Here is the FORTRAN code that predicts the position of the Sun glint given the position of the Moon and the time.

PROGRAM SUNGLINT_MOON
c—————————————————————————
c code that calculates longitude and latitude of the sunglint
c as seen from the Moon
c—————————————————————————
c compile with: gfortran -O3 -fbounds-check sunglintFORTRAN_moon.f -o sung.exe
c or like this: f77 sunglintFORTRAN_moon.f -o sung.exe
c—————————————————————————
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
IMPLICIT logical (A-Z)
DOUBLE PRECISION GMT,SANG,DIFF,GLON,GLAT,GLAT1,AERR,GLON1,SLON1
DOUBLE PRECISION SLAT1,DEC1,DLAT,DLON,OLDGLAT1,DEC,RA,ASAT,ZSAT
DOUBLE PRECISION OLDGLON1,GLON2,U1,U2,U3,U4,V1,V2,V3,HANG1,HANG
DOUBLE PRECISION F0,G0,DUDT1,DUDT2,DUDT3,DUDT4,DUDP1,DUDP2,DUDP3
DOUBLE PRECISION DUDP4,HOURANG,ATND,DVDT1,DVDT2,DVDT3,XX1,XX2
DOUBLE PRECISION DVDP1,DVDP2,DVDP3,T1,T2,T3,T4,TEMP1,TEMP2,TEMP3
DOUBLE PRECISION AK,AH,TEMP4,TEMP5,TEMP6,DFDT,DFDP,DGDT,DGDP,JD
DOUBLE PRECISION ALATD,ALOND,ECLAT,ECLON,PI,SLAT,SLON,ALT,AZI
PARAMETER (PI=.3141592654D1)
CHARACTER DATE*15,TIME*8,INSTR*8
INTEGER HOUR,MIN,SEC
c READ IN DATE,TIME(GMT) AND SUB-LUNAR POINT (SLAT,SLON)
PRINT ‘(/5X,A,$)’,’ENTER DATE (DD-MM-YYYY):’
READ ‘(A)’,DATE
PRINT ‘(/5X,A,$)’,’ENTER TIME(GMT) (HH:MM:SS):’
READ ‘(A)’,TIME
PRINT ‘(/5X,A,$)’,’ENTER SUB-LUNAR POSITION (SLAT,SLON)’
READ *,SLAT,SLON
c CONVERT TIME (HH:MM:SS) TO DECIMAL HOURS
WRITE (INSTR,'(A)’) TIME
READ (INSTR,100) HOUR,MIN,SEC
100 FORMAT (3(I2,1X))
GMT=FLOAT(HOUR)+FLOAT(MIN)/.6D2+FLOAT(SEC)/.36D4
c COMPUTE POSITION OF SPECULAR POINT (GLAT,GLON)
CALL ECCS (DATE,GMT,ECLAT,ECLON,JD)
CALL EQCS (DATE,GMT,ECLAT,ECLON,DEC,RA)
CALL NEWRAPH (DATE,GMT,SLAT,SLON,GLAT,GLON,AERR)
CALL GECS(GLAT,GLON,SLAT,SLON,ASAT,ZSAT)
CALL HOCS(DATE,GMT,GLAT,GLON,DEC,RA,ALT,AZI)
PRINT 200,DATE,TIME
200 FORMAT (//,5X,’DATE: ‘,A12,10X,’TIME:-‘,A10,'(GMT)’/)
PRINT 300
300 FORMAT (5X,’POSITION OF SUN :’/5X,17(‘=’)/)
PRINT 400,ECLON
400 FORMAT (5X,’ECLIPTIC LONGITUDE:’,F7.2)
PRINT 500,DEC,RA
500 FORMAT(5X,’DECLINATION:’F9.2/5X,’RIGHT ASCENTION:’,F9.2)
PRINT 600,ALT,AZI
600 FORMAT(5X,’ELEVATION:’,F9.2/5X,’AZIMUTH:’,F9.2/)
PRINT 700
700 FORMAT(5X,’POSITION OF THE MOON:’/5X,27(‘=’)/)
PRINT 800,SLAT,SLON
800 FORMAT(5X,’SUB-LUNAR POINT:(SLAT=’,F6.2,’,SLON=’,F7.2,’)’/)
PRINT 900, ASAT,ZSAT
900 FORMAT(5X,’ELEVATION:’,F9.2/5X,’AZIMUTH:’,F9.2/)
PRINT 905
905 FORMAT(5X,’POSITION OF THE SPECULAR POINT :’/5X,32(‘=’)/)
IF (AERR .EQ. .0D0) THEN
PRINT 910,GLAT,GLON
910 FORMAT (5X,’LATITUDE:’,F9.2/5X,’LONGITUDE:’,F7.2)
ELSE
PRINT 915
915 FORMAT(5X,’GLINT DOES NOT LIE WITH IN THE VIEW AREA’)
END IF
END

DOUBLE PRECISION FUNCTION HOURANG(DATE,GMT,GLON,RA)
IMPLICIT LOGICAL (A-Z)
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
CHARACTER*15 DATE
DOUBLE PRECISION GMT,GLON,RA,GLON1,HANG
DOUBLE PRECISION LST,GST
GLON1=GLON
IF (GLON1 .GT. .18d3) GLON1=GLON1-.36D3
lst=glon1/.15d2+gst(date,gmt)
IF (LST .GT. .24D2) LST=LST-.24D2
IF (LST .LT. .0D0) LST=LST+.24D2
HANG=(LST-RA/.15D2)
IF (HANG .LT. .0D0) HANG=HANG+.24D2
HOURANG=HANG
RETURN
END

SUBROUTINE NEWRAPH(DATE,GMT,SLAT,SLON,GLAT,GLON,AERR)
IMPLICIT logical (A-Z)
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INTEGER KK
DOUBLE PRECISION HSAT,ERAD,PI,RAD,RADI,CDIFF,DEC,RA,SLAT,GLAT
DOUBLE PRECISION GMT,SANG,DIFF,SLON,GLON,GLAT1,AERR,GLON1,SLON1
DOUBLE PRECISION SLAT1,DEC1,DLAT,DLON,OLDGLAT1,jd
DOUBLE PRECISION OLDGLON1,GLON2,U1,U2,U3,U4,V1,V2,V3,HANG1,HANG
DOUBLE PRECISION F0,G0,DUDT1,DUDT2,DUDT3,DUDT4,DUDP1,DUDP2,DUDP3
DOUBLE PRECISION DUDP4,HOURANG,ATND,DVDT1,DVDT2,DVDT3,XX1,XX2
DOUBLE PRECISION DVDP1,DVDP2,DVDP3,T1,T2,T3,T4,TEMP1,TEMP2,TEMP3
DOUBLE PRECISION AK,AH,TEMP4,TEMP5,TEMP6,DFDT,DFDP,DGDT,DGDP
DOUBLE PRECISION ALATD,ALOND,ECLAT,ECLON
CHARACTER*15 DATE
PARAMETER (HSAT=.384d9,ERAD=.6378D7)
c PARAMETER (HSAT=.35786D8,ERAD=.6378D7)
PARAMETER (PI=.3141592654D1)
RAD=PI/.18D3
RADI=.18D3/PI
CDIFF=.1D1/.36D4*RAD
CALL ECCS(DATE,GMT,ECLAT,ECLON,jd)
CALL EQCS(DATE,GMT,ECLAT,ECLON,DEC,RA)
GLAT=(DEC+SLAT)/.2D1
SANG=(.12D2-GMT)*.15D2
IF (SANG.LT. .0D0) SANG=SANG+.36D3
DIFF=dabs(SANG-SLON)
IF (DIFF .GT. .18D3) THEN
DIFF=.36D3-DIFF
GLON=DMAX1(SANG,SLON)+DIFF/.2D1
ELSE
GLON=DMIN1(SANG,SLON)+DIFF/.2D1
END IF
IF (GLON .GT. .36D3) GLON=GLON-.36D3
IF (DIFF .GT. .12D3) THEN
AERR=-.1D1
RETURN
END IF
GLAT1=GLAT*RAD
GLON1=GLON*RAD
SLAT1=SLAT*RAD
SLON1=SLON*RAD
DEC1=DEC*RAD
KK=0
150 KK=KK+1
DLAT=GLAT1-SLAT1
DLON=GLON1-SLON1
OLDGLAT1=GLAT1
OLDGLON1=GLON1
GLON2=GLON1*RADI
HANG=HOURANG ( DATE , GMT , GLON2 , RA)
HANG1=HANG* .15D2*RAD
U1= ( HSAT+ERAD) *DCOS ( DLAT) *DCOS( DLON) -ERAD
U2=DSIN(GLAT1)*DSIN(DEC1)+DCOS(DEC1)*DCOS(GLAT1)*DCOS(HANG1)
U3=DSIN( DLON)
U4=-DCOS(DEC1)*DCOS(GLAT1)*DSIN(HANG1)
V1=HSAT**.2D1+.2D1*ERAD* (ERAD+HSAT)*(.1D1-DCOS(DLAT)*DCOS(DLON))
V2=DCOS ( DLON ) *DSIN (DLAT)
V3=DSIN(DEC1)-DSIN(GLAT1)*U2
F0=DASIN(U1/SQRT(V1) )-DASIN(U2)
G0=ATND(U3 ,V2 ) -ATND(U4 ,V3)
DUDT1=- ( ERAD+HSAT) *DSIN ( DLAT ) *DCOS( DLON)
DUDT2=DCOS(GLAT1)*DSIN(DEC1)-DSIN(GLAT1)*DCOS(DEC1)*DCOS(HANG1)
DUDT3= .0D0
DUDT4=DCOS ( DEC1 ) *DSIN(GLAT1 ) *DSIN(HANG1)
DUDP1=- ( ERAD+HSAT) *DCOS ( DLAT ) *DSIN ( DLON)
DUDP2= .0D0
DUDP3=DCOS( DLON)
DUDP4= .0d0
DVDT1= .2D1*ERAD* (HSAT+ERAD) *DSIN ( DLAT) *DCOS (DLON)
DVDT2=DCOS( DLAT) *DCOS ( DLON)
XX1=-.2D1*DSIN(GLAT1 )*DCOS(GLAT1)*DSIN(DEC1 )
XX2=DCOS(GLAT1) *DSIn(GLAT1)*DCOS(DEC1)*DCOS(HANG1)
DVDT3=XX1+XX2
DVDP1=.2D1*ERAD* (HSAT+ERAD) *DCOS( DLAT) *DSIN (DLON )
DVDP2=-DSIN( DLAT) *DSIN ( DLON)
DVDP3=.0D0
T1=.1D1/(SQRT(.1D1-(U1/SQRT(V1))**.2D1))
T2=.1D1/(SQRT(.1D1-U2**.2D1))
T3=.1D1/(.1D1+(U3/V2)**.2D1)
T4=.1D1/(.1D1+(U4/V3)**.2D1)
TEMP1=(SQRT(V1)*DUDT1-U1*DVDT1/(SQRT(V1)*.2D1))/V1
TEMP2=(SQRT(V1)*DUDP1-U1*DVDP1/(SQRT(V1)*.2D1))/V1
TEMP3=(V2*DUDT3-U3*DVDT2)/V2**.2D1
TEMP4=(V2*DUDP3-U3*DVDP2)/V2**.2D1
TEMP5=(V3*DUDT4-U4*DVDT3)/V3**.2D1
TEMP6=(V3*DUDP4-U4*DVDP3)/V3**.2D1
DFDT=T1*TEMP1-T2*DUDT2
DFDP=T1*TEMP2-T2*DUDP2
DGDT=T3*TEMP3+T4*TEMP5*DVDT3
DGDP=T3*TEMP4+T4*TEMP6*DVDP3
AK=(F0*DGDT-G0*DFDT)/(DGDP*DFDT-DFDP*DGDT)
AH=-(AK*DFDP+F0)/DFDT
GLAT1=GLAT1+AH
GLON1=GLON1+AK
IF (GLON1.LT. .0D0) GLON1=GLON1+.2D1*PI
IF (GLON1.GT. .2D1*PI) GLON1=GLON1-.2D1*PI
IF (GLAT1.LT. -PI/.2D1) GLAT1=-PI-GLAT1
IF (GLAT1.GT. PI/.2D1) GLAT1=PI-GLAT1
ALATD=dabs(GLAT1-OLDGLAT1)
ALOND=dabs(GLON1-OLDGLON1)
IF (ALOND .GT.PI) ALOND=.2D1*PI-ALOND
IF (KK .GT.150) THEN
AERR=-.2D0
RETURN
END IF
IF (ALOND .GT.CDIFF .AND.ALATD .GT.CDIFF) GOTO 150
GLAT=GLAT1*RADI
GLON=GLON1*RADI
AERR=.0D0
RETURN
END

SUBROUTINE ECCS (DATE , GMT , ECLAT , ECLON, JD)
IMPLICIT LOGICAL (A-Z)
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DOUBLE PRECISION GMT , ECLAT , ECLON, JD,ELE,ELP,ECC,PI
DOUBLE PRECISION EC,JDEP,RAD,AJDATE,DAYS,AN,M,AM
CHARACTER*15 DATE
PARAMETER (ELE=.279403303D3 ,ELP=.282768422D3)
PARAMETER (ECC=.167131D-1 ,PI=.3141592654D1)
RAD=PI/.18D3
JDEP=.24478915D7
JD=AJDATE(DATE,GMT)
DAYS=JD-JDEP
AN=(.36D3/.365242191D3)*DAYS
M=DINT(AN/.36D3)
AN=AN-(M*.36D3)
AM=AN+ELE-ELP
IF (AM .LT. .0D0) AM=AM+.36D3
EC=( .36D3 /PI ) *ECC*DSIN(Am*RAD)
ECLON=AN+EC+ELE
IF (ECLON .GT. .36d3) ECLON=ECLON-.36D3
IF (ECLON .LT. .0D0) ECLON=ECLON+.36D3
ECLAT=.0D0
RETURN
END

SUBROUTINE EQCS ( DATE, GMT , ECLAT , ECLON , DEC,RA)
IMPLICIT LOGICAL (A-Z)
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
CHARACTER*15 DATE
DOUBLE PRECISION JD,JDEP,PI,GMT , ECLAT , ECLON , DEC,RA
DOUBLE PRECISION RAD,RADI,T,EP,ECLON1,ECLAT1,TEMP1,TEMP2
DOUBLE PRECISION AJDATE,DEP,ANR,DNR,ATND
PARAMETER (PI=.3141592654D1)
RAD=PI/.18D3
RADI=.18D3/PI
JDEP=.2451545D7
JD=AJDATE(DATE,GMT)
T=(JD-JDEP)/.36525D5
DEP=.46815D2*T+.6D-3*T**.2D1-.181D-2*T**.3D1
EP=.23439292D2-DEP/.36D4
ECLON1=ECLON*RAD
ECLAT1=ECLAT*RAD
EP=EP*RAD
TEMP1=DSIN(ECLAT1)*DCOS(EP)
TEMP2=DCOS(ECLAT1)*DSIN(EP)*DSIN(ECLON1)
DEC=DASIN(TEMP1+TEMP2)*RADI
ANR=DSIN(ECLON1)*DCOS(EP)-DTAN(ECLAT1)*DSIN(EP)
DNR=DCOS(ECLON1)
RA=ATND(ANR,DNR)*RADI
RETURN
END

SUBROUTINE HOCS(DATE,GMT,GLAT,GLON,DEC,RA,ALT,AZI)
IMPLICIT LOGICAL (A-Z)
c IMPLICIT DOUBLE PRECISION (A-Z)
DOUBLE PRECISION GMT,GLAT,GLON,DEC,RA,ALT,AZI,U1,U2,V2
DOUBLE PRECISION PI,RAD,RADI,HANG,HANG1,GLAT1,DEC1
DOUBLE PRECISION HOURANG,ATND
PARAMETER (PI=.3141592654D1)
CHARACTER*15 DATE
RAD=PI/.18D3
RADI=.18D3/PI
HANG=HOURANG(DATE,GMT,GLON,RA)
HANG1=HANG*.15D2*RAD
DEC1=DEC*RAD
GLAT1=GLAT*RAD
U1=DSIN(DEC1)*DSIN(GLAT1)+DCOS(DEC1)*DCOS(GLAT1)*DCOS(HANG1)
ALT=DASIN(U1)*RADI
U2=-DCOS(DEC1)*DSIN(HANG1)*DCOS(GLAT1)
V2=DSIN(DEC1)-DSIN(GLAT1)*DSIN(ALT*RAD)
AZI=ATND(U2,V2)*RADI
RETURN
END

DOUBLE PRECISION FUNCTION GST(DATE,GMT)
IMPLICIT LOGICAL (A-Z)
c IMPLICIT DOUBLE PRECISION (A-Z)
CHARACTER*15 DATE
DOUBLE PRECISION JD,JDEP,T,T0,TT,GST1,GMT,AJDATE
JDEP=.2451545D7
JD=AJDATE(DATE,.0D0)
T=(JD-JDEP)/.36525D5
T0=.6697374558D1+.2400051336D4*T+.25862D-4*T**.2D1
TT=DINT(abs(T0)/.24D2)+.1D1
T0=T0+TT*.24D2
GST1=GMT*.1002737909D1+T0
TT=DINT(GST1/.24D2)
GST1=GST1-TT*.24D2
GST=GST1
RETURN
END

DOUBLE PRECISION FUNCTION ATND(Y,X)
IMPLICIT LOGICAL (A-Z)
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DOUBLE PRECISION x,y,pi,dir
PARAMETER (PI=.3141592654D1)
IF (X .EQ. .0D0 .OR.Y .EQ. .0D0) THEN
IF (X .EQ. .0D0 .AND.Y .EQ. .0D0) DIR=.0D0
IF (X .EQ. .0D0 .AND.Y .GT. .0D0) DIR=PI/.2d1
IF (X .EQ. .0D0 .AND.Y .LT. .0D0) DIR=.15D1*PI
IF (Y .EQ. .0D0 .AND.X .GT. .0D0) DIR=.0D0
IF (Y .EQ. .0D0 .AND.X .LT. .0D0) DIR=PI
ELSE
DIR=ATAN(Y/X)
IF (Y .GT. .0D0 .AND.X .LT. .0D0 ) DIR=DIR+PI
IF (Y .LT. .0D0 .AND.X .LT. .0D0 ) DIR=DIR-PI
IF (DIR .LT. .0D0) DIR=DIR+.2D1*PI
END IF
ATND=DIR
RETURN
END

SUBROUTINE GECS(GLAT,GLON,SLAT,SLON,ASAT,ZSAT)
IMPLICIT LOGICAL (A-Z)
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DOUBLE PRECISION HSAT,ERAD,PI,GLAT,GLON,SLAT,SLON,ASAT,ZSAT
DOUBLE PRECISION RAD,RADI,GLAT1,GLON1,SLAT1,SLON1,DLAT,DLON
DOUBLE PRECISION U1,V1,U2,V2,ATND
PARAMETER (HSAT=.384d9,ERAD=.6378D7)
c PARAMETER (HSAT=.35786D8,ERAD=.6378D7)
PARAMETER (PI=.3141592654D1)
RAD=PI/.18D3
RADI=.18D3/PI
GLAT1=GLAT*RAD
GLON1=GLON*RAD
SLAT1=SLAT*RAD
SLON1=SLON*RAD
DLAT=(GLAT1-SLAT1)
DLON=(GLON1-SLON1)
U1=(HSAT+ERAD)*DCOS(DLAT)*DCOS(DLON)-ERAD
V1=HSAT**.2D1+.2D1*ERAD*(ERAD+HSAT)*(.1D1-DCOS(DLAT)*DCOS(DLON))
U2=DSIN(DLON)
V2=DCOS(DLON)*DSIN(DLAT)
ASAT=DASIN(U1/SQRT(V1))*RADI
ZSAT=(ATND(U2,V2)+PI)*RADI
IF (ZSAT .GT. .36D3) ZSAT=ZSAT-.36D3
RETURN
END

DOUBLE PRECISION FUNCTION AJDATE(DATE,GMT)
IMPLICIT LOGICAL (A-Z)
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DOUBLE PRECISION A,B,C,D,MONTH,JDBC,GMT,DAY,YEAR
PARAMETER (JDBC=.17209945D7)
CHARACTER*15 DATE,INSTR
WRITE(INSTR,100) DATE
100 FORMAT (A15)
READ (INSTR,200) DAY,MONTH,YEAR
200 FORMAT (2(F2.0,1X),F4.0)
DAY=DAY+GMT/.24D2
IF (MONTH .LT. .3D1) THEN
YEAR=YEAR-.1D1
MONTH=MONTH+.12D2
END IF
A=DINT(YEAR/.1D3)
B=.2D1-A+DINT(A/.4D1)
C=DINT(.36525D3*YEAR)
D=DINT(.306001D2*(MONTH+.1D1))
ajdate=b+c+d+day+jdbc
return
end