def get_observer_look(self, utc_time, lon, lat, alt):
"""Calculate observers look angle to a satellite.
http://celestrak.com/columns/v02n02/
utc_time: Observation time (datetime object)
lon: Longitude of observer position on ground in degrees east
lat: Latitude of observer position on ground in degrees north
alt: Altitude above sea-level (geoid) of observer position on ground in km
Return: (Azimuth, Elevation)
"""
utc_time = dt2np(utc_time)
(pos_x, pos_y, pos_z), (vel_x, vel_y,
vel_z) = self.get_position(utc_time,
normalize=False)
(opos_x, opos_y, opos_z), (ovel_x, ovel_y, ovel_z) = \
astronomy.observer_position(utc_time, lon, lat, alt)
lon = np.deg2rad(lon)
lat = np.deg2rad(lat)
theta = (astronomy.gmst(utc_time) + lon) % (2 * np.pi)
rx = pos_x - opos_x
ry = pos_y - opos_y
rz = pos_z - opos_z
sin_lat = np.sin(lat)
cos_lat = np.cos(lat)
sin_theta = np.sin(theta)
cos_theta = np.cos(theta)
top_s = sin_lat * cos_theta * rx + \
sin_lat * sin_theta * ry - cos_lat * rz
top_e = -sin_theta * rx + cos_theta * ry
top_z = cos_lat * cos_theta * rx + \
cos_lat * sin_theta * ry + sin_lat * rz
az_ = np.arctan(-top_e / top_s)
az_ = np.where(top_s > 0, az_ + np.pi, az_)
az_ = np.where(az_ < 0, az_ + 2 * np.pi, az_)
rg_ = np.sqrt(rx * rx + ry * ry + rz * rz)
el_ = np.arcsin(top_z / rg_)
return np.rad2deg(az_), np.rad2deg(el_)
def get_observer_look(self, utc_time, lon, lat, alt):
"""Calculate observers look angle to a satellite.
http://celestrak.com/columns/v02n02/
utc_time: Observation time (datetime object)
lon: Longitude of observer position on ground in degrees east
lat: Latitude of observer position on ground in degrees north
alt: Altitude above sea-level (geoid) of observer position on ground in km
Return: (Azimuth, Elevation)
"""
utc_time = dt2np(utc_time)
(pos_x, pos_y, pos_z), (vel_x, vel_y, vel_z) = self.get_position(
utc_time, normalize=False)
(opos_x, opos_y, opos_z), (ovel_x, ovel_y, ovel_z) = \
astronomy.observer_position(utc_time, lon, lat, alt)
lon = np.deg2rad(lon)
lat = np.deg2rad(lat)
theta = (astronomy.gmst(utc_time) + lon) % (2 * np.pi)
rx = pos_x - opos_x
ry = pos_y - opos_y
rz = pos_z - opos_z
sin_lat = np.sin(lat)
cos_lat = np.cos(lat)
sin_theta = np.sin(theta)
cos_theta = np.cos(theta)
top_s = sin_lat * cos_theta * rx + \
sin_lat * sin_theta * ry - cos_lat * rz
top_e = -sin_theta * rx + cos_theta * ry
top_z = cos_lat * cos_theta * rx + \
cos_lat * sin_theta * ry + sin_lat * rz
az_ = np.arctan(-top_e / top_s)
az_ = np.where(top_s > 0, az_ + np.pi, az_)
az_ = np.where(az_ < 0, az_ + 2 * np.pi, az_)
rg_ = np.sqrt(rx * rx + ry * ry + rz * rz)
el_ = np.arcsin(top_z / rg_)
return np.rad2deg(az_), np.rad2deg(el_)
def propagate(self, utc_time):
kep = {}
# get the time delta in minutes
# ts = astronomy._days(utc_time - self.t_0) * XMNPDA
# print utc_time.shape
# print self.t_0
utc_time = dt2np(utc_time)
ts = (utc_time - self.t_0) / np.timedelta64(1, 'm')
em = self.eo
xinc = self.xincl
xmp = self.xmo + self.xmdot * ts
xnode = self.xnodeo + ts * (self.xnodot + ts * self.xnodcf)
omega = self.omegao + self.omgdot * ts
if self.mode == SGDP4_ZERO_ECC:
raise NotImplementedError('Mode SGDP4_ZERO_ECC not implemented')
elif self.mode == SGDP4_NEAR_SIMP:
raise NotImplementedError('Mode "Near-space, simplified equations"'
' not implemented')
elif self.mode == SGDP4_NEAR_NORM:
delm = self.xmcof * \
((1.0 + self.eta * np.cos(xmp))**3 - self.delmo)
temp0 = ts * self.omgcof + delm
xmp += temp0
omega -= temp0
tempa = 1.0 - \
(ts *
(self.c1 + ts * (self.d2 + ts * (self.d3 + ts * self.d4))))
tempe = self.bstar * \
(self.c4 * ts + self.c5 * (np.sin(xmp) - self.sinXMO))
templ = ts * ts * \
(self.t2cof + ts *
(self.t3cof + ts * (self.t4cof + ts * self.t5cof)))
a = self.aodp * tempa**2
e = em - tempe
xl = xmp + omega + xnode + self.xnodp * templ
else:
raise NotImplementedError('Deep space calculations not supported')
if np.any(a < 1):
raise Exception('Satellite crashed at time %s', utc_time)
elif np.any(e < ECC_LIMIT_LOW):
raise ValueError(
'Satellite modified eccentricity too low: %s < %e' %
(str(e[e < ECC_LIMIT_LOW]), ECC_LIMIT_LOW))
e = np.where(e < ECC_EPS, ECC_EPS, e)
e = np.where(e > ECC_LIMIT_HIGH, ECC_LIMIT_HIGH, e)
beta2 = 1.0 - e**2
# Long period periodics
sinOMG = np.sin(omega)
cosOMG = np.cos(omega)
temp0 = 1.0 / (a * beta2)
axn = e * cosOMG
ayn = e * sinOMG + temp0 * self.aycof
xlt = xl + temp0 * self.xlcof * axn
elsq = axn**2 + ayn**2
if np.any(elsq >= 1):
raise Exception('e**2 >= 1 at %s', utc_time)
kep['ecc'] = np.sqrt(elsq)
epw = np.fmod(xlt - xnode, 2 * np.pi)
# needs a copy in case of an array
capu = np.array(epw)
maxnr = kep['ecc']
for i in range(10):
sinEPW = np.sin(epw)
cosEPW = np.cos(epw)
ecosE = axn * cosEPW + ayn * sinEPW
esinE = axn * sinEPW - ayn * cosEPW
f = capu - epw + esinE
if np.all(np.abs(f) < NR_EPS):
break
df = 1.0 - ecosE
# 1st order Newton-Raphson correction.
nr = f / df
# 2nd order Newton-Raphson correction.
nr = np.where(np.logical_and(i == 0,
np.abs(nr) > 1.25 * maxnr),
np.sign(nr) * maxnr, f / (df + 0.5 * esinE * nr))
epw += nr
# Short period preliminary quantities
temp0 = 1.0 - elsq
betal = np.sqrt(temp0)
pl = a * temp0
r = a * (1.0 - ecosE)
invR = 1.0 / r
temp2 = a * invR
temp3 = 1.0 / (1.0 + betal)
cosu = temp2 * (cosEPW - axn + ayn * esinE * temp3)
sinu = temp2 * (sinEPW - ayn - axn * esinE * temp3)
u = np.arctan2(sinu, cosu)
sin2u = 2.0 * sinu * cosu
cos2u = 2.0 * cosu**2 - 1.0
temp0 = 1.0 / pl
temp1 = CK2 * temp0
temp2 = temp1 * temp0
# Update for short term periodics to position terms.
rk = r * (1.0 - 1.5 * temp2 * betal * self.x3thm1) + \
0.5 * temp1 * self.x1mth2 * cos2u
uk = u - 0.25 * temp2 * self.x7thm1 * sin2u
xnodek = xnode + 1.5 * temp2 * self.cosIO * sin2u
xinck = xinc + 1.5 * temp2 * self.cosIO * self.sinIO * cos2u
if np.any(rk < 1):
raise Exception('Satellite crashed at time %s', utc_time)
temp0 = np.sqrt(a)
temp2 = XKE / (a * temp0)
rdotk = ((XKE * temp0 * esinE * invR -
temp2 * temp1 * self.x1mth2 * sin2u) *
(XKMPER / AE * XMNPDA / 86400.0))
rfdotk = ((XKE * np.sqrt(pl) * invR + temp2 * temp1 *
(self.x1mth2 * cos2u + 1.5 * self.x3thm1)) *
(XKMPER / AE * XMNPDA / 86400.0))
kep['radius'] = rk * XKMPER / AE
kep['theta'] = uk
kep['eqinc'] = xinck
kep['ascn'] = xnodek
kep['argp'] = omega
kep['smjaxs'] = a * XKMPER / AE
kep['rdotk'] = rdotk
kep['rfdotk'] = rfdotk
return kep
def jdays2000(utc_time):
"""Get the days since year 2000.
"""
return _days(dt2np(utc_time) - np.datetime64('2000-01-01T12:00'))
def propagate(self, utc_time):
kep = {}
# get the time delta in minutes
# ts = astronomy._days(utc_time - self.t_0) * XMNPDA
# print utc_time.shape
# print self.t_0
utc_time = dt2np(utc_time)
ts = (utc_time - self.t_0) / np.timedelta64(1, 'm')
em = self.eo
xinc = self.xincl
xmp = self.xmo + self.xmdot * ts
xnode = self.xnodeo + ts * (self.xnodot + ts * self.xnodcf)
omega = self.omegao + self.omgdot * ts
if self.mode == SGDP4_ZERO_ECC:
raise NotImplementedError('Mode SGDP4_ZERO_ECC not implemented')
elif self.mode == SGDP4_NEAR_SIMP:
raise NotImplementedError('Mode "Near-space, simplified equations"'
' not implemented')
elif self.mode == SGDP4_NEAR_NORM:
delm = self.xmcof * \
((1.0 + self.eta * np.cos(xmp))**3 - self.delmo)
temp0 = ts * self.omgcof + delm
xmp += temp0
omega -= temp0
tempa = 1.0 - \
(ts *
(self.c1 + ts * (self.d2 + ts * (self.d3 + ts * self.d4))))
tempe = self.bstar * \
(self.c4 * ts + self.c5 * (np.sin(xmp) - self.sinXMO))
templ = ts * ts * \
(self.t2cof + ts *
(self.t3cof + ts * (self.t4cof + ts * self.t5cof)))
a = self.aodp * tempa**2
e = em - tempe
xl = xmp + omega + xnode + self.xnodp * templ
else:
raise NotImplementedError('Deep space calculations not supported')
if np.any(a < 1):
raise Exception('Satellite crased at time %s', utc_time)
elif np.any(e < ECC_LIMIT_LOW):
raise ValueError('Satellite modified eccentricity to low: %s < %e'
% (str(e[e < ECC_LIMIT_LOW]), ECC_LIMIT_LOW))
e = np.where(e < ECC_EPS, ECC_EPS, e)
e = np.where(e > ECC_LIMIT_HIGH, ECC_LIMIT_HIGH, e)
beta2 = 1.0 - e**2
# Long period periodics
sinOMG = np.sin(omega)
cosOMG = np.cos(omega)
temp0 = 1.0 / (a * beta2)
axn = e * cosOMG
ayn = e * sinOMG + temp0 * self.aycof
xlt = xl + temp0 * self.xlcof * axn
elsq = axn**2 + ayn**2
if np.any(elsq >= 1):
raise Exception('e**2 >= 1 at %s', utc_time)
kep['ecc'] = np.sqrt(elsq)
epw = np.fmod(xlt - xnode, 2 * np.pi)
# needs a copy in case of an array
capu = np.array(epw)
maxnr = kep['ecc']
for i in range(10):
sinEPW = np.sin(epw)
cosEPW = np.cos(epw)
ecosE = axn * cosEPW + ayn * sinEPW
esinE = axn * sinEPW - ayn * cosEPW
f = capu - epw + esinE
if np.all(np.abs(f) < NR_EPS):
break
df = 1.0 - ecosE
# 1st order Newton-Raphson correction.
nr = f / df
# 2nd order Newton-Raphson correction.
nr = np.where(np.logical_and(i == 0, np.abs(nr) > 1.25 * maxnr),
np.sign(nr) * maxnr,
f / (df + 0.5 * esinE * nr))
epw += nr
# Short period preliminary quantities
temp0 = 1.0 - elsq
betal = np.sqrt(temp0)
pl = a * temp0
r = a * (1.0 - ecosE)
invR = 1.0 / r
temp2 = a * invR
temp3 = 1.0 / (1.0 + betal)
cosu = temp2 * (cosEPW - axn + ayn * esinE * temp3)
sinu = temp2 * (sinEPW - ayn - axn * esinE * temp3)
u = np.arctan2(sinu, cosu)
sin2u = 2.0 * sinu * cosu
cos2u = 2.0 * cosu**2 - 1.0
temp0 = 1.0 / pl
temp1 = CK2 * temp0
temp2 = temp1 * temp0
# Update for short term periodics to position terms.
rk = r * (1.0 - 1.5 * temp2 * betal * self.x3thm1) + \
0.5 * temp1 * self.x1mth2 * cos2u
uk = u - 0.25 * temp2 * self.x7thm1 * sin2u
xnodek = xnode + 1.5 * temp2 * self.cosIO * sin2u
xinck = xinc + 1.5 * temp2 * self.cosIO * self.sinIO * cos2u
if np.any(rk < 1):
raise Exception('Satellite crashed at time %s', utc_time)
temp0 = np.sqrt(a)
temp2 = XKE / (a * temp0)
rdotk = ((XKE * temp0 * esinE * invR - temp2 * temp1 * self.x1mth2 * sin2u) *
(XKMPER / AE * XMNPDA / 86400.0))
rfdotk = ((XKE * np.sqrt(pl) * invR + temp2 * temp1 *
(self.x1mth2 * cos2u + 1.5 * self.x3thm1)) *
(XKMPER / AE * XMNPDA / 86400.0))
kep['radius'] = rk * XKMPER / AE
kep['theta'] = uk
kep['eqinc'] = xinck
kep['ascn'] = xnodek
kep['argp'] = omega
kep['smjaxs'] = a * XKMPER / AE
kep['rdotk'] = rdotk
kep['rfdotk'] = rfdotk
return kep
def days_since_2000(utc_time):
"""Returns the days since year 2000.
"""
return days_from_dt(dt2np(utc_time) - np.datetime64('2000-01-01T12:00'))
def jdays2000(utc_time):
"""Get the days since year 2000.
"""
return _days(dt2np(utc_time) - np.datetime64('2000-01-01T12:00'))
def findtask(norad_id, observation_time, LAT, LONG, ALT):
id = norad_id
id = id.rjust(5)
counter = 0
with open('3le.txt', 'r') as TLEs:
for line in TLEs:
if line[2:7] == id and counter == 0:
# print(line)
line1 = line
counter = 1
elif line[2:7] == id and counter == 1:
line2 = line
# print(line)
break
R_site_ECI, V_site_ECI = observer_position(observation_time, LONG, LAT, ALT)
sat = satellite.get_sat(line1, line2)
R_sat_ECI, V_sat_ECI = sat.propagate(observation_time.year, observation_time.month, observation_time.day, observation_time.hour, observation_time.minute,
(observation_time.second + observation_time.microsecond * 10 ** (-6)))
delta_R = np.array([[R_sat_ECI[0] - R_site_ECI[0]], [R_sat_ECI[1] - R_site_ECI[1]], [R_sat_ECI[2] - R_site_ECI[2]]])
delta_V = np.array([[V_sat_ECI[0] - V_site_ECI[0]], [V_sat_ECI[1] - V_site_ECI[1]], [V_sat_ECI[2] - V_site_ECI[2]]])
utc_time = dt2np(observation_time)
lon = np.deg2rad(LONG)
lat = np.deg2rad(LAT)
theta = (astronomy.gmst(utc_time) + lon) % (2 * np.pi)
sin_lat = np.sin(lat)
cos_lat = np.cos(lat)
sin_theta = np.sin(theta)
cos_theta = np.cos(theta)
top_s = sin_lat * cos_theta * delta_R[0] + \
sin_lat * sin_theta * delta_R[1] - cos_lat * delta_R[2]
top_e = -sin_theta * delta_R[0] + cos_theta * delta_R[1]
top_z = cos_lat * cos_theta * delta_R[0] + \
cos_lat * sin_theta * delta_R[1] + sin_lat * delta_R[2]
az_ = np.arctan(-top_e / top_s)
az_ = np.where(top_s > 0, az_ + np.pi, az_)
az_ = np.where(az_ < 0, az_ + 2 * np.pi, az_)
rg_ = np.sqrt(top_s * top_s + top_e * top_e + top_z * top_z)
el_ = np.arcsin(top_z / rg_)
AZ = np.rad2deg(az_)
EL = np.rad2deg(el_)
mag_delta_R = math.sqrt(delta_R[0] ** 2 + delta_R[1] ** 2 + delta_R[2] ** 2)
unit_delta_R = np.array([delta_R[0] / mag_delta_R, delta_R[1] / mag_delta_R, delta_R[2] / mag_delta_R])
V_orth_R_ECI = logical_cross(logical_cross(unit_delta_R, delta_V), unit_delta_R)
total_look_angular_rate = (math.sqrt(V_orth_R_ECI[0] ** 2 + V_orth_R_ECI[1] ** 2 + V_orth_R_ECI[2] ** 2) / \
math.sqrt(delta_R[0] ** 2 + delta_R[1] ** 2 + delta_R[2] ** 2)) * (180.0 / math.pi)
exposure_time = 0.955/total_look_angular_rate
if exposure_time > 10:
exposure_time = 10
return [AZ[0], EL[0], total_look_angular_rate, exposure_time]
