Astronomical corrections – identify the single incorrect statement In standard altitude reductions for celestial observations, which of the following statements is incorrect when using the nautical “corrections” convention?

Introduction / Context:
Nautical and geodetic astronomy apply a sequence of “corrections” to an observed sextant altitude to obtain a true (apparent or geocentric) altitude. The algebraic signs in the nautical almanac convention can be counterintuitive unless one remembers what each term represents physically and how it is applied.

Given Data / Assumptions:

• Nautical (sextant) altitude reduction convention is assumed.
• Refraction makes celestial bodies appear higher than their true position.
• Parallax in altitude for solar/lunar observations is considered with respect to the Earth’s centre.
• Semi-diameter correction depends on whether the observed limb is upper or lower.
• Dip corrects for eye height above sea level.

Concept / Approach:

Under the nautical convention: refraction correction is negative (subtract) because apparent altitude is too high. Parallax correction is positive (add) because the geocentric altitude is greater than the topocentric apparent when reducing to the Earth’s centre (for bodies like the Moon). Dip is negative (subtract) because eye height causes the observed sea horizon to fall below the celestial horizon. Semi-diameter, however, is not of fixed sign: you add the Sun’s or Moon’s semi-diameter for lower-limb observations and subtract for upper-limb observations. Therefore, any statement that the semi-diameter correction is “always negative” is incorrect.

Step-by-Step Solution:

Verification / Alternative check:

Nautical almanacs list separate semi-diameter entries with notes to add for lower limb and subtract for upper limb, confirming the variable sign.

Why Other Options Are Wrong:

(a), (b), and (d) match the standard sign convention; “None of these” is invalid because (c) is demonstrably incorrect.

Common Pitfalls:

Mixing geodetic (zenith distance-based) signs with nautical (altitude-based) signs; forgetting to change the semi-diameter sign when switching limb observations.

Final Answer:

Correction for semi-diameter is always negative