Question

The zenith distances of a star at upper culmination (south of the zenith) and lower culmination are 24◦ and 74◦ respectively. Calculate the latitude of the observer and the declination of the star.

Answer 1

Answer on Question #54950, Physics / Astronomy | Astrophysics

Let the latitude and declination be $\varphi$ and $\delta$ degrees respectively. Then:

$$PF = PZ + ZF$$

that is:

$$90 - \delta = 90 - \varphi + ZF$$

or:

$$\varphi - \delta = 24{}^\circ$$

Also,

$$PG = ZG - PZ$$

giving:

$$90 - \delta = ZG - 90 + \varphi$$

or:

$$\varphi + \delta = 180 - 74{}^\circ = 106{}^\circ$$

Adding equations we obtain:

$$2\varphi = 130{}^\circ \text{ or } \varphi = 65{}^\circ N.$$

Substituting $65{}^\circ$ for $\varphi$ in equation gives $\delta = 41{}^\circ N$.

Answer: $\delta = 41{}^\circ \mathrm{N}$

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