sexagesimal system and celestial formulas

sexagesimal system and celestial formulas: the context of celestial calculations and the sexagesimal system, computations involve degrees, minutes, and tenths of minutes.

To facilitate these calculations, one can utilize a scientific calculator to perform the necessary operations.

This page on this self-instruction website is written to emphasize the importance of using a simple scientific calculator for handling celestial formulas, which are used in the calculation of the Line of Position (LOP).

sexagesimal system and celestial formulas, formula for azimuth calculation
sexagesimal system and celestial formulas, formula for calculated altitude
San Francisco. Author image: Brocken Inaglory

A common way to measure and express angles in geometry and trigonometry.

-degrees

-minutes

-tenths of minutes

Example: 24°45′,5

Twenty-four degrees and forty-five point five minutes.

and not: 24°45′ 30” (degrees/minutes/seconds)

and not: 24,75833 (decimal degrees)

See also the 360° formulas


Carmel River State Beach (Breaking wave). Author image: Tewy

sexagesimal system and celestial formulas:

Explanation of the scientific calculator and the sexagesimal system

Also, on this page, I work with the basic scientific calculator from Casio, which contains the DMS function as you can see in the picture below.

sexagesimal system image casio calculator

Additionally, the programmable versions work differently than the basic scientific calculators.

As a matter of fact, a scientific calculator is extremely useful for solving trigonometric equations.

Firstly, be careful that it is in degree mode (D) and that it contains the button [D M S] or [ ° ‘ “ ]

sexagesimal system image degree mode
degree mode!! Casio style

the river Scheldt flows into the English Channel. Author image: Socket0

Sexagesimal system and celestial formulas: Example with scientific calculator (Casio) and sexagesimal system

    

K=arcsin (sin(24°15’,6 )✕cos(42°45’,2) ) 

Calcul K

K=arcsin(sin (24[ ° ‘ ‘’ ]15,6[ ° ‘ ‘’ ] )

✕ cos(42[ ° ‘ ‘’ ] 45,2[ ° ‘ ‘’ ] ))

As a result, The calculator gives us K  =  17,559781    (decimal)

sexagesimal system image decimal mode

[ 2nde ]   [ ° ‘ ‘’ ]     gives us 17°  33’  35,21’’   (degrees/minutes/seconds) 

sexagesimal system image degrees/minutes/tenths of minutes

Finally, now it’s up to us to convert to degrees/minutes/tenths of minutes

k = 17°33′,6

Here an other example of how to calculate with the scientific calculator. Try it yourself


sexagesimal system and scientific calculator

To clarify how to round seconds in tenths of minutes:

60” = 1′ (60 seconds equal 1 minute)

10°10’ 06’’⇨  10°10’,1
10°10’ 12’’⇨  10°10’,2
10°10’ 18’’⇨  10°10’,3
10°10’ 24’’⇨  10°10’,4
etc…
10°10’ 26, 28’’⇨  10°10’,4
10°10’ 27, 00’’⇨  10°10’,5
10°10’ 27, 31’’⇨  10°10’,5
10°10’ 30, 00’’⇨  10°10’,5
etc…

Hence, even if we are wrong on a tenth of a minute

It’s not that important


Sexagesimal system and celestial formulas: Casio calculators:

Firstly, a reflection Summary on the Casio and Texas Instruments Calculators

Certainly, Casio and Texas Instruments are two popular manufacturers of calculators, and they offer different features and functionalities.

When it comes to the DMS (Degrees, Minutes, and Seconds) function or angle function, here’s how you can explain the differences between Casio and Texas Instruments calculators:

Casio calculators often have a user-friendly interface and a wide range of models to choose from. In relation to the DMS or angle function, Casio calculators generally provide easy access to these features. They usually have dedicated buttons or menu options specifically designed for working with angles in degree, minute, and second format. In summary, these calculators allow you to input and manipulate angles in DMS format directly, perform calculations with them, and convert between degrees and DMS.

Sexagesimal system and celestial formulas: Texas Instruments calculators

Since, texas Instruments calculators are also popular among students and professionals. Moreover, in terms of the DMS or angle function, Texas Instruments calculators usually offer similar functionality to Casio calculators. However, the specific methods for accessing these features may vary depending on the model. Texas Instruments calculators typically have dedicated buttons or functions for working with angles in degree mode, but they may require additional steps or specific commands to input or manipulate angles in DMS format. The exact steps can vary between different models of Texas Instruments calculators.

sexagesimal system and celestial formulas:

In summary, both Casio and Texas Instruments calculators can handle DMS or angle calculations. Casio calculators often have dedicated buttons or menu options specifically designed for easy access to these features, while Texas Instruments calculators may require additional steps or specific commands to work with angles in DMS format. It’s essential to consult the user manual or guide for the specific calculator model to understand how to perform DMS or angle calculations accurately on that particular device.

It is very important that you can resolve the issue presented on this page with your type of scientific calculator!