Sight Data
Date
/
/
Lat-s
°
'
Lon-s
°
'
Ts (UTC)
h
m
s
Hm (Moon alt)
°
'
Hb (Body alt)
°
'
D (SD-corrected)
°
'
Almanac Data
Moon
Gm− (GHA at T−)
°
'
Dm− (Dec at T−)
°
'
Gm+ (GHA at T+)
°
'
Dm+ (Dec at T+)
°
'
HP Moon
arcmin
Body (Sun / Star / Planet)
Gb− (GHA at T−)
°
'
Db− (Dec at T−)
°
'
Gb+ (GHA at T+)
°
'
Db+ (Dec at T+)
°
'
Clear the Lunar
y
P
x
R
Dc
Find UTC & Longitude
D−
D+
Tc
dUTC
dLon
Equations (J. S. Letcher Jr.)
| y | [cos(D)·sin(Hm) − sin(Hb)] / sin(D) | dimensionless |
| P | HP · { y + 0.000145·HP·cot(D)·[cos²(Hm) − y²] } | arcmin (HP in arcmin from almanac) |
| x | 0.5 · [sin(Hm)/sin(Hb) + sin(Hb)/sin(Hm)] | dimensionless |
| R | 1.90 · (x − cos D) / sin D | arcmin |
| Dc | D + (P + R) / 60 | degrees (P and R converted from arcmin) |
| D± | arccos[sin(Dm±)·sin(Db±) + cos(Dm±)·cos(Db±)·cos(Gm± − Gb±)] | geocentric LD at T− and T+ |
| Tc | T− + (Dc − D−) / (D+ − D−) | T− = INT(Ts) ; result in decimal hours |
| dUTC | Ts − Tc [× 3600 → seconds] | + = Ts fast ; − = Ts slow |
| dLon | dUTC [sec] × 0.25′ | arcmin of longitude ; 0.25′ per 1 sec of UTC error |
Notes
- Ts is the best estimate of a common UTC for the lunar distance and altitude measurements.
- D is the lunar distance corrected for semidiameters.
- Hm and Hb can be observed (Ho) or computed (Hc) altitudes.
- T− and T+ are the whole UTC hours bracketing Ts: T− = INT(Ts), T+ = INT(Ts) + 1.
- P and R are in arcmin; Dc = D + (P + R)/60 adds them to D in degrees.
- dUTC > 0 (Ts fast): true UTC is earlier than Ts. dUTC < 0: Ts is slow.
- dLon = dUTC [sec] × 0.25′ ; equivalently 15′ per 1 minute of UTC error.
- For discussion and references see Lunar Distance by Calculator: The Letcher Method.