Starguide - A Practical Guide to Astro-Photography

A collection of useful astronomical formulas. 

Coordinate Conversions (see also Coordinate Converter - Deep Space Place):

DECdms  to Degreedecimal

where 

DECh = hour part of DECdms

DECm = minute part of DECdms 

DECs = seconds part of DECdms

This formula will convert a DEC coordinate string like 42° 01' 45.726" to 42,0293683°

R.A.hms to Degreedecimal

where 

RAh = hour part of R.A.hms

RAm = minute part of R.A.hms 

RAs = seconds part of R.A.hms

This formula will convert a R.A. coordinate string like 13h 15' 49.27385" to 198,955307708333°

Greenwich Mean Sidereal Timedeg or GMSTdeg from JulianDate (JDate)

       : The number of Julian centuries (each = 36525 days) that have passed since the epoch J2000.0

where:

JDate = the Julian Date for which you want to compute GMST

JD2000 = 2451545                : Julian Date of J2000.0 (January 1, 2000, 12:00 TT)

Dcentury = 36525                : number of days in one Julian century

where:

d1  = 67310.54841         : GMST at 0h UT on 1 January 2000 (J2000.0), expressed in seconds

At 2000‑01‑01 00:00:00 UT, the sidereal time in Greenwich was:

  18h41m50.54841s

  Converted to seconds:

  18⋅3600+41⋅60+50.54841=>67310.54841

d2  = 8640184.812866         : Linear rate of increase of GMST per Julian century, in seconds

It accounts for:

 No of seconds per sidera day:  ~86164.0905 seconds

 Over 36525 days (one Julian century), GMST accumulates

 Plus precession of Earth’s rotation axis

 Plus small corrections from Earth rotation irregularities

d3  = 0.093104                : Quadratic correction term accounting for long‑term changes in Earth’s rotation.

It accounts for:

  Tidal braking of Earth’s rotation

  Redistribution of mass inside Earth

  Long‑term secular variations

d4  = 0.0000062        : Cubic correction term for very long‑term rotational drift.
                         It models extremely slow, long‑term changes in Earth’s rotation rate. 
                         Its effect is tiny for modern dates but necessary for accuracy over ± several centuries

h100 = 876600                        : 100 years * 265,25 days * 24 hours

sph =  60*60 = 3600                : seconds per hour

sper° = 60*60* 24/360°        = 240        : Sideral Seconds Per Degree

 The result must be normalized to keep it within the 360° boundary.

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