Planetary Fluxes
Incoming visible and IR fluxes contributed by nearby bodies can be specified, for example Mars shine on Phobos, or Jupiter shine on Europa. Set:
PFlux = "T" Lon_Hr = [0-24]
in KRC, fluxes take the form of sin functions characterized by various nonintuitive parameters (see helplist).
The DaVinci interface generates these parameters and feed them to KRC from default parameters or user-defined values. In both cases, various assumptions and fits are performed.
While the incoming visible flux is generally straightforward to calculate, the incoming IR flux can be more complex to determine for bodies with strong diurnal temperature variations (like Mars, unlike Jupiter for example).
Fixed Diurnal Temperatures (Jupiter, Saturn, Uranus, Neptune, etc.)
This case applies to satellites revolving around gas giants, or low diurnal contrast bodies (Venus, if it had satellites) etc. The IR flux is only a function of the solid angle of the emitting body. The visible flux follows a sin function over the course of a day. Fewest assumptions used.
The simplest approach consist in using default builtin values from the KRC support files:
OUT = krc(lat = 0., INERTIA = 70., body = "Jupiter,Europa", bodytype = "minor", ALBEDO = 0.55, PFlux = "T", Lon_Hr = 12., LKofT = "F")
But any input value can be forced:
- BT_Avg : Average Brightness Temperature [K]
- BT_Min : Min Brightness Temperature, if diurnal cycle [K]
- BT_Max : Max Brightness Temperature [K]
- Dis_AU : Distance from Sun in AU
- Geom_alb : Geometric Albedo [1]
- Mut_Period : Mutual Period [?]
- Orb_Radius : Orbiting Radius [km]
- Radius : Radius of the Orbiting body [km]
- Lon_Hr : Longitude Hour of the surface point (see above)
OUT = krc(lat = 0., INERTIA = 70., body = "Jupiter,Europa", bodytype = "minor", ALBEDO = 0.55, PFlux = "T", BT_Avg = 127., BT_Min = 127., BT_Max = 127., Dis_AU = 5.203, Geom_alb = 0.52, Mut_Period = 3.55, Orb_Radius = 670900, Radius = 670900, Lon_Hr = 12., LKofT = "F")
Noticeable Diurnal Temperatures Cycle (Mars, Pluto, etc.)
This case applies to satellites revolving around planets experienced pronounced diurnal cycles like Phobos around Mars. The IR flux is not only a function of the solid angle of the emitting body, but also a function of the local time of the emitting body.
- The IR and visible fluxes are modeled by fitting a sin wave through the max and min radiance values, and KRC accepts parameters describing these two sin functions (IR, and VIS).
EXAMPLE HERE. NOT SURE HOW TO DO THIS HERE.
- The IR and visible fluxes are derived elsewhere, and fit with a sin function.
Buffer = ascii("~/Google Drive/THEMIS_PHOBOS/09_29_2017/67.1_AvgFluxes.txt",format=float)
Vis = cat(Buffer[3,,1]+00,(Buffer[1,,1]+00.)%24.,axis=x) #Potential Bug with the IR flux? => Check this
IR = cat(Buffer[2,,1]+65,(Buffer[1,,1]+00.)%24,axis=x)
Lon_Hr = 12.
test = krc_planetary_flux_table(IR,Vis,Lon_Hr)
test_T = krc(INERTIA=35.,lat=10.,lon=0.,body="Mars,Phobos",bodytype="minor",ls=Ls,PFlux="T",Lon_Hr=Lon_Hr,IR=IR,Vis=Vis,ALBEDO=Alb,EMISS=EMIS)
Time = (test_T.time + 12.) % 24.
plot(test_T.tsurf[,1,1],xaxis=Time)
EXAMPLE HERE. NOT SURE HOW TO DO THIS HERE.
printf("\nKRC supports Eclipses but requires the following parameters\n")
printf("PFlux = forces a planetary flux on a orbiting body (Default = \"F\") \n")
printf(" Needs the following Parameters (Default Provided for common bodies)\n") printf(" BT_Avg : Average Brightness Temperature [K] \n") printf(" BT_Min : Min Brightness Temperature, if diurnal cycle [K] \n") printf(" BT_Max : Max Brightness Temperature [K] \n") printf(" Dis_AU : Distance form Sun in AU \n") printf(" Geom_alb : Geometric Albedo [1]\n") printf(" Mut_Period : Mutual Period [?]\n") printf(" Orb_Radius : Orbiting Radius [km] \n") printf(" Radius : Radius of the Obiting body [km] \n") printf(" Lon_Hr : Longitude Hour of the surface point \n")
printf(" OR: \n")
printf(" IR : A 2 x n x 1 array with IR flux (1st col.) vs. LTST (2nd col.) \n") printf(" Vis : A 2 x n x 1 array with Vis flux (1st col.) vs. LTST (2nd col.) \n")
define krc_planetary_flux_porb(porb,porb_Planet,Lon_Hr){
if($ARGC == 0){
printf (" Generates the change card for planetary heat loads in KRC \n")
printf (" $1: porb for the satellite \n")
printf (" $2: porb for the main body (planet) \n")
printf (" $3: Lon_Hr, Longitude Hour of the surface point \n")
}
pi = 3.14159
#porb=load("/Applications/davinci.app/Contents/Resources/library/script_files/krc_support/porb_defaults/Mars_Phobos.porb.hdf")
#porb_Planet=load("/Applications/davinci.app/Contents/Resources/library/script_files/krc_support/porb_defaults/Mars_Mars.porb.hdf")
porb = $1 porb_Planet = $2 Data_Plan = porb_Planet.planet_flux #Gets satellites data Data_Sat = porb.planet_flux #Gets planet data Lon_Hr = $3 #Longitude Hour
Radiance = 5.56E-8 * float(Data_Plan.BT_Avg)^4 #Calculates Average Radiance from Planet Min_Rad = 5.56E-8 * float(Data_Plan.BT_Min)^4 #Calculates the Min Radiance from Planet Max_Rad = 5.56E-8 * float(Data_Plan.BT_Max)^4 #Calculates the Max Radiance from Planet Delta_Radiance = 5.56E-8 * (float(Data_Plan.BT_Max)^4 - float(Data_Plan.BT_Min^4)) #Calculates Max - Min Radiance form Planet Plan_Ang_Surf = pi*((360./pi)*atan(Data_Plan.Radius/(2*Data_Sat.Orb_Radius)))^2/3282.80635#Angular Surface of Planet IR_Flux = Radiance * Plan_Ang_Surf/pi #IR Flux from Planet on Satellite IR_Half_Amp = (Radiance - Min_Rad ) * Plan_Ang_Surf * 0.5 / pi #1/2 Amplitude IR_Phase_Lag = 0. #Will need to Look at that for Eclipses Vis_Flux_Peak = Data_Plan.Geom_alb * 1361./(Data_Plan.Dis_AU^2) * Plan_Ang_Surf #Peak Visible Flux from Planet Vis_Flux = 0.5 * Vis_Flux_Peak #Average Visible Flux from the planet Vis_Half_Amp = Vis_Flux #Most often 0. Vis_Phase_Lag = 0. #Will need to Look at that for Eclipses
line = sprintf("15 %.2f %.2f %.2f %.2f %.2f %.2f %.2f / Forcing from Planet on Satellite",IR_Flux,IR_Half_Amp,IR_Phase_Lag,Vis_Flux,Vis_Half_Amp,Vis_Phase_Lag,Lon_Hr) return(line) }
define krc_planetary_flux_table(IR,Vis,Lon_Hr){
- 05/17/2018: Fixes issue with average fluxes definition (HHK email of 05/07/2018)
if($ARGC == 0){
printf (" Generates the change card for planetary heat loads in KRC \n")
printf (" $1: IR array vs LTST (2xnx1)\n")
printf (" $2: Vis array vs LTST (2xnx1)\n")
printf (" $3: Lon_Hr, Longitude Hour of the surface point \n")
}
pi = 3.14159 IR_1 = $1 IR = IR_1[1,,1] #IR array, y axis LTST_IR = IR_1[2,,1] #LTST for the IR array, y axis Vis_1 = $2 Vis = Vis_1[1,,1] #Vis array, y axis LTST_Vis = Vis_1[2,,1] #LTST for the Vis array, y axis Lon_Hr = $3 #Longitude Hour
Peak_IR = maxpos(IR,showval=1) Min_IR = minpos(IR,showval=1) LTST_IR_Peak = LTST_IR[1,int(Peak_IR[2,1,1]),1] #int(Peak_IR[2,1,1]) is the index Half_Amp_IR = 0.5*(Peak_IR[4]-Min_IR[4]) Phase_IR = 360.*LTST_IR_Peak/24. #in degree IR_KRC = Min_IR[4] + Half_Amp_IR * (1 + cosd(360.*LTST_IR/24. - Phase_IR)) #labelxy("LTST","Flux") #plot(IR,"IR",Xaxis=LTST_IR,IR_KRC)
Peak_Vis = maxpos(Vis,showval=1)
Min_Vis = minpos(Vis,showval=1)
LTST_Vis_Peak = LTST_Vis[1,int(Peak_Vis[2,1,1]),1] #int(Peak_IR[2,1,1]) is the index
Half_Amp_Vis = 0.5*(Peak_Vis[4]-Min_Vis[4])
Phase_Vis = 360.*LTST_Vis_Peak/24. #in degree
Vis_KRC = Min_Vis[4] + Half_Amp_Vis * (1 + cosd(360.*LTST_Vis/24. - Phase_Vis))
#plot(Vis,"Vis",Xaxis=LTST_Vis,Vis_KRC)
Vis_Flux = Min_Vis[4] + Half_Amp_Vis #Average solar Flux Vis_Half_Amp = Half_Amp_Vis #Visible Half Amplitude Vis_Phase_Lag = Phase_Vis #Vis Phase Lag in degrees IR_Flux = Min_IR[4] + Half_Amp_IR #Average Thermal Emission IR_Half_Amp = Half_Amp_IR #IR Half Amplitude IR_Phase_Lag = Phase_IR #IR Phase Lag in degrees
line = sprintf("15 %.2f %.2f %.2f %.2f %.2f %.2f %.2f / Forcing from Planet on Satellite",IR_Flux,IR_Half_Amp,IR_Phase_Lag,Vis_Flux,Vis_Half_Amp,Vis_Phase_Lag,Lon_Hr) #IR, then Vis return(line) }
