Unit vector to Right Ascension/Declination

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SUMMARY

This discussion focuses on converting a unit vector to right ascension and declination, essential for celestial navigation and astronomy. The user seeks clarification on the correct formulae and resources for understanding these spherical coordinates, where declination corresponds to latitude and right ascension to longitude. Key resources provided include a Wikipedia article on celestial coordinate systems and a PDF on positional astronomy. The importance of deriving the metric tensor for accurate transformations between coordinate systems is emphasized.

PREREQUISITES
  • Understanding of spherical coordinates, specifically right ascension and declination.
  • Familiarity with unit vectors in three-dimensional space.
  • Basic knowledge of tensor mathematics and differential geometry.
  • Ability to interpret and manipulate mathematical formulae related to coordinate transformations.
NEXT STEPS
  • Study the Wikipedia article on celestial coordinate systems.
  • Review the PDF on positional astronomy for detailed transformations.
  • Learn about deriving the metric tensor and its applications in coordinate transformations.
  • Explore Jacobian transformations and their role in converting between different coordinate systems.
USEFUL FOR

Astronomers, astrophysicists, and students of celestial mechanics who require a solid understanding of coordinate transformations in astronomy.

Scott S
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OK, I'm really rusty on this.

I need to convert a unit vector to right ascension and declination.
I believe I recall the formulae correctly, as I seem to have gotten 1 as my radius.
So, that's good.

In the pic I have my unit vector (P2), my actual answer below, my expected answer in red and the formulae I (believe) I need in blue shaded cells.

Any help greatly appreciated.
 

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Hey Scott S.

Can you point out a wiki or some other resource that outlines the concept you are talking about for ascension and declination?
 
A quick google search gave me this which discusses a lot of common transformations.

http://www2.astro.psu.edu/users/rbc/a501/positional_astronomy.pdf

If you wanted to derive the results yourself you should derive the metric tensor that goes between two systems and check if the tensor you derive gives the same results.

The metric tensor is related to the Jacobian transformation between the two systems and you can learn it by reading about tensor mathematics or differential geometry.
 
Last edited by a moderator:
Got it, thanks.

Wrong formulae.
 

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