def plot_satellite_orbit_plotly(eccentricity, orbital_period, inclination,
RAAN, argument_of_perigee, number):
standard_gravitational_parameter = 3.986004418e14
orbital_period = int(orbital_period * 60)
semi_major_axis = calculate_semi_major_axis(
orbital_period, standard_gravitational_parameter)
earth_radius = 6.371009e6
semi_major_axis = semi_major_axis / earth_radius
ke = pyasl.KeplerEllipse(
semi_major_axis,
orbital_period,
e=eccentricity,
Omega=RAAN,
i=inclination,
w=argument_of_perigee,
)
t = np.linspace(0, orbital_period, 200)
cis_vector = ke.xyzPos(t)
ascn, descn = ke.xyzNodes_LOSZ()
orbit = go.Scatter3d(
x=cis_vector[:, 0],
y=cis_vector[:, 1],
z=cis_vector[:, 2],
mode="lines",
name=f"Orbit {number}",
)
ascending_node = go.Scatter3d(
x=[ascn[0]],
y=[ascn[1]],
z=[ascn[2]],
mode="markers",
name=f"Ascending node {number}",
)
descending_node = go.Scatter3d(
x=[descn[0]],
y=[descn[1]],
z=[descn[2]],
mode="markers",
name=f"Descending node {number}",
)
periapsis = go.Scatter3d(
x=[cis_vector[0, 0]],
y=[cis_vector[0, 1]],
z=[cis_vector[0, 2]],
mode="markers",
name=f"Periapsis {number}",
)
return [orbit, ascending_node, descending_node, periapsis]
def zeroD_e(plotTitle):
# Independent Variables
waterDepth = 4000 # (m)
albedo = c.albedo_Earth # how much light gets reflected by atmosphere
epsilon = c.epsilonSurface_Earth # how good of a blackbody the body is
R_star = c.R_Sun # Radius of star (AU)
d_planet = c.d_Earth # Distance of planet from body it is orbiting (AU)
T_star = c.T_Sun # Surface Temperature of star (K)
e = float(input("Eccentricity (0.01671): ")) # Eccentricity of planet
periodFractions = 1000 # number of fractions of period
# Initialisation
heat_capacity = waterDepth * 1000 * 4200 # (J / K m^2)
period = math.pow(d_planet, 1.5) # Period of planet's orbit (years)
Power_output = PowerOut(T_star) # Power output of star (Watts/m^2)
solar_Constant = planetInsolation(Power_output, R_star, d_planet)
t = [0]
T = [0]
ke = pyasl.KeplerEllipse(d_planet, period, e, Omega=0., i=0.0, w=0.0)
heat_in = generate_heat_in(ke, periodFractions, d_planet, solar_Constant,
albedo)
# print(*heat_in, sep="\n") <- Used for debugging
# Generating Surface Temperature Data
heat_content = heat_capacity * T[0] # (J / m^2)
periods = int(input('Number of periods (1500): '))
for i in range(periods):
for j in range(periodFractions):
t.append(t[-1] + (period / periodFractions))
heat_out = epsilon * PowerOut(T[-1])
heat_content += (heat_in[j] - heat_out) * (period /
periodFractions) * c.SiY
T.append(heat_content / heat_capacity) # (K)
# Plotting data
fig = plt.figure(plotTitle)
plt.plot(t, T, c='r', linewidth=1.75)
# Modifying Visual aspect of plot
fig = beautifyPlot(fig, plotTitle, 'time (years)',
'Surface temperature (K)')
fig = plotCelciusLine(fig, t[0], t[-1])
fig = addLegend(fig)
return fig
def insolation_single(plotTitle, iterated, parsedE):
if not iterated:
e = float(input("Eccentricity: "))
else:
e = parsedE
# Independent Variables
R_star = c.R_Sun # Radius of star (AU)
d_planet = c.d_Earth # Distance of planet from body it is orbiting (AU)
T_star = c.T_Sun # (K)
periodFractions = 1000 # fraction of period acts as timeStep
# Initialisation
period = math.pow(d_planet, 1.5)
solar_Constant = solarConstant(T_star, R_star, d_planet)
t = []
L = []
ke = pyasl.KeplerEllipse(d_planet, period, e, Omega=0., i=0.0, w=0.0)
# Generating Data
for i in range(periodFractions):
t.append(((i / periodFractions) * period) * 365.25)
r = ke.radius((i / periodFractions) * period) # Applying Kepler's First Law to find r
newL = solar_Constant / (r / d_planet) ** 2 # Calculating insolation based on position in orbit relative to the starting point
L.append(newL)
if not iterated:
# Plotting data
fig = plt.figure(plotTitle)
plt.plot(t, L, c='r', linewidth=1.75)
# Modifying Visual aspect of plot
fig = beautifyPlot(fig, plotTitle + ' (e=' + str(e) + ')', 'time (days)', 'Light Insolation (W/m^2)')
return fig
else:
return t, L
Produced for "Python for Mechanical and Aerospace Engineering" by Alex Kenan, ISBN 978-1-7360606-0-5 and 978-1-7360606-1-2.
Copyright © 2020 Alexander Kenan. Some Rights Reserved. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
See http://creativecommons.org/licenses/by-nc-sa/4.0/ for more information.
"""
import numpy as np
from PyAstronomy import pyasl
import matplotlib.pyplot as plt
import matplotlib.animation as animation
import mpl_toolkits.mplot3d.axes3d as p3
# Create a Keplerian elliptical orbit with
# semi-major axis of 1.0 length units,
# a period of 1.0 time units, eccentricity of 0.5,
# longitude of ascending node of 0 degrees, an inclination
# of 30 deg, and a periapsis argument of 0 deg.
orbit = pyasl.KeplerEllipse(a=1.0, per=1.0, e=0.50, Omega=0.0,
i=30.0, w=0.0)
# Get a time axis
t = np.linspace(0, 4, 200)
# Calculate the orbit position at the given points
# in a Cartesian coordinate system.
pos = orbit.xyzPos(t)
# Plot x and y coordinates of the orbit with a few different options
# 2D, animated, and space
'''
plt.style.use('dark_background')
fig, ax = plt.subplots()
l = plt.plot(pos[::,1], pos[::,0], 'k-')
def calcOrbit():
"""
This is a tool to produce a Keplerian orbit in RA,Dec,RV to verify exosoft.
It just computes Kepler orbit positions and velocities then rotates
them into the observed values in the plane of the sky.
NOTE: the accuracy of the output values is to 'one part in 10^5',
due to the simple center differencing used to calculate the velocities
from the positions and times.
Outputs are 2 files matching formats used in exosoft DI and RV.
outBaseName+'DIdata.dat' has columns:
#1. JD
#2. RA (x) ["]
#3. RA ERROR ["]
#4. Dec (y) ["]
#5. Dec ERROR ["]
outBaseName+'RVdata.dat' has colunns:
#1. JD
#6. RV of primary (or secondary) rel to CofM [m/s]
#7. RV ERROR [m/s]
"""
quiet = False
## Important output directory and filename settings
###################################################
# Computer Directory
outDir='./'
# Base name for output files
outBaseName='syntheticdata_'
## Basic sample settings
########################
NumDataPointsOutRV = 25 #must be much less than 10000. values between 10-500 are suitable.
NumDataPointsOutDI = 10 #must be much less than 10000. values between 10-500 are suitable.
storePrimaryRVs = True
percentError = 0.5 #error is set to a percentage of the median
realizeErrors = True
percentCoverage = 100.00 #percent of total orbit for data to span. Over 100% is ok if you want overlapping data.
## System settings
##################
M_secondary = 1.0*(const.M_jup.value/const.M_sun.value) # [Solar masses]
M_primary = 1.0 # [Solar masses]
distance = 20.0 # [parsecs]
#Orbital Elements
TimeLastPeri =2450639.5 # [JD]
e =0.048 # Eccentricity [unitless]
period = 11.9 # [years]
Omega =100.6*np.pi/180# Longitude of ascending node [deg]
omega = 14.8*np.pi/180 # Argument of periastron [deg]
i = 45.0*np.pi/180 # Inclination [deg]
km_to_arcsec = 1.0/(const.au.value/1000.0)/distance # convert km to arcsecond
massratio=M_primary/M_secondary
mu = const.G.cgs.value*M_primary*(const.M_sun.value*1000.0)*(1.0 + 1.0/massratio) #gravitational parameter
a = (mu*(period*sec_per_year)**2/4.0/np.pi**2)**(1.0/3.0) #in cm
a_km = a/1.0e5 #to km
a_AU = a_km/(const.au.value/1000.0) #to AU
a2 = a_km/(massratio + 1.0)
a1 = a_km - a2 # Semimajor axis of the low-mass component (in km)
# print input orbital elements
if quiet==False:
print("\n\nOrbital Elements Used:\ne = "+str(e))
print("period = "+str(period)+" Years")
print("LongAN = "+str(Omega*180.0/np.pi)+" deg")
print("ArgPeri = "+str(omega*180.0/np.pi)+" deg")
print("a_total = "+str(a_AU)+" AU")
print("inclination = "+str(i*180.0/np.pi)+" deg")
print("Time of Last Periapsis = "+str(TimeLastPeri)+" JD")
print("Mass 1 = "+str(M_primary)+" Msun")
print("Mass 2 = "+str(M_secondary)+" Msun")
print("Mass 2 = "+str(M_secondary*(const.M_sun.value/const.M_jup.value))+" Mjupiter")
print("System distance = "+str(distance)+" PC, or "+str(1.0/(distance/1000.0))+' [mas]')
#settings prints
if storePrimaryRVs:
print("Saving RVs of primary star relative to Center of Mass\n")
else:
print("Saving RVs of companion relative to Center of Mass\n")
print('Errors were calculated as '+str(percentError)+"% of the median value in the observables")
if realizeErrors:
print('Data values were realized from the errors')
else:
print('Data values are perfect with NO realization of the errors')
print(str(NumDataPointsOutRV)+" RV, and "+str(NumDataPointsOutDI)+" DI epochs will be calculated and stored")
print('The data will cover '+str(percentCoverage)+'% of the total orbit.\n')
# Positions of both components in km relative to center of mass
ke = pyasl.KeplerEllipse(a1, period, e=e, Omega=0.)
NptsBIG = 10000
t = (np.arange(NptsBIG) - 1)/(NptsBIG - 2.)*period
## update t to cover the percent of total orbit requested.
#print 'len(t) before = '+str(len(t))
t2=np.empty(( int((percentCoverage/100)*len(t)) ))
if percentCoverage<=100.0:
t2[0:t2.size]=t[0:t2.size]
elif percentCoverage<200.0:
t2[0:t.size]=t
t2[t.size:]=t[0:( int(((percentCoverage-100.0)/100)*len(t)) )]+period
t=t2
#print 'len(t) after = '+str(len(t))
pos_A = ke.xyzPos(t)
pos_B = -pos_A/massratio
# Velocities in km/s using centered differencing
vel_A = (pos_A[2:] - pos_A[:-2])/(t[2] - t[0])/(86400*365.2422)
pos_A = pos_A[1:-1]
vel_B = (pos_B[2:] - pos_B[:-2])/(t[2] - t[0])/(86400*365.2422)
pos_B = pos_B[1:-1]
t = t[1:-1]
# Construct rotation matrix (from wikipedia [http://en.wikipedia.org/wiki/Orbital_elements#Euler_angle_transformations])
x1 = np.cos(Omega)*np.cos(omega) - np.sin(Omega)*np.cos(i)*np.sin(omega)
x2 = np.sin(Omega)*np.cos(omega) + np.cos(Omega)*np.cos(i)*np.sin(omega)
x3 = np.sin(i)*np.sin(omega)
y1 = -np.cos(Omega)*np.sin(omega) - np.sin(Omega)*np.cos(i)*np.cos(omega)
y2 = -np.sin(Omega)*np.sin(omega) + np.cos(Omega)*np.cos(i)*np.cos(omega)
y3 = np.sin(i)*np.cos(omega)
z1 = np.sin(i)*np.sin(Omega)
z2 = -np.sin(i)*np.cos(Omega)
z3 = np.cos(i)
rotmat = np.asarray([[x1, x2, x3], [y1, y2, y3], [z1, z2, z3]])
# Rotate positions, velocities
pos_A = np.dot(pos_A, rotmat)
vel_A = np.dot(vel_A, rotmat)
pos_B = np.dot(pos_B, rotmat)
vel_B = np.dot(vel_B, rotmat)
## Randomly re-sample position, vel and time arrays to requested number of samples
pos_Anew = []
pos_Bnew = []
vel_Anew = []
vel_Bnew = []
tnew = []
i=0
js=[]
while i<NumDataPointsOutRV:
j = np.random.randint(0,len(t))
if j not in js:
js.append(j)
pos_Anew.append(pos_A[j])
pos_Bnew.append(pos_B[j])
vel_Anew.append(vel_A[j])
vel_Bnew.append(vel_B[j])
tnew.append(t[j])
i+=1
pos_A = np.array(pos_Anew)
pos_B = np.array(pos_Bnew)
vel_A = np.array(vel_Anew)
vel_B = np.array(vel_Bnew)
t=np.array(tnew)
#make an ary for raw forms of the data.
data = np.zeros((pos_A.shape[0], 8))
data[:, 0] = t*2*np.pi/period #1. phase
data[:, 1] = t # 2. time (years)
data[:, 2] = pos_A[:, 0]*km_to_arcsec #3. x position of secondary (arcsec)
data[:, 3] = pos_A[:, 1]*km_to_arcsec #4. y position of secondary (arcsec)
data[:, 4] = vel_A[:, 2] #5. radial velocity of secondary (km/s)
data[:, 5] = pos_B[:, 0]*km_to_arcsec #6. x position of primary (arcsec)
data[:, 6] = pos_B[:, 1]*km_to_arcsec #7. y position of primary (arcsec)
data[:, 7] = vel_B[:, 2] #8. radial velocity of primary (km/s)
#update raw forms to initial NewBEAT versions
data2 = np.zeros((pos_A.shape[0],5))
data2[:,0] = data[:, 1]*days_per_year+TimeLastPeri #JD
data2[:,1] = pos_A[:, 1]*km_to_arcsec - pos_B[:, 1]*km_to_arcsec #Ythi=Xplot=RA separation between two bodies based on primary being at 0,0 ["]
data2[:,2] = pos_A[:, 0]*km_to_arcsec - pos_B[:, 0]*km_to_arcsec #Xthi=Yplot=Dec separation between two bodies based on primary being at 0,0 ["]
data2[:,3] = vel_B[:, 2]*1000.0 # RV of primary compared to center of mass origin[ m/s]
data2[:,4] = vel_A[:, 2]*1000.0 # RV of secondary compared to center of mass origin[ m/s]
#calculate error and use it to realize the errors in the DI data if requested
errorRA = np.median(np.abs(data2[:,1]))*(percentError/100.0)
errorDec = np.median(np.abs(data2[:,2]))*(percentError/100.0)
errorRA = np.max([errorRA,errorDec])
errorDec = np.max([errorRA,errorDec])
#print 'Using larger of two DI errors for both = '+str(errorDec)
if realizeErrors:
for i in range(pos_A.shape[0]):
data2[i,1]+=np.random.normal(0,errorRA)
data2[i,2] += np.random.normal(0,errorDec)
#calculate error and use it to realize the errors in the RV data if requested
errorRVprimary = np.median(np.abs(data2[:,3]))*(percentError/100.0)
errorRVsecondary = np.median(np.abs(data2[:,4]))*(percentError/100.0)
if realizeErrors:
for i in range(pos_A.shape[0]):
data2[i,3] += np.random.normal(0,errorRVprimary)
data2[i,4] += np.random.normal(0,errorRVsecondary)
#########################################################
#load up data for into arys for exosoft DI, exosoft RV.
#########################################################
#dataDI2 has columns:
#1. JD
#2. RA (x) ["]
#3. RA ERROR ["]
#4. Dec (y) ["]
#5. Dec ERROR ["]
#dataRV has colunns:
#1. JD
#6. RV of primary (or secondary) rel to CofM [m/s]
#7. RV ERROR [m/s]
dataDI2 = np.empty((pos_A.shape[0],5))
dataDI2[:,0] = data2[:, 0]#1. JD
dataDI2[:,1] = data2[:,1]#2. RA (x) ["]
dataDI2[:,2] = errorRA #3. RA ERROR ["]
dataDI2[:,3] = data2[:,2]#4. Dec (y) ["]
dataDI2[:,4] = errorDec#5. Dec ERROR ["]
dataRV = np.empty((pos_A.shape[0],3))
dataRV[:,0] = data2[:, 0]#1. JD
if storePrimaryRVs:
dataRV[:,1] = data2[:,3] #RV primary [m/s]
dataRV[:,2] = errorRVprimary#RV primary error [m/s]
else:
dataRV[:,1] = data2[:,4]#RV secondary [m/s]
dataRV[:,2] = errorRVsecondary#RV secondary error [m/s]
if True:
## Randomly re-sample the DI data to half that of the RV to mimick the fact that there is usually more much RV data than DI data
dataDI3=[]
i=0
js=[]
while i<NumDataPointsOutDI:
j = np.random.randint(0,len(dataDI2[:,0]))
if j not in js:
js.append(j)
dataDI3.append(dataDI2[j,:])
i+=1
dataDI3 = np.array(dataDI3)
else:
dataDI3 = dataDI2
#print "resulting RV data files have "+str(len(dataRV[:,0]))+" epochs"
#print "resulting DI data files have "+str(len(dataDI3[:,0]))+" epochs"
##write files to disk
if False:
# raw all-in-one format, NOT for ExoSOFT use.
np.savetxt(os.path.join(outDir,outBaseName+'.dat'), data, fmt="%.10g")
if True:
# 2 files for ExoSOFT use
np.savetxt(os.path.join(outDir,outBaseName+'RVdata.dat'), dataRV, fmt="%.10g")
np.savetxt(os.path.join(outDir,outBaseName+'DIdata.dat'), dataDI3, fmt="%.10g")
if quiet==False:
print('\nOutput data files written to:\n'+outDir)
def modelview(StellarRadius, limb1, limb2, PlanetRadius, PlanetImpact,
MoonRadius, MoonAxis, MoonEccentricity, MoonAscendingNode,
MoonLongitudePeriastron, MoonInclination, PhaseToHighlight,
Quality):
"""Calculate the 3D model view. This is the vector version (v2)"""
# Convert values from km to internal measure (stellar radius = 1)
PlanetRadius = PlanetRadius / StellarRadius
MoonRadius = MoonRadius / StellarRadius
MoonAxis = MoonAxis / StellarRadius
# Make background unicolor black or white
#allwhite = plt.Circle((0, 0), 100, color=(1, 1, 1))
#allblack = plt.Circle((0, 0), 100, color=(0, 0, 0))
#plt.gcf().gca().add_artist(allwhite)
# Alternatively plot a gradient map as background
X = [[-1, 0], [0, 1]]
plt.imshow(X,
interpolation='bicubic',
cmap=cm.gray,
extent=(-1.1, 1.1, -1.1, 1.1),
alpha=1)
# Star
StarQuality = Quality
StarQuality = 100
for i in range(StarQuality):
Impact = i / float(StarQuality)
LimbDarkening = QuadraticLimbDarkening(Impact, limb1, limb2)
Sun = plt.Circle((0, 0),
1 - i / float(StarQuality),
color=(LimbDarkening, LimbDarkening, LimbDarkening))
# for a yellow shaded star, replace the last LimbDarkening with 0
plt.gcf().gca().add_artist(Sun)
# Moon's orbit: Kepler ellipse normalized to 1x1 stellar radii
Ellipse = pyasl.KeplerEllipse(MoonAxis,
MoonAxis,
e=MoonEccentricity,
Omega=MoonAscendingNode,
w=MoonLongitudePeriastron,
i=MoonInclination)
NumerOfSamples = 1 / float(Quality)
time = np.linspace(0., MoonAxis, Quality)
coordinates = np.zeros((len(time), 3), dtype=np.float)
for i in xrange(len(time)):
coordinates[i, ::] = Ellipse.xyzPos(time[i])
OccultedDataPoints = [] # To clip the moon ellipse "behind" the planet
for i in range(Quality / 2):
CurrentMoonImpact = coordinates[i, 1]
CurrentHorizontalMoonPosition = coordinates[i, 0]
CurrentDistanceMoonPlanet = sqrt(
CurrentMoonImpact**2 +
CurrentHorizontalMoonPosition**2) * StellarRadius
if CurrentDistanceMoonPlanet < PlanetRadius * StellarRadius:
OccultedDataPoints.append(i)
if len(OccultedDataPoints) > 0:
FirstOcculted = OccultedDataPoints[0]
LastOcculted = OccultedDataPoints[-1] + 1
plt.plot(-coordinates[:FirstOcculted, 0],
coordinates[:FirstOcculted, 1] + PlanetImpact,
'k',
zorder=5)
plt.plot(-coordinates[LastOcculted:, 0],
coordinates[LastOcculted:, 1] + PlanetImpact,
'k',
zorder=5)
else:
plt.plot(-coordinates[::, 0],
coordinates[::, 1] + PlanetImpact,
'k',
zorder=5)
# Planet
PlanetCircle = plt.Circle((0, PlanetImpact),
PlanetRadius,
color='k',
zorder=4)
plt.gcf().gca().add_artist(PlanetCircle)
# Moon
PosPhase = PhaseToHighlight / float(NumerOfSamples)
coordinates[1, ::] = Ellipse.xyzPos(time[PosPhase])
if PhaseToHighlight < 0.5:
CurrentOrder = 2 # behind the planet
else:
CurrentOrder = 4 # in front of the planet
MoonCircle = plt.Circle(
(-coordinates[1, 0], coordinates[1, 1] + PlanetImpact),
MoonRadius,
color='k',
zorder=CurrentOrder)
plt.gcf().gca().add_artist(MoonCircle)
# Square not functional?
plt.axis([-1.1, +1.1, -1.1, +1.1], set_aspect='equal', fontsize=16)
return plt
def riverwithoutnoise(StellarRadius, limb1, limb2, PlanetRadius, PlanetAxis,
PlanetImpact, PlanetPeriod, MoonRadius, MoonAxis,
MoonEccentricity, MoonAscendingNode,
MoonLongitudePeriastron, MoonInclination,
ShowPlanetMoonEclipses, Quality, NumberOfSamples):
"""Core function projecting Kepler Moon Ellipse onto PixelGrid"""
# Moon's orbit: Kepler ellipse normalized to 1x1 stellar radii
NormalizedMoonAxis = MoonAxis / StellarRadius
NormalizedMoonRadius = MoonRadius / StellarRadius
CounterFullEclipses = 0
CounterPartialEclipses = 0
CurrentEclipsedRatio = 0
Ellipse = pyasl.KeplerEllipse(NormalizedMoonAxis,
NormalizedMoonAxis,
e=MoonEccentricity,
Omega=MoonAscendingNode,
w=MoonLongitudePeriastron,
i=MoonInclination)
time = np.linspace(0., NormalizedMoonAxis, NumberOfSamples)
coordinates = np.zeros((len(time), 3), dtype=np.float)
for i in xrange(len(time)):
coordinates[i, ::] = Ellipse.xyzPos(time[i])
StretchSpace = 5 # 5 Grid size [multiples of planet transit duration]
UnStretchedTransitDuration = PlanetPeriod / pi * arcsin(
sqrt((MoonRadius + StellarRadius)**2) / PlanetAxis)
cache = np.zeros((NumberOfSamples, Quality), dtype=np.float)
output = np.zeros((NumberOfSamples, StretchSpace * Quality),
dtype=np.float)
ma = forTrans.MandelAgolLC() # Prepare light curves
ma["T0"] = 0
ma["b"] = 0.
ma["linLimb"] = limb1
ma["quadLimb"] = limb2
ma["per"] = PlanetPeriod
ma["a"] = PlanetAxis / StellarRadius
ma["p"] = MoonRadius / StellarRadius
time = np.linspace(ma["per"] - (0.5 * UnStretchedTransitDuration),
ma["per"] + (0.5 * UnStretchedTransitDuration), Quality)
for i in range(NumberOfSamples): # Fetch curves: The core of this function
CurrentMoonImpact = coordinates[i, 1] # Position-dependent moon impact
CurrentHorizontalMoonPosition = coordinates[i, 0]
ma["i"] = ImpactToInclination(CurrentMoonImpact + PlanetImpact,
StellarRadius, PlanetAxis)
cache[i, ::] = ma.evaluate(time) # Fetch each curve
# Mutual eclipses: calculate distance moon --> planet [km]
if ShowPlanetMoonEclipses:
CurrentDistanceMoonPlanet = sqrt(
CurrentMoonImpact**2 +
CurrentHorizontalMoonPosition**2) * StellarRadius
CurrentEclipsedRatio = EclipsedRatio(CurrentDistanceMoonPlanet,
PlanetRadius, MoonRadius)
for k in range(Quality): # Transform flux from e.g. 0.995 to -5ppm
cache[i, k] = -(1 - cache[i, k]) * 10**6
# And reduce the flux according to the eclipsed area
if ShowPlanetMoonEclipses and cache[i, k] < 0:
cache[i, k] = -(1 - cache[i, k]) * (1 - CurrentEclipsedRatio)
for i in range(NumberOfSamples): # Apply time shift due to moon orbit
for k in range(Quality):
HorizontalPixelPosition = (coordinates[i, 0] * Quality) / 2
MidShift = (0.5 * StretchSpace - 0.5) * Quality
output[i, k + HorizontalPixelPosition + MidShift] = cache[i, k]
return output
def __init__(self,
planes=1,
nodes_per_plane=4,
inclination=0,
semi_major_axis=6372000,
ecc=0.0,
minCommunicationsAltitude=100000,
minSatElevation=40,
linkingMethod='SPARSE',
arcOfAscendingNodes=360.0):
"""
Parameters
----------
planes : int
the number of planes in the constillation
nodes_per_plane : int
the number of satellites per plane
inclination : float
the inclination of all planes in constillation
semi_major_axis : float
semi major axis of the orbits (radius, if orbits circular)
ecc : float
the eccentricity of the orbits; range = 0.0 - 1.0
minCommunicationsAltitude : int32
The minimum altitude that inter satellite links must pass
above the Earth's surface.
minSatElevation : int
The minimum angle of elevation in degrees above the horizon a satellite
needs to have for a ground station to communicate with it.
linkingMethod : string
The current linking method used by the constillation
currently only used for generating GML files.
arcOfAscendingNodes : float
The angle of arc (in degrees) that the ascending nodes of all the
orbital planes is evenly spaced along. Ex, seting this to 180 results
in a Pi constellation like Iridium
"""
self.number_of_planes = planes
self.nodes_per_plane = nodes_per_plane
self.total_sats = planes * nodes_per_plane
self.ground_node_counter = 0
self.inclination = inclination
self.semi_major_axis = semi_major_axis
self.period = self.calculateOrbitPeriod(
semi_major_axis=self.semi_major_axis)
self.eccentricity = ecc
self.current_time = 0
self.number_of_isl_links = 0
self.number_of_gnd_links = 0
self.total_links = 0
self.link_array_size = LINK_ARRAY_SIZE
self.min_communications_altitude = 100000
self.min_sat_elevation = 40
self.linking_method = 'SPARSE'
self.G = None
# this is not written to zero, because it has it's own init
# function a a few lines down: initSatelliteArray()
self.satellites_array = np.empty(self.total_sats,
dtype=SATELLITE_DTYPE)
# declare an empty ground
self.groundpoints_array = np.zeros(NUM_GROUND_POINTS,
dtype=GROUNDPOINT_DTYPE)
# declare an empty link array
self.link_array = np.zeros(self.link_array_size, dtype=LINK_DTYPE)
# figure out how many degrees to space right ascending nodes of the planes
self.raan_offsets = [(arcOfAscendingNodes / self.number_of_planes) * i
for i in range(0, self.number_of_planes)]
# generate a list with a kepler ellipse solver object for each plane
self.plane_solvers = []
for raan in self.raan_offsets:
self.plane_solvers.append(
pyasl.KeplerEllipse(
per=self.period, # how long the orbit takes in seconds
a=self.
semi_major_axis, # if circular orbit, this is same as radius
e=self.
eccentricity, # generally close to 0 for leo constillations
Omega=raan, # right ascention of the ascending node
w=0.0, # initial time offset / mean anamoly
i=self.inclination)) # orbit inclination
# figure out the time offsets for nodes withen a plane
self.time_offsets = [(self.period / nodes_per_plane) * i
for i in range(0, nodes_per_plane)]
# initialize the satellite array
self.initSatelliteArray()
def zeroD_e_mmm(plotTitle):
# Independent Variables
waterDepth = 4000 # (m)
albedo = c.albedo_Earth # how much light gets reflected by atmosphere
epsilon = c.epsilonSurface_Earth # how good of a blackbody the body is
R_star = c.R_Sun # Radius of star (AU)
d_planet = c.d_Earth # Distance of planet from body it is orbiting (AU)
T_star = c.T_Sun # Surface Temperature of star (K)
periodFractions = 365 # number of fractions of period
# Global Initialisation
heat_capacity = waterDepth * 1000 * 4200 # (J / K m^2)
period = math.pow(d_planet, 1.5) # Period of planet's orbit (years)
Power_Output = PowerOut(T_star) # incidentPower from star (W)
solar_Constant = planetInsolation(Power_Output, R_star, d_planet) # Insolation incident on the planet's surface (W/m^2)
eccentricities = generateList(0, 1, 0.01)
minTemps = []
meanTemps = []
maxTemps = []
for e in eccentricities: # Iterating through each eccentricity from 0.01 to 0.99
# Initialisation
T = [0]
heat_content = heat_capacity * T[0] # (J / m^2)
periods = 1000
tempMin = 1E24
ke = pyasl.KeplerEllipse(d_planet, period, e, Omega=0., i=0.0, w=0.0)
heat_in = generate_heat_in(ke, periodFractions, d_planet, solar_Constant, albedo)
tempMean = 0
countMean = 0
for k in range(periods):
for i in range(periodFractions):
heat_out = epsilon * PowerOut(T[-1])
heat_content += (heat_in[i] - heat_out) * (period / periodFractions * c.SiY)
T.append(heat_content / heat_capacity) # (K)
if periods - k < 20: # Only keeps track of minimum temperatures for the last 20 periods in EBM
if T[-1] < tempMin:
tempMin = T[-1] # keeping track of the minimum temperature
tempMean += T[-1]
countMean += 1
minTemps.append(tempMin)
maxTemps.append(max(T))
meanTemps.append(tempMean / countMean)
print(str(round(e, 2)))
# Plotting data
fig = plt.figure(plotTitle)
plt.plot(eccentricities, minTemps, c='r', linewidth=0.75, label='Minimum')
plt.plot(eccentricities, meanTemps, c='g', linewidth=0.75, label="Mean")
plt.plot(eccentricities, maxTemps, c='b', linewidth=0.75, label='Maximum')
# Modifying Visual aspect of plot
fig = beautifyPlot(fig, plotTitle, 'Eccentricity', 'Surface temperature (K)')
fig = plotCelciusLine(fig, min(eccentricities), max(eccentricities))
fig = addLegend(fig, 'upper left', 'Plots: ')
return fig
def orbit():
# Instantiate a Keplerian elliptical orbit with
# semi-major axis of __ length units,
# a period of __ time units, eccentricity of __,
# longitude of ascending node of __ degrees, an inclination
# of __ deg, and a periapsis argument of __ deg.
ke = pyasl.KeplerEllipse(1.3, 10., e=0.9, Omega=70., i=10.0, w=110.0)
# Get a time axis
t = np.linspace(0, 20, 100)
# Calculate the orbit position at the given points
# in a Cartesian coordinate system.
pos = ke.xyzPos(t)
#print("Shape of output array: ", pos.shape)
# x, y, and z coordinates for 50th time point
#print("x, y, z for 50th point: ", pos[50, ::])
# Calculate orbit radius
radius = ke.radius(t)
# Calculate velocity on orbit
vel = ke.xyzVel(t)
# Find the nodes of the orbit (Observer at -z)
ascn, descn = ke.xyzNodes_LOSZ()
velocity = np.zeros(vel.shape[0])
for i in range(vel.shape[0]):
velocity[i] = velocity[i] + (vel[i][0]**2 + vel[i][1]**2 +
vel[i][2]**2)**(0.5)
print(velocity.size)
vmin = velocity.min()
vmax = velocity.max()
#Freq Shift
smax = 480
smin = 240
if (vmax - vmin < 0.001):
sh = 0
else:
sh = (smax - smin) / (vmax - vmin)
for i in range(velocity.shape[0]):
velocity[i] = (velocity[i] - vmin) * sh + smin
s = np.zeros(1)
for i in range(velocity.size):
if (velocity[i] < 270):
f = 240
elif (velocity[i] < 300):
f = 270
elif (velocity[i] < 320):
f = 300
elif (velocity[i] < 360):
f = 320
elif (velocity[i] < 400):
f = 360
elif (velocity[i] < 450):
f = 400
else:
f = 450
#print(f)
x = np.zeros(480)
#x[f]=20/radius[i]
x[f] = np.exp(-1 * radius[i]) * 100
y = np.fft.irfft(x)
s = np.concatenate((s, y), axis=0)
print(s.size)
write_wavfile("e=0.9_exp.wav", 4096, s)
def zeroD_e_bar(plotTitle):
# Independent Variables
waterDepth = 4000 # (m)
albedo = c.albedo_Earth # how much light gets reflected by atmosphere (0-1)
epsilon = c.epsilonSurface_Earth # how good of a blackbody the body is (0-1)
R_star = c.R_Sun # Radius of star (AU)
d_planet = c.d_Earth # Distance of planet from body it is orbiting (AU)
T_star = c.T_Sun # Surface Temperature of star (K)
periodFractions = 365 # number of fractions of period
# Global Initialisation
heat_capacity = waterDepth * 1000 * 4200 # (J / K m^2)
period = math.pow(d_planet, 1.5) # Period of planet's orbit (years)
Power_Output = PowerOut(
T_star) # Power irradiated from the star's surface (W/m^2)
solar_Constant = planetInsolation(
Power_Output, R_star,
d_planet) # Insolation incident on the planet's surface (W/m^2)
eccentricities = generateList(
0, 1, 0.01) # List containing all the eccentricities being plotted
minTemps = []
maxTemps = []
for e in eccentricities: # Iterating through each eccentricity from 0.01 to 0.99
# Initialisation
T = [0]
heat_content = heat_capacity * T[0] # (J / m^2)
periods = 1000
tempMin = 1E24
ke = pyasl.KeplerEllipse(d_planet, period, e, Omega=0., i=0.0, w=0.0)
heat_in = generate_heat_in(ke, periodFractions, d_planet,
solar_Constant, albedo)
for k in range(periods):
for i in range(periodFractions):
heat_out = epsilon * PowerOut(T[-1])
heat_content += (heat_in[i] -
heat_out) * (period / periodFractions * c.SiY)
T.append(heat_content / heat_capacity) # (K)
if periods - k < 20: # Only keeps track of minimum temperatures for the last 20 periods in EBM
if T[-1] < tempMin:
tempMin = T[
-1] # Keeping track of the minimum temperature
print(str(round(e, 2)))
minTemps.append(tempMin)
maxTemps.append(max(T))
# Plotting data
fig = plt.figure(plotTitle)
for i in range(len(eccentricities)):
# Height minimum
minBarHeight = 2
height = round(maxTemps[i] - minTemps[i], 3)
if height < minBarHeight:
height = minBarHeight
barWidth = 0.006 # Set to 0.006 for default or 0.01 for connected bars
plt.bar(round(eccentricities[i], 2),
height,
width=barWidth,
bottom=round(minTemps[i], 3),
align='center',
color='r')
# Modifying Visual aspect of plot
fig = beautifyPlot(fig, plotTitle, 'Eccentricity',
'Surface temperature (K)')
fig = plotCelciusLine(fig, min(eccentricities), max(eccentricities))
fig = addLegend(fig, 'upper left', 'Plots: ')
return fig
