Hour angle transformation: the hour angle of a celestial body at the Greenwich meridian equals the hour angle at any local meridian plus the longitude correction for which references?

Introduction / Context:
Hour angle (HA) is the angular distance of a celestial object west of a reference meridian. Converting between local hour angle (LHA) and Greenwich hour angle (GHA) is central to astronomical observations and navigation.

Given Data / Assumptions:

• LHA is measured at the observer's meridian; GHA is measured at Greenwich.
• Longitude is used algebraically (E positive or W positive per convention).

Concept / Approach:
The universal relation is GHA = LHA + longitude (with sign convention). This applies to bodies referenced to the mean sun (mean solar time), true sun (apparent solar time), the vernal equinox (sidereal time), and fixed stars.

Step-by-Step Solution:
Start with LHA(body) at local meridian.Add longitude (east +, west −, or as defined) to obtain GHA(body).Recognize identical form for mean sun, true sun, vernal equinox, and any star.

Verification / Alternative check:
Navigation formulae: LHA = GHA − longitude; rearranged gives GHA = LHA + longitude for every celestial reference.

Why Other Options Are Wrong:

• No single reference is unique; the relationship holds for all listed references.

Common Pitfalls:

• Incorrect longitude sign (east vs west) leading to hour-angle errors.

Final Answer:
all the above