INTERACTIVE CELESTIAL WORKSHEET CALCULATOR is designed to help learners understand how to calculate a simple sun’s line of position (LOP) using a scientific calculator. It also provides feedback on the accuracy of the answers along with theoretical explanations.
While written for the completion of the eight exercises, the page additionally only presents the solution for the La Rochelle exercise.
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.
The 6 sections
see symbols and abbreviations of the worksheet
Ho = observed height
P = polar angle
D = sun’s declination
Hc = calculated height
Zv = true azimuth
Intercept = Ho ⎼ Hc
Each of the six different expressions mentioned above from the worksheet will be treated separately on this page.
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 CALCULATOR
Section 1
-Ho- (observed height)
We will calculate and explain Ho in two steps:
Blue table
Apparent height of the sun (theory Ha)
Red table
Observed height of the sun (theory Ho)
INTERACTIVE CELESTIAL WORKSHEET CALCULATOR
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 = _ _ ° _ _ ‘, _
INTERACTIVE CELESTIAL WORKSHEET CALCULATOR
Section 4
-Hc- (calculated height)
L = _ _ ° _ _ ‘, _
D = _ _ ° _ _ ‘, _
P = _ _ ° _ _ ‘, _
INTERACTIVE CELESTIAL WORKSHEET CALCULATOR
Section 5
-Zv- (true azimuth)
L = _ _ ° _ _ ‘, _
D = _ _ ° _ _ ‘, _
Hc = _ _ ° _ _ ‘, _
Z = _ _ _ , _ °
ロ Sun in the East ⟹ Zv = Z
ロ Sun in the West ⟹ Zv = 360° – Z
True azimuth: Zv = _ _ _ , _ °=
theory Zv / How to calculate Zv
INTERACTIVE WORKSHEET CALCULATOR
Section 6
-intercept-
Ho = _ _ ° _ _ ‘, _
Hc = _ _ ° _ _ ‘, _
______________________ –
intercept = _ _ ‘, _
Ho – Hc = intercept
Intercept towards the sun (+)
And intercept away from the sun (-)
INTERACTIVE CELESTIAL WORKSHEET CALCULATOR: 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 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 WORKSHEET (calculator)
Hence, On this page, you will discover a set of recommendations to follow.
If you’re familiar with the process, feel free to skip ahead, as the following text may be tedious and unnecessary.
In the South Pacific, a solo sailor described a sunset where the sun seemed to split into two horizontally, briefly forming an almond shape with a black bar in the middle before disappearing. Possible cause: a rare optical refraction combined with a layer of warm air over cold water.
Furthermore, for individuals who are fluent in French, there exists a French rendition of this website that goes by the name www.ladroitedehauteur.com
The Importance of Persistence and Effort
Learning celestial navigation isn’t something you master in an afternoon — but that’s what makes it rewarding. Every calculation you complete brings you one step closer to understanding the Sun’s position and your own.
Expect challenges along the way:
- Some exercises will feel straightforward, others may slow you down.
- You might double-check a formula three times before it clicks.
- At first, your calculator and tables may feel like strangers. They won’t for long.
Stay Committed
The real key is consistent practice:
- Even 10–15 minutes a day will compound into real skill.
- Don’t skip a section just because it looks intimidating — each one builds on the last.
- Think of every solved exercise as another “tool” in your mental navigation kit.
Focus on Small Wins
Celestial navigation is built from small, repeatable actions:
- Apply one correction.
- Check one calculation.
- Confirm one value in the table.
It’s a chain — link by link, your knowledge grows stronger. You’ll notice the difference when you return to an earlier exercise and find yourself solving it in half the time.
Make It Enjoyable
Try to treat the learning process like a voyage:
- Plot your course: set a realistic pace for completing each section.
- Mark your position: note your progress at the end of each session.
- Celebrate landfall: when you finish the La Rochelle exercise, take a moment to appreciate what you’ve achieved.
Why It’s Worth the Effort
Mastering these calculations gives you:
- A reliable backup if GPS fails.
- The ability to cross-check electronic navigation for safety.
- A direct link to centuries of seafaring tradition.
- Greater self-reliance and confidence at sea.
In Summary
This worksheet is not just an exercise — it’s a foundation. The patience and persistence you invest here will make the rest of your celestial navigation journey smoother, faster, and more rewarding.
And remember: even if the process feels slow at times, every observation, every correction, and every plotted line is another mile toward mastering your craft.