Time systems in field astronomy — converting Local Mean Time (L.M.T.) to Greenwich Mean Time (G.M.T.) Which relation gives G.M.T. corresponding to a given Local Mean Time for an observer at a specified east or west longitude (expressed in time)?

Introduction / Context:
In astronomical surveying, observations are reduced using a consistent time system. Converting between Local Mean Time (L.M.T.) at a meridian and Greenwich Mean Time (G.M.T.) requires applying the longitude difference expressed as time. This ensures star positions from ephemerides (tabulated for Greenwich) are used correctly at any location.

Given Data / Assumptions:

• Longitudes are converted to time using 15° = 1 hour.
• East longitudes are positive; west longitudes are negative in the standard convention.
• Mean (not apparent) solar time is used for both L.M.T. and G.M.T.

Concept / Approach:

The relationship is derived from the fact that local noon occurs earlier to the east and later to the west relative to Greenwich. Therefore, for an east longitude λ_E (in time), the local clock leads Greenwich, and we subtract λ_E to get Greenwich time. For a west longitude λ_W, we add λ_W to move from local time back to Greenwich.

Step-by-Step Solution:

Verification / Alternative check:

Example: At 45° E (3 h east), when L.M.T. = 12:00, G.M.T. = 09:00, which matches the subtract-east rule.

Why Other Options Are Wrong:

• (b) reverses the sign for east longitude.
• (c) would subtract for west longitudes, which is incorrect; we add for west.
• (e) is meaningless; a fixed offset ignores longitude.

Common Pitfalls:

• Forgetting to normalize the result to 0–24 h after addition/subtraction.
• Mixing signs when using degrees versus hours.

Final Answer:

G.M.T. = L.M.T. − East longitude (in time).