Public Function phyAitkenDoubleStarCriteria(ByVal Mag1_tmp As Double, ByVal Mag2_tmp As Double) As Double
'  Receives magnitudes of two close stars and returns the maximum separation at which they might be
'  considered a double star

' Source: Sinachopoulos, D.; Mouzourakis, P. 1991. Statistically physical pairs in Aitken's Double Star Catalogue. 1991AGAb....6...84S
'   Romero, F.R. 2006. Aitken's Double Star Criteria. Journal of Double Stars Observations. 2(1):36-41
'   www.jdso.org

' Uses phyIntegratedMag2Stars

' Test and usage
' Romero 2006 computation for GRB 34 AB at mag 8.07, 11.04 is Rho(max)=15.8"
' ? phyAitkenDoubleStarCriteria(8.07,11.04)
' 15.8359886943105

' Define variables
Dim Mag1, Mag2 As Double
Dim A, B, C, D, E As Double ' Working variables
                                  
' Get input
Mag1 = Mag1_tmp
Mag2 = Mag2_tmp

' Find the integrated magnitude
B = phyIntegratedMag2Stars(Mag1, Mag2)

' Find Aitken's criteria
C = 2.8 - (0.2 * B)
D = 10 ^ C

' Return result
phyAitkenDoubleStarCriteria = D

End Function


Public Function phyIntegratedMag2Stars(ByVal Mag1_tmp As Double, ByVal Mag2_tmp As Double) As Double
'  Receives magnitudes of two close stars and returns their combined magnitude

' Source: Sidqwick at 34

' Test and usage
'  Sidgwick: What is the integrated magnitude of a close double whose
'  individual magnitudes at 2.7 and 3.0? Ans: ~ 2.1
' ? phyIntegratedMag2Stars(2.7,3.0)
' 2.08710252520251

' Define variables
Dim Mag1, Mag2 As Double
Dim A, B, C, D, E As Double ' Working variables
                                  
' Get input
Mag1 = Mag1_tmp
Mag2 = Mag2_tmp

' Find the integrated magnitude
A = 2.512 ^ (Mag2 - Mag1)
A = 1# + (1# / A)
A = Log10(A)
A = A / 0.4

' Return result
phyIntegratedMag2Stars = Mag1 - A

End Function