Answer & Solution
Answer: Option
C
Solution:
Correct Answer: Option C: Equator and Zenith
Explanation:
Latitude (φ): Latitude measures how far north or south a location is from the Earth's equator, expressed in degrees (0° at the equator, 90° at the poles).
Declination (δ): Declination is similar to latitude but for celestial objects, measuring how far a star is from the celestial equator. A star on the celestial equator has \( \delta = 0^\circ \), while a star at the celestial north pole has \( \delta = +90^\circ \).
Zenith Distance (z): Zenith distance is the angle between a star and the observer's zenith (the point directly overhead). A star at the zenith has \( z = 0^\circ \), while a star on the horizon has \( z = 90^\circ \).
Formula:
The given formula is:
\[
\phi = z - \delta
\]
This formula applies when the observed star is positioned between the observer's zenith and the equator.
Reason:
- Zenith distance is measured from the zenith downward.
- Declination is measured from the celestial equator.
- The subtraction only works when the star is south of the zenith, which means the star lies between the equator and the zenith.
Conclusion:
The correct answer is Option C: Equator and Zenith because the given formula holds only in this case.
