How to calculate observer's latitude from declination and culmination of a star?

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    A star culminates at 50°. It has a declination of +20°. What is the latitude from where it is observed?

    What is the relationship between a culmination, declination, and latitude? How would one work this out?

    This is the answer:
    50 - 30 = 20°
    Latitude = 20°

    There is something wrong, either in the website's answer or the way you typed it. A star at +20 declination would culminate at the zenith (90 degrees) for an observer at +20 latitude. No wonder you are confused!

  • Mike G

    Mike G Correct answer

    4 years ago

    Let $\delta$ be the star's declination and $\phi$ be the observer's terrestrial latitude.
    Neglecting atmospheric refraction, the altitude at culmination is
    $$\mathsf{alt_{max}} = 90^\circ - |\phi - \delta| $$

    Here are some special cases:

    • A star whose declination equals the observer's latitude ($\delta = \phi$) culminates at the zenith (altitude 90$^\circ$).

    • A star on the celestial equator ($\delta$ = 0) culminates at altitude 90$^\circ$ - $|\phi|$.

    For the example in the question, if we solve for $\phi$,
    $$\phi = \delta \pm (90^\circ - \mathsf{alt_{max}}) $$

    Then the observer's latitude is 20$^\circ$ $\pm$ 40$^\circ$, either 20$^\circ$S or 60$^\circ$N.
    GCSE Astronomy's answer is incorrect.

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Content dated before 7/24/2021 11:53 AM

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