INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES page is designed to help learners understand how to calculate a simple Line of Position (LOP) of the sun using the tables. It also provides feedback on the correctness of answers or solutions.

While written for the completion of the eight exercises, the page additionally only presents the solution for the La Rochelle exercise.

Furthermore, the interactive worksheet page goes beyond this particular exercise by providing additional examples for each step throughout the entire process.

I recommend fully mastering the free La Rochelle exercise on this page **before making a purchase**. In addition, within the logarithm and azimuth section, you’ll find five exercises, each complemented by a fully worked-out solution.

This way, testing your skills on the remaining exercises will be enjoyable.

Remember that it is also the groundwork for the stars, moon, and planets.

Furthermore, this immediate feedback allows learners to assess their understanding and progress in real time, enabling them to identify areas that need improvement.

### INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES: the six sections

Ho = observed height

P = polar angle

D = sun’s declination

Hc = calculated height

Zv = true azimuth

Intercept = difference between Ho and Hc

see: blank worksheet (spreadsheets) PDF file for the tables

see symbols and abbreviations of the worksheet

Our observations on the La Rochelle exercise page

Now that you were supposed to find these red entries from our observations on the La Rochelle exercise page, we can proceed with the calculations.

INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES

Section 1

#### -Ho- (observed height)

We will calculate and explain Ho in two steps:

Blue section

Apparent height of the sun (theory Ha)

Red section

Observed height of the sun (theory Ho)

INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES

Section 2

### Local Hour Angle (LHA) and (Polar Angle) P

GHA = _ _ ° _ _ ‘, _

+pp = _ _° _ _ ‘, _

GHA = _ _° _ _’, _

___________________

*G = _ _ ° _ _ ‘, _

_____________________

LHA ** = _ _ ° _ _ ‘, _**

In fact *G add if East / subtract if West

Sun in the East !

How to calculate GHA + pp ( increment)

dead reckoning position L and G

After finding LHA, how to deduce P ?

ロ LHA < 180°

sun in the West P = LHA

ロ LHA > 180°

sun in the East P = 360- LHA

P = _ _ ° _ _ ‘, _

NE / NW / SE / SW

(To clarify, for example P = _ _ ° _ _ ‘, _ SE , We are situated in the Southern Hemisphere, and the sun is in the East at the time of our observation.

** **

Section 3

#### -D- (Declination of the sun)

D = _ _ ° _ _ ‘, _

correc. d = _ _ ° _ _ ‘, _

___________________

D ** = _ _ ° _ _ ‘, _ **

Section 4

### INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables: Hc (calculated height)

L…………..= _ _ ° _ _ ‘, _

D………….= _ _ ° _ _ ‘, _

__________

(L +/- D)….= _ _ ° _ _ ‘, _

1T 1………….LOG COS L =

2T 1………….LOG COS D =

3T 2….LOG VERSINE P =

_______________________________+

………………LOG 2e Term =

T 3………..COS (L +/- D) =

T4………………..NAT 2eT =

____________________________-

………………………..SIN Hc =

T 5………………………….Hc** **=

1) Explanation of the logarithms tables.

2) example Hc with the logarithm tables

3 Two exercises Hc with logarithm tables and solutions

Once we have examined the preceding examples and exercises, we will complete the La Rochelle (Hc) exercise!

Entries:

L = 46°12′ N

D = 18°39,7′ S

P = 27°33,4′ NE

Section 5

### INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES: Zv (true azimuth)

*part 1* azimut table:

*lc* =

*dc *= ______________+

*zc*** ** = acute ou obtuse

*part *2 azimut table:

Z =

Zv =

Firstly , Explanation and example Zv calculation with the azimuth tables

Then, Four exercises with the azimuth tables

Once we have examined the preceding examples and exercises, we will complete the La Rochelle Zv exercise.

Entries:

L = 46°12′ N

D = 18°39,7′ S

P = 27°33,4′ NE

The first and third pages serve as separate reminders on how to utilize these azimuth tables, while the second and fourth pages are specifically designed for the La Rochelle exercise.

Section 6

## Intercept

Ho………….= ** **_ _ ° _ _ ‘,** _**

Hc…………. =** ** _ _ ° _ _ ‘,** _**

Intercept…= ** **_ _ ° _ _ ‘, _

#### intercept = Ho – Hc

Then** **+** **Intercept towards the sun / – away from the sun

### INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES: Additional Knowledge

Concerning the time interval between two Lines of Position (LOPs), the process of transferring a LOP, and understanding the uncertainty area associated with a LOP

Sun’s LOP running fix and the uncertainty zone.

Day planning with the two sun LOP’s

Using the local apparent noon sight latitude with the sun is a widely adopted technique in maritime navigation.

It offers a straightforward and swift approach for determining latitude.

Local apparent noon sight latitude

Calculate Local Apparent Noon Time

INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables:

Indeed, the answers to the remaining exercises (2 madagascar/3 perth/4 san francisco/5 galapagos/6 tokyo/ 7 pointe-a-pitre/ 8 rotterdam ) can be purchased at the store. They also provide the fully extended logarithm and azimuth tables for download.

I recommend fully mastering the free La Rochelle exercise on this page before making a purchase. This way, testing your skills on the remaining exercises will be enjoyable. Remember that it is also the groundwork for the stars, moon, and planets.

###### INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables, The Importance of Persistence and Effort in Achieving Progress

In fact, it’s essential to set realistic expectations and understand that working through the worksheet will take effort and time on your part. However, with dedication and persistence, you will eventually see progress.

Certainly, as you work through the exercises, you may encounter challenges or feel frustrated at times.

Therefore, don’t be discouraged if you don’t see progress right away; it’s all part of the process.

###### In summary

In summary, remember that progress takes time, effort. If you find yourself feeling overwhelmed or frustrated, however, step away from the worksheet for a little while.

Furthermore, for individuals who are fluent in French, there exists a French rendition of this website that goes by the name www.ladroitedehauteur.com