def continue_condition(state_i):
# Define the rough ground level
lat = ECEF2LLH(np.vstack((state_i[:3])))[0]
R_sealevel = EarthRadius(lat)
r_end = R_sealevel #+ h_ground
r_beg = R_sealevel + 120e3
# brightness = fn()
# if brightness < threshold: # Not luminous anymore
if norm(state_i[3:6]) < 2e3: # Get a better measure
print('Successfully found the end of the trajectory: v < 2km/s.')
return False # Ends the integration
elif norm(state_i[:3]) > r_beg: # Escaped the atmosphere
print('Successfully found the start of the trajectory: h > 120km.')
return False # Ends the integration
elif norm(state_i[:3]) < r_end: # Reached ground
print('Your meteoroid became a meteorite!!')
return False # Ends the integration
elif state_i[6] < 1e-3: # Lost all mass [<1g]
print('Your meteoroid is dust!')
return False # Ends the integration
else:
return True # Continues integration
def PointTriangulation(data, directory=None, mc=1):
# Find the times with multiple data points
[dt_vals, dt_counts] = np.unique(data['time'], return_counts=True)
dt_vals_plus = dt_vals[dt_counts > 1]
# Triangulate all paired points
x = np.zeros((3, len(dt_vals_plus)))
cov = np.zeros((3, 3, len(dt_vals_plus)))
for k, dt_val in enumerate(dt_vals_plus):
# Get all the observation data
obs_ECEF_all = []
for i in range(dt_counts[dt_vals == dt_val][0]):
Times = np.array(data['time'])
obs_lat = data['obs_lat'][Times == dt_val][i]
obs_lon = data['obs_lon'][Times == dt_val][i]
obs_hei = data['obs_hei'][Times == dt_val][i]
obs_LLH = np.vstack((obs_lat, obs_lon, obs_hei))
obs_ECEF = LLH2ECEF(obs_LLH)
obs_ECEF_all.append(obs_ECEF)
x_particles = np.zeros((3, mc))
for particle in range(mc):
# Calculate each line of sight in the paired points
UV_ECEF_all = []
for i in range(dt_counts[dt_vals == dt_val][0]):
Times = np.array(data['time'])
# Extract some raw data
alt = np.deg2rad(data['altitude'][Times == dt_val][i])
azi = np.deg2rad(data['azimuth'][Times == dt_val][i])
if mc != 1:
alt_err = np.deg2rad(
data['err_plus_altitude'][Times == dt_val][i])
azi_err = np.deg2rad(
data['err_plus_azimuth'][Times == dt_val][i])
alt += np.random.normal(0, alt_err)
azi += np.random.normal(0, azi_err)
# Convert from spherical to cartesian
UV_ENU = np.vstack(
(np.cos(alt) * np.sin(azi), np.cos(alt) * np.cos(azi),
np.sin(alt)))
# Convert from ENU to ECEF coordinates
UV_ECEF = ENU2ECEF(
data['obs_lon'][Times == dt_val][i],
data['obs_lat'][Times == dt_val][i]).dot(UV_ENU)
UV_ECEF_all.append(UV_ECEF)
# Calculate the best position between the first two lines
x_est = ShortestMidPoint(obs_ECEF_all, UV_ECEF_all)
# Minimizing angular separation between all the lines
result = minimize(TotalAngSep,
x_est,
args=(obs_ECEF_all, UV_ECEF_all),
method='Nelder-Mead')
x_particles[:, particle] = result.x
if mc > 1:
PointsTable = Table()
PointsTable['datetime'] = [data['datetime'][Times == dt_val][0]
] * mc
PointsTable['X_geo'] = x_particles[0]
PointsTable['Y_geo'] = x_particles[1]
PointsTable['Z_geo'] = x_particles[2]
partices_LLH = ECEF2LLH(x_particles)
PointsTable['latitude'] = np.rad2deg(partices_LLH[0])
PointsTable['longitude'] = np.rad2deg(partices_LLH[1])
PointsTable['height'] = partices_LLH[2]
PointsFile = os.path.join(directory,
'{:.3f}_particles.ecsv'.format(dt_val))
PointsTable.write(PointsFile, format='ascii.ecsv', delimiter=',')
print('\Points file written to: ' + PointsFile)
Points(PointsFile)
x[:, k] = np.mean(x_particles, axis=1)
cov[:, :, k] = np.cov(x_particles)
print('\nTime step: {0:.2f} sec'.format(dt_val))
# print('Normalised Residuals Before: {0:8.4f}'.format(
# np.rad2deg(TotalAngSep(x_est, obs_ECEF_all, UV_ECEF_all))*3600))
# print('Normalised Residuals After: {0:8.4f}'.format(
# np.rad2deg(result.fun)*3600))
if mc == 1:
return x, dt_vals_plus, dt_counts[dt_counts > 1]
else:
return x, dt_vals_plus, dt_counts[dt_counts > 1], cov
24 * 60 * 60), 2)
if errors:
mc = 1000 # Number of particles
ParticleFolder = os.path.join(PointDir,
str(mc) + '_particles_per_timestep')
os.mkdir(ParticleFolder)
[Pos_ECEF, t_rel, N_cams,
Cov_ECEF] = PointTriangulation(AllData, ParticleFolder, mc)
else:
[Pos_ECEF, t_rel, N_cams] = PointTriangulation(AllData)
# Coordinate transforms
T_jd = t0.jd + t_rel / (24 * 60 * 60)
Pos_LLH = ECEF2LLH(Pos_ECEF)
Pos_ECI = ECEF2ECI(Pos_ECEF, Pos_ECEF, T_jd)[0]
# Raw velocity calculations
vel_eci = norm(Pos_ECI[:, 1:] - Pos_ECI[:, :-1],
axis=0) / (t_rel[1:] - t_rel[:-1])
vel_geo = norm(Pos_ECEF[:, 1:] - Pos_ECEF[:, :-1],
axis=0) / (t_rel[1:] - t_rel[:-1])
gamma = np.arcsin((Pos_LLH[2][1:] - Pos_LLH[2][:-1]) /
(vel_geo * (t_rel[1:] - t_rel[:-1])))
vel_eci = np.hstack((vel_eci, np.nan))
vel_geo = np.hstack((vel_geo, np.nan))
gamma = np.hstack((gamma, np.nan))
t_isot_col = Column(name='datetime',
data=Time(T_jd, format='jd', scale='utc').isot)
def NRLMSISE_00(pos, time, pos_type='eci'):
''' Courtesy of Ellie Sansom '''
"""
Inputs: inertial position and time
Outputs: [altitude, temp, atm_pres, atm density, sos, dyn_vis]
"""
from nrlmsise_00_header import nrlmsise_input, nrlmsise_output, nrlmsise_flags
from nrlmsise_00 import gtd7
time = Time(time, format='jd', scale='utc')
# Convert ECI to LLH coordinates
if pos_type == 'eci':
Pos_LLH = ECEF2LLH(ECI2ECEF_pos(pos, time))
elif pos_type == 'ecef':
Pos_LLH = ECEF2LLH(pos)
elif pos_type == 'llh':
Pos_LLH = pos
else:
print('NRLMSISE_00 error: Invalid pos_type')
exit()
g_lat = np.rad2deg(Pos_LLH[0][0])
g_long = np.rad2deg(Pos_LLH[1][0])
alt = Pos_LLH[2][0]
# Break up time into year, day of year, and seconds of the day
yDay = time.yday.split(':')
yr = float(yDay[0])
doy = float(yDay[1])
sec = float(yDay[2]) * 60 * 60 + float(yDay[3]) * 60 + float(yDay[4])
# Assign our variables into the nrmsise inputs
Input = nrlmsise_input(yr, doy, sec, alt / 1000, g_lat, g_long)
Output = nrlmsise_output()
Flags = nrlmsise_flags()
# Switches
for i in range(1, 24):
Flags.switches[i] = 1
# GTD7 atmospheric model subroutine
gtd7(Input, Flags, Output)
# Temperature at alt [deg K]
T = Output.t[1]
# Molecular number densities [m-3]
He = Output.d[0] # He
O = Output.d[1] # O
N2 = Output.d[2] # N2
O2 = Output.d[3] # O2
Ar = Output.d[4] # Ar
H = Output.d[6] # H
N = Output.d[7] # N
# ano_O = Output.d[8] # Anomalous oxygen
sum_mass = He + O + N2 + O2 + Ar + H + N
# Molar mass
He_mass = 4.0026 # g/mol
O_mass = 15.9994 # g/mol
N2_mass = 28.013 # g/mol
O2_mass = 31.998 # g/mol
Ar_mass = 39.948 # g/mol
H_mass = 1.0079 # g/mol
N_mass = 14.0067 # g/mol
# Molecular weight of air [kg/mol]
mol_mass_air = (He_mass * He + O_mass * O + N2_mass * N2 + O2_mass * O2 +
Ar_mass * Ar + H_mass * H + N_mass * N) / (1000 * sum_mass)
# Total mass density [kg*m-3]
po = Output.d[5] * 1000
Ru = 8.3144621 # Universal gas constant [J/(K*mol)]
R = Ru / mol_mass_air # Individual gas constant [J/(kg*K)] #287.058
# Ideal gas law
atm_pres = po * T * R
# Speed of sound in atm
sos = 331.3 * np.sqrt(1 + T / 273.15)
# Dynamic viscosity (http://en.wikipedia.org/wiki/Viscosity)
C = 120 #Sutherland's constant for air [deg K]
mu_ref = 18.27e-6 # Reference viscosity [[mu_Pa s] * e-6]
T_ref = 291.15 # Reference temperature [deg K]
dyn_vis = mu_ref * (T_ref + C) / (T + C) * (T / T_ref)**1.5
return T, atm_pres, po, sos, dyn_vis
def EarthDynamics(t, X, WindData, t0, return_abs_mag=False):
'''
The state rate dynamics are used in Runge-Kutta integration method to
calculate the next set of equinoctial element values.
'''
''' State Rates '''
# State parameter vector decomposed
Pos_ECI = np.vstack((X[:3]))
Vel_ECI = np.vstack((X[3:6]))
M = X[6]
rho = X[7]
A = X[8]
c_ml = X[9] # c_massloss = sigma*cd_hyp
t_jd = t0 + t / (24 * 60 * 60) # Absolute time [jd]
''' Primary Gravitational Acceleration '''
a_grav = gravity_vector(Pos_ECI)
''' Atmospheric Drag Perturbation - Better Model Needed '''
Pos_ECEF = ECI2ECEF_pos(Pos_ECI, t_jd)
Pos_LLH = ECEF2LLH(Pos_ECEF)
# Atmospheric velocity
if type(WindData) == Table: #1D vertical profile
maxwindheight = max(WindData['# Height'])
if float(Pos_LLH[2]) > maxwindheight:
[v_atm, rho_a, temp] = AtmosphericModel([], Pos_ECI, t_jd)
else:
[v_atm, rho_a, temp] = AtmosphericModel(WindData, Pos_ECI, t_jd)
else: #3D wind profile
maxwindheight = max(WindData[2, :, :, :])
if float(Pos_LLH[2]) > maxwindheight:
[v_atm, rho_a, temp] = AtmosphericModel([], Pos_ECI, t_jd)
else:
[Wind_ENU, rho_a, temp] = WRF3D(WindData, Pos_LLH)
Wind_ECEF = ENU2ECEF(Pos_LLH[1], Pos_LLH[0]).dot(Wind_ENU)
v_atm = ECEF2ECI(Pos_ECEF, Wind_ECEF, t_jd)[1]
# Velocity relative to the atmosphere
v_rel = Vel_ECI - v_atm
v = norm(v_rel)
# New drag equations - function that fits the literature
cd = dragcoeff(v, temp, rho_a, A)[0]
# Total drag perturbation
a_drag = -cd * A * rho_a * v * v_rel / (2 * M**(1. / 3) * rho**(2. / 3))
''' Total Perturbing Acceleration '''
a_tot = a_grav + a_drag
# Mass-loss equation
dm_dt = -c_ml * A * rho_a * v**3 * M**(2. / 3) / (2 * rho**(2. / 3))
# See (Sansom, 2019) as reference
if return_abs_mag: # sigma = c_ml / cd
lum = -X[10] * (v**2 / 2 + cd / c_ml) * dm_dt * 1e7
return -2.5 * np.log10(lum / 1.5e10)
''' State Rate Equation '''
X_dot = np.zeros(X.shape)
X_dot[:3] = Vel_ECI.flatten()
X_dot[3:6] = a_tot.flatten()
X_dot[6] = dm_dt
return X_dot
def Propagate(state0, args):
'''
Inputs: Initial ECI position (m), ECI velocity (m/s), and mass (kgs).
Outputs: ECI position (m), ECI velocity (m/s) throughout the dark flight.
'''
# Calculate the meteor's initial state parameters
Pos_ECI = np.vstack((state0[1:4]))
t0 = float(state0[0])
X = state0.flatten()[1:] # Add mass to the state
[WindData, h_ground, windspd_err, winddir_err, mc] = args
newWindData = copy.deepcopy(WindData)
if mc: # Randomise every layer independently
if type(newWindData) == Table: #wind profile
# newWindData['Wind'] = WindData['Wind'] + np.random.normal( 0.0, windspd_err, size = len(WindData['Wind']) )
# newWindData['WDir'] = WindData['WDir'] + np.random.normal( 0.0, winddir_err, size = len(WindData['Wind']) )
newWindData['Wind'] = WindData['Wind'] + np.random.uniform(
-windspd_err, windspd_err, size=len(WindData['Wind']))
newWindData['WDir'] = WindData['WDir'] + np.random.uniform(
-windspd_err, winddir_err, size=len(WindData['Wind']))
newWindData['WDir'] = np.mod(newWindData['WDir'],
360.0) #mod the wind to 0-360a
else: #3d wind ###TODO untested
#winddata[3] wind north
newWindData[3, :, :, :] = WindData[3, :, :, :] + np.random.uniform(
-windspd_err, windspd_err, size=np.shape(WindData[3, :, :, :]))
#winddata[4] wind east
newWindData[4, :, :, :] = WindData[4, :, :, :] + np.random.uniform(
-windspd_err, windspd_err, size=np.shape(WindData[4, :, :, :]))
#winddata[5] wind up
#left untouched
elevation_data = srtm.get_data(local_cache_dir=SRTM_cache)
# Initialise the time step
# R_sealevel = EarthRadius(ECEF2LLH(Pos_ECI)[0])
# r_end = R_sealevel + h_ground
state, T_rel = [], []
def solout(t, X):
state.extend([X.copy()])
T_rel.extend([t])
Pos_ECI = np.vstack((X[:3]))
Pos_ECF = ECI2ECEF_pos(Pos_ECI, t0 + (t / (24 * 60 * 60)))
lt, ln, ht = ECEF2LLH(Pos_ECF)
R_sealevel = EarthRadius(lt)
if h_ground == 'a':
# print( 'lat,lon, time, ', np.rad2deg(lt).item(), np.rad2deg(ln).item(), str(t+t0) )
h_gnd = elevation_data.get_elevation(
np.rad2deg(lt).item(),
np.rad2deg(ln).item())
if h_gnd == None: #in case of voids or geo file not found
print('WARNING elevation file issue, ',
np.rad2deg(lt).item(),
np.rad2deg(ln).item(), ht, X[6])
h_gnd = 0.0
else:
h_gnd = float(h_ground)
r_end = R_sealevel + h_gnd
if norm(X[:3]) < r_end: # Reached ground or below
return -1 # Ends the integration
elif X[6] < 1e-3: # Lost all mass [<1g]
print('Your meteoroid is dust!')
return -1 # Ends the integration
else:
return 0 # Continues integration
# Setup integrator
dt0 = 0.1
dt_max = 3 #60 # sec
solver = ode(EarthDynamics).set_integrator('dopri5', \
first_step=dt0, max_step=dt_max, rtol=1e-4) #'dop853',
solver.set_solout(solout)
solver.set_initial_value(X, 0).set_f_params(newWindData, t0)
# Integrate with RK4 until impact
t_max = np.inf
solver.integrate(t_max)
# Assign the variables
T = np.array(T_rel) / (24 * 60 * 60) + t0
X_all = np.array(state).T
# Make sure we end precisely on the ground, rather than below
#so we backtrack a fraction of a step
Pos_ECF_final = ECI2ECEF_pos(X_all[:3, -1], T[-1])
lt, ln, ht = ECEF2LLH(Pos_ECF_final)
if h_ground == 'a':
h_gnd = elevation_data.get_elevation(
np.rad2deg(lt).item(),
np.rad2deg(ln).item())
if h_gnd == None:
h_gnd = 0.0
print('WARNING final ground issue, ',
np.rad2deg(lt).item(),
np.rad2deg(ln).item(), ht, X_all[6])
else:
h_gnd = float(h_ground)
r_end = EarthRadius(lt) + h_gnd
fraction = (norm(X_all[:3, -2:-1]) - r_end) / (norm(X_all[:3, -2:-1]) -
norm(X_all[:3, -1:]))
if len(X_all[0]) > 1:
X_all[:, -1:] = X_all[:, -2:-1] + fraction * (X_all[:, -1:] -
X_all[:, -2:-1])
T[-1] = T[-2] + fraction * (T[-1] - T[-2])
Pos_ECI = X_all[:3]
Vel_ECI = X_all[3:6]
M = X_all[6]
rho = X_all[7]
A = X_all[8]
c_ml = X_all[9]
return {
'time_jd': T,
'pos_eci': Pos_ECI,
'vel_eci': Vel_ECI,
'mass': M,
'rho': rho,
'shape': A,
'c_ml': c_ml
}
def AtmosphericModel(WindData, Pos_ECI, t_jd):
# The rotational component of the wind in the ECI frame
north_pole_ecef = np.vstack((0, 0, 6356.75231e3))
north_pole_eci = ECEF2ECI_pos(north_pole_ecef, t_jd)
earth_ang_rot = OMEGA_EARTH * north_pole_eci / norm(north_pole_eci)
v_rot = np.cross(earth_ang_rot, Pos_ECI, axis=0)
if len(WindData):
# Pos_LLH = ECEF2LLH(Pos_ECI) # There is a max of +-40m height error here
Pos_ECEF = ECEF2LLH(Pos_ECI)
Pos_LLH = ECEF2LLH(Pos_ECEF)
h = float(Pos_LLH[2]) # (m)
# Get the relevent wind data from that height
if h > max(
WindData['# Height']): # Think about using a model for +30km
i = np.argmax(WindData['# Height'])
Wind = WindData['Wind'][i] # (m/s)
WDir = WindData['WDir'][i] # (deg)
TempK = WindData['TempK'][i] # (deg K)
Press = WindData['Press'][i] # (Pa)
RHum = WindData['RHum'][i] # (%)
elif h <= max(WindData['# Height']) and h >= min(WindData['# Height']):
Wind = interp1d(WindData['# Height'],
WindData['Wind'],
kind='cubic')(h)
WDir = interp1d(WindData['# Height'],
WindData['WDir'],
kind='cubic')(h)
TempK = interp1d(WindData['# Height'],
WindData['TempK'],
kind='cubic')(h)
Press = interp1d(WindData['# Height'],
WindData['Press'],
kind='cubic')(h)
RHum = interp1d(WindData['# Height'],
WindData['RHum'],
kind='cubic')(h)
elif h < min(WindData['# Height']):
i = np.argmin(WindData['# Height'])
Wind = WindData['Wind'][i] # (m/s)
WDir = WindData['WDir'][i] # (deg)
TempK = WindData['TempK'][i] # (deg K)
Press = WindData['Press'][i] # (Pa)
RHum = WindData['RHum'][i] # (%)
else:
input('There is a problem in AtomosphericModel.')
# Calculate the atmospheric density
rho_a = density_from_pressure(TempK, Press, RHum) # (kg/m3)
# Construct the wind vector (start with clockwise N=0, coming from!!)
Wind_ENU = -np.vstack((Wind * np.sin(np.deg2rad(WDir)),
Wind * np.cos(np.deg2rad(WDir)), 0))
# Convert the ENU to ECI coordinates (using lat/lon from ECI frame)
lat = float(Pos_LLH[0])
lon = float(Pos_LLH[1]) # (rad)
C_ENU2ECI = np.array([[
-np.sin(lon), -np.sin(lat) * np.cos(lon),
np.cos(lat) * np.cos(lon)
], [
np.cos(lon), -np.sin(lat) * np.sin(lon),
np.cos(lat) * np.sin(lon)
], [0, np.cos(lat), np.sin(lat)]])
Wind_ECI = np.dot(C_ENU2ECI, Wind_ENU) + v_rot
else:
#no winds, use NRLMSISE model
Pos_ECEF = ECI2ECEF_pos(Pos_ECI, t_jd)
Pos_LLH = ECEF2LLH(Pos_ECEF)
h = float(Pos_LLH[2]) # (m)
[TempK, Press, rho_a] = NRLMSISE_00(Pos_LLH, t_jd, pos_type='llh')[:3]
Wind_ENU = np.vstack((0, 0, 0))
Wind_ECI = v_rot
# Save the variables
WRF_history.append(np.vstack((h, Wind_ENU, rho_a, TempK)))
return Wind_ECI, rho_a, TempK
def Propagate(state0, args):
'''
Inputs: Initial ECI position (m), ECI velocity (m/s), and mass (kgs).
Outputs: ECI position (m), ECI velocity (m/s) throughout the dark flight.
'''
# Calculate the meteor's initial state parameters
Pos_ECI = np.vstack((state0[1:4]))
t0 = float(state0[0])
X = state0.flatten()[1:] # Add mass to the state
[WindData, h_ground] = args
# Initialise the time step
R_sealevel = EarthRadius(ECEF2LLH(Pos_ECI)[0])
r_end = R_sealevel + h_ground
state, T_rel = [], []
def solout(t, X):
state.extend([X.copy()])
T_rel.extend([t])
if norm(X[:3]) < r_end: # Reached ground
return -1 # Ends the integration
elif X[6] < 1e-3: # Lost all mass [<1g]
print('Your meteoroid is dust!')
return -1 # Ends the integration
else:
return 0 # Continues integration
# Setup integrator
dt0 = 0.1
dt_max = 5 #60 # sec
solver = ode(EarthDynamics).set_integrator('dopri5', \
first_step=dt0, max_step=dt_max, rtol=1e-4) #'dop853',
solver.set_solout(solout)
solver.set_initial_value(X, 0).set_f_params(WindData, t0)
# Integrate with RK4 until impact
t_max = np.inf
solver.integrate(t_max)
# Assign the variables
T = np.array(T_rel) / (24 * 60 * 60) + t0
X_all = np.array(state).T
# Make sure we end on the ground
r_end = EarthRadius(ECEF2LLH(X_all[:3, -1:])[0]) + h_ground
fraction = (norm(X_all[:3, -2:-1]) - r_end) / (norm(X_all[:3, -2:-1]) -
norm(X_all[:3, -1:]))
if len(X_all[0]) > 1:
X_all[:, -1:] = X_all[:, -2:-1] + fraction * (X_all[:, -1:] -
X_all[:, -2:-1])
T[-1] = T[-2] + fraction * (T[-1] - T[-2])
Pos_ECI = X_all[:3]
Vel_ECI = X_all[3:6]
M = X_all[6]
rho = X_all[7]
A = X_all[8]
c_ml = X_all[9]
return {
'time_jd': T,
'pos_eci': Pos_ECI,
'vel_eci': Vel_ECI,
'mass': M,
'rho': rho,
'shape': A,
'c_ml': c_ml
}
def EarthDynamics(t, X, WindData, t0, return_abs_mag=False):
'''
The state rate dynamics are used in Runge-Kutta integration method to
calculate the next set of equinoctial element values.
'''
''' State Rates '''
# State parameter vector decomposed
Pos_ECI = np.vstack((X[:3]))
Vel_ECI = np.vstack((X[3:6]))
M = X[6]
rho = X[7]
A = X[8]
c_ml = X[9] # c_massloss = sigma*cd_hyp
t_jd = t0 + t / (24 * 60 * 60) # Absolute time [jd]
''' Primary Gravitational Acceleration '''
a_grav = gravity_vector(Pos_ECI)
''' Atmospheric Drag Perturbation - Better Model Needed '''
# Atmospheric velocity
if type(WindData) == Table: #1D vertical profile
[v_atm, rho_a, temp] = AtmosphericModel(WindData, Pos_ECI, t_jd)
else: #3D wind profile
Pos_ECEF = ECI2ECEF_pos(Pos_ECI, t_jd)
Pos_LLH = ECEF2LLH(Pos_ECEF)
[Wind_ENU, rho_a, temp] = WRF3D(WindData, Pos_LLH)
Wind_ECEF = ENU2ECEF(Pos_LLH[1], Pos_LLH[0]).dot(Wind_ENU)
v_atm = ECEF2ECI(Pos_ECEF, Wind_ECEF, t_jd)[1]
# Velocity relative to the atmosphere
v_rel = Vel_ECI - v_atm
v = norm(v_rel)
# # Constants for drag coeff
# d = 2 * np.sqrt(A / rho**(2./3) * M**(2./3))
# mu_a = viscosity(temp) # Air Viscosity (Pa.s)
# mach = v / SoS(temp) # Mach Number
# re = reynolds(v, rho_a, mu_a, d) # Reynolds Number
# kn = knudsen(mach, re) # Knudsen Number
# cd = dragcoef(re, mach, kn)#, A) # Drag Coefficient
# # cd = 2.0 # Approximation
# New drag equations - function that fits the literature
cd = dragcoeff(v, temp, rho_a, A)[0]
# cd = 1
# # New drag equations 2
# mach = v / SoS(temp) # Mach Number
# cd = dragcoefff(mach, A)
# Total drag perturbation
a_drag = -cd * A * rho_a * v * v_rel / (2 * M**(1. / 3) * rho**(2. / 3))
''' Total Perturbing Acceleration '''
a_tot = a_grav + a_drag
# Mass-loss equation
dm_dt = -c_ml * A * rho_a * v**3 * M**(2. / 3) / (2 * rho**(2. / 3))
# See (Sansom, 2019) as reference
if return_abs_mag: # sigma = c_ml / cd
lum = -X[10] * (v**2 / 2 + cd / c_ml) * dm_dt * 1e7
return -2.5 * np.log10(lum / 1.5e10)
''' State Rate Equation '''
X_dot = np.zeros(X.shape)
X_dot[:3] = Vel_ECI.flatten()
X_dot[3:6] = a_tot.flatten()
X_dot[6] = dm_dt
return X_dot
def write_rays_kml(obs_lat,
obs_lon,
obs_hei,
alt,
azi,
dist,
cam_name,
outputname,
colour='33ff0000'):
# Convert from spherical to cartesian
UV_ENU = np.vstack(
(np.cos(alt) * np.sin(azi), np.cos(alt) * np.cos(azi), np.sin(alt)))
UV_ECEF = ENU2ECEF(obs_lon, obs_lat).dot(UV_ENU)
Obs_ECEF = LLH2ECEF(np.vstack((obs_lat, obs_lon, obs_hei)))
Proj_ECEF = Obs_ECEF + dist * UV_ECEF
Proj_LLH = ECEF2LLH(Proj_ECEF)
[Proj_lat, Proj_lon, Proj_hei] = [Proj_LLH[0], Proj_LLH[1], Proj_LLH[2]]
# Open the file to be written.
f = open(outputname, 'w')
f.write('<?xml version="1.0" encoding="UTF-8"?>\n')
f.write('<kml xmlns="http://earth.google.com/kml/2.1">\n')
f.write('<Document>\n')
f.write('<open>1</open>\n')
f.write('<Placemark>\n')
f.write(' <Style id="camera">\n')
f.write(' <LineStyle>\n')
f.write(' <width>1</width>\n')
f.write(' </LineStyle>\n')
f.write(' <PolyStyle>\n')
f.write(' <color>' + str(colour) + '</color>\n')
f.write(' </PolyStyle>\n')
f.write(' </Style>\n')
f.write(' <styleUrl>#camera</styleUrl>\n')
f.write('<name>' + str(cam_name) + '</name>\n')
f.write('<Polygon>\n')
f.write(' <extrude>0</extrude>\n')
f.write(' <altitudeMode>absolute</altitudeMode>\n')
f.write(' <outerBoundaryIs>\n')
f.write(' <LinearRing>\n')
f.write(' <coordinates>\n')
f.write(' ' + str(np.rad2deg(obs_lon)) + ',' +
str(np.rad2deg(obs_lat)) + ',' + str(obs_hei) + '\n')
for i in range(len(Proj_lat)):
f.write(' ' + str(np.rad2deg(Proj_lon[i])) + "," +
str(np.rad2deg(Proj_lat[i])) + "," + str(Proj_hei[i]) + '\n')
f.write(' ' + str(np.rad2deg(obs_lon)) + ',' +
str(np.rad2deg(obs_lat)) + ',' + str(obs_hei) + '\n')
f.write(' </coordinates>\n')
f.write(' </LinearRing>\n')
f.write(' </outerBoundaryIs>\n')
f.write('</Polygon>\n')
f.write('</Placemark>\n')
f.write('</Document>\n')
f.write('</kml>\n')
f.close()
return {'fname': outputname, 'kml_type': 'rays', 'camera': cam_name}