**Casio fx-9750GIII: Equatorial to Galactic Coordinates Conversions **

**Introduction**

__Coordinate Systems__

There are several coordinate systems used by astronomers to determine the placement of celestial objects, such as stars, galaxies, planets, and black holes, in our night skies.

Two coordinate systems are:

Equatorial System:

The equatorial system frames the University with the Earth's center as the center of the university.

Right Ascension (α): Customarily stated in hours, minutes, and seconds (H°M°S°). Each hour is equivalent to 15 degrees. The right ascension at 0 hours is aligned where the sun would be during the vernal equinox.

Declination (δ): Customarily stated in degrees, minutes, and seconds (D°M°S°).

Galactic System:

The galactic system frames the University, aligning it with the Milky Way Galaxy. The center of the system is our Sun. The galactic longitude at 0 degrees aligns with the center of our galaxy (Sagittarius A*).

Galactic Longitude (l): Customarily stated in degrees, minutes, and seconds (D°M°S°).

Galactic Latitude (b): Customarily stated in degrees, minutes, and seconds (D°M°S°).

The program EQT2GLT converts equatorial coordinates (α, δ) to galactical coordinates (l, b).

b = arcsin( cos δ × cos 27.1284° × cos(α - 192.8595°) + cos δ × cos 27.1284° )

l =

arctan( ( sin δ - sin b × sin 27.1284° ) ÷ ( cos δ × sin(α -192.8595°) × cos 27.1284°) + 32.93117169°

= atan2((sin δ - sin b × sin 27.1284°), (cos δ × sin(α -192.8595°) × cos 27.1284°)) + 32.93117169°

b is in hours, from -90 to 90 degrees.

l is in degrees, from 0 to 360 degrees. Be sure to consider quadrants in your calculation.

The program GLT2EQT converts galactical coordinates (l, b) to equatorial coordinates (α, δ).

δ = arcsin( (cos b × cos 27.1284° × sin( l - 32.93117169° ) + sin b × sin 27.1284° )

α = arctan( ( cos b × cos( l - 32.93117169° ) ) ÷ ( sin b × cos 27.1284° - cos b × sin 27.1284° × sin( l - 32.93117169° ) ) + 192.8595°

= atan2((cos b × cos(l - 32.93117169°),(sin b × cos 27.1284° - cos b × sin 27.1284° × sin(l-32.93117169°)) + 192.8595°

δ is in degrees, from -90 to 90 degrees.

α is in hours, from 0 to 24 hours. Be sure to consider quadrants in your calculation. Remember that 1 hour is equivalent to 15 degrees.

The equations are from Practical Astronomy With Your Calculator by Peter Duffett-Smith, with the constants updated for J2000.0.

From the "Conversion of coordinates" page of Tobias Westmeier's webpage, the J2000.0 of the north pole are:

α0 ≈ 192.8595° (12h 51m 26.28s)

δ0 ≈ 27.1284° (27°07'42.24")

(Sources: Duffett-Smith, Westmeier - refer to the Source section)

For more details, please refer to the Equatorial to Galactic Coordinates: Updating the Constants posted on January 6, 2023.

**Casio fx-9750GIII Program: EQT2GLT**

**Casio fx-9750GIII Program: EQT2GLT**

**Sources**

"Equatorial coordinate system" Wikipedia. Last Edited April 10, 2023. Accessed December 10, 2023. https://en.wikipedia.org/wiki/Equatorial_coordinate_system

"Galactic coordinate system" Wikipedia. Last Edited April 21, 2023. Accessed November 23, 2023. https://en.wikipedia.org/wiki/Galactic_coordinate_system

Duffett-Smith, Peter. __Practical Astronomy With Your Calculator__ Second Edition. Cambridge University Press: Cambridge, UK. 1981.

ISBN: 0 521 28411 2 (paperback)

National Aeronautics and Space Administration (NASA). "Coordinate Calculator" NASA/IPAC Extragalactic Database. Operated by the California Institute of Technology. 2023. Accessed November 26, 2023. https://ned.ipac.caltech.edu/coordinate_calculator?in_csys=Equatorial&in_equinox=J2000.0&obs_epoch=2000.0&ra=17h45m40.036s&dec=-29d00m28.17s&pa=0.0&out_csys=Galactic&out_equinox=J2000.0

Westmeier, Tobias. "Conversion of coordinates" Homepage of Tobias Westmeier. The University of Western Australia. Last Modified 26 September 2023. Accessed November 26, 2023. https://www.atnf.csiro.au/people/Tobias.Westmeier/index.php

Eddie

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