
037:  32 72      R➝P
038:  35 53      R↓
039:  35 22      RTN

Cheers
Thomas