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[parent] example converting ecliptic coordinates to rectangular coordinates (Example)

Consider an object with ecliptic coordinates:

  • Longitude: $l = 30^\circ $,
  • Latitude: $b = 15^\circ $,
  • Distance: $r = 1 $ AU.

The conversion to rectangular coordinates is given in ecliptic coordinate system:

$\displaystyle x$ $\displaystyle = r \cos b \cos l,$    
$\displaystyle y$ $\displaystyle = r \cos b \sin l,$    
$\displaystyle z$ $\displaystyle = r \sin b.$    

Convert to radians:

$\displaystyle l = 30^\circ = \frac{\pi}{6} \approx 0.5236, \quad b = 15^\circ = \frac{\pi}{12} \approx 0.2618. $

Compute:

$\displaystyle \cos b \approx 0.9659, \quad \sin b \approx 0.2588, \quad \cos l \approx 0.8660, \quad \sin l = 0.5000. $

Then:

$\displaystyle x = 1 \times 0.9659 \times 0.8660 \approx 0.8365, $

$\displaystyle y = 1 \times 0.9659 \times 0.5000 \approx 0.4830, $

$\displaystyle z = 1 \times 0.2588 \approx 0.2588. $

Thus, the rectangular coordinates are:

$\displaystyle (x, y, z) \approx (0.8365, 0.4830, 0.2588) \,$   AU$\displaystyle . $

This example was generated by Grok, an AI developed by xAI, on March 13, 2025.



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See Also: ecliptic coordinate system


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Cross-references: ecliptic coordinate system, ecliptic, object

This is version 2 of example converting ecliptic coordinates to rectangular coordinates, born on 2025-03-14, modified 2025-03-14.
Object id is 990, canonical name is ExampleConvertingEclipticCoordinatesToRectangularCoordinates.
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Physics Classification: 95.10.-a (Fundamental astronomy)
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