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

• Ben D

4 years ago

From gcseastronomy.co.uk:
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 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.