Question

Two stars of declinations 56◦ 30` 10`` and 56◦ 30` 50`` are used for observation with a
zenith tube. After observation of the first star, the instrument is rotated through 180◦ and in order to
observe the transit of the second star, the micrometer needs to be turned by 0·4 of a thread in a direction moving the wire away from the zenith. If the plate scale of the telescope is 30 seconds of arc per mm and the pitch of the thread 1 turn per mm, what is the latitude of the observing station?

Answer 1

Answer on Question #54964 - Physics / Astronomy | Astrophysics

Question:

Two stars of declinations $56{}^{\circ}30'10''$ and $56{}^{\circ}30'50''$ are used for observation with a zenith tube. After observation of the first star, the instrument is rotated through $180{}^{\circ}$ and in order to observe the transit of the second star, the micrometer needs to be turned by $0.4$ of a thread in a direction moving the wire away from the zenith. If the plate scale of the telescope is 30 seconds of arc per mm and the pitch of the thread 1 turn per mm, what is the latitude of the observing station?

Solution:

The movement of the micrometer:

$$l = 0.4 \text{ threads} \equiv 0.4 \text{ mm}$$ $$\Delta z = 0.4 \text{ mm} \times 30 \text{ arc sec} = 12 \text{ arc sec}$$

Using the equation:

$$\frac{z_1 - z_2}{2} = \frac{12 \text{ arc sec}}{2} = 6 \text{ arc sec}$$

Therefore:

$$\varphi = 56{}^{\circ}30'30'' - 6'' = 56{}^{\circ}30'24''$$

Answer: $\varphi = 56{}^{\circ}30'24''$

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