def test_atmospheric_demise():
# Test an orbital decay that hits Earth. No analytic solution.
R = Earth.R.to(u.km).value
orbit = Orbit.circular(Earth, 230 * u.km)
t_decay = 48.2179 * u.d # not an analytic value
# parameters of a body
C_D = 2.2 # dimentionless (any value would do)
A_over_m = ((np.pi / 4.0) * (u.m**2) / (100 * u.kg)).to_value(
u.km**2 / u.kg) # km^2/kg
# parameters of the atmosphere
rho0 = rho0_earth.to(u.kg / u.km**3).value # kg/km^3
H0 = H0_earth.to(u.km).value # km
tofs = [365] * u.d # actually hits the ground a bit after day 48
lithobrake_event = LithobrakeEvent(R)
events = [lithobrake_event]
rr, _ = cowell(
Earth.k,
orbit.r,
orbit.v,
tofs,
ad=atmospheric_drag_exponential,
R=R,
C_D=C_D,
A_over_m=A_over_m,
H0=H0,
rho0=rho0,
events=events,
)
assert_quantity_allclose(norm(rr[0].to(u.km).value), R,
atol=1) # below 1km
assert_quantity_allclose(lithobrake_event.last_t, t_decay, rtol=1e-2)
# make sure having the event not firing is ok
tofs = [1] * u.d
lithobrake_event = LithobrakeEvent(R)
events = [lithobrake_event]
rr, _ = cowell(
Earth.k,
orbit.r,
orbit.v,
tofs,
ad=atmospheric_drag_exponential,
R=R,
C_D=C_D,
A_over_m=A_over_m,
H0=H0,
rho0=rho0,
events=events,
)
assert lithobrake_event.last_t == tofs[-1]
def test_atmospheric_drag_exponential():
# http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node94.html#sair (10.148)
# Given the expression for \dot{r} / r, aproximate \Delta r \approx F_r * \Delta t
R = Earth.R.to(u.km).value
k = Earth.k.to(u.km**3 / u.s**2).value
# Parameters of a circular orbit with h = 250 km (any value would do, but not too small)
orbit = Orbit.circular(Earth, 250 * u.km)
r0, _ = orbit.rv()
r0 = r0.to(u.km).value
# Parameters of a body
C_D = 2.2 # dimentionless (any value would do)
A_over_m = ((np.pi / 4.0) * (u.m**2) / (100 * u.kg)).to_value(
u.km**2 / u.kg) # km^2/kg
B = C_D * A_over_m
# Parameters of the atmosphere
rho0 = rho0_earth.to(u.kg / u.km**3).value # kg/km^3
H0 = H0_earth.to(u.km).value # km
tof = 100000 # s
dr_expected = -B * rho0 * np.exp(-(norm(r0) - R) / H0) * np.sqrt(
k * norm(r0)) * tof
# Assuming the atmospheric decay during tof is small,
# dr_expected = F_r * tof (Newton's integration formula), where
# F_r = -B rho(r) |r|^2 sqrt(k / |r|^3) = -B rho(r) sqrt(k |r|)
def f(t0, u_, k):
du_kep = func_twobody(t0, u_, k)
ax, ay, az = atmospheric_drag_exponential(t0,
u_,
k,
R=R,
C_D=C_D,
A_over_m=A_over_m,
H0=H0,
rho0=rho0)
du_ad = np.array([0, 0, 0, ax, ay, az])
return du_kep + du_ad
rr, _ = cowell(
Earth.k,
orbit.r,
orbit.v,
[tof] * u.s,
f=f,
)
assert_quantity_allclose(norm(rr[0].to(u.km).value) - norm(r0),
dr_expected,
rtol=1e-2)
def test_atmospheric_drag():
# http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node94.html#sair (10.148)
# given the expression for \dot{r} / r, aproximate \Delta r \approx F_r * \Delta t
R = Earth.R.to(u.km).value
k = Earth.k.to(u.km**3 / u.s**2).value
# parameters of a circular orbit with h = 250 km (any value would do, but not too small)
orbit = Orbit.circular(Earth, 250 * u.km)
r0, _ = orbit.rv()
r0 = r0.to(u.km).value
# parameters of a body
C_D = 2.2 # dimentionless (any value would do)
A = ((np.pi / 4.0) * (u.m**2)).to(u.km**2).value # km^2
m = 100 # kg
B = C_D * A / m
# parameters of the atmosphere
rho0 = rho0_earth.to(u.kg / u.km**3).value # kg/km^3
H0 = H0_earth.to(u.km).value # km
tof = 100000 # s
dr_expected = -B * rho0 * np.exp(-(norm(r0) - R) / H0) * np.sqrt(
k * norm(r0)) * tof
# assuming the atmospheric decay during tof is small,
# dr_expected = F_r * tof (Newton's integration formula), where
# F_r = -B rho(r) |r|^2 sqrt(k / |r|^3) = -B rho(r) sqrt(k |r|)
rr, _ = cowell(
Earth.k,
orbit.r,
orbit.v,
[tof] * u.s,
ad=atmospheric_drag,
R=R,
C_D=C_D,
A=A,
m=m,
H0=H0,
rho0=rho0,
)
assert_quantity_allclose(norm(rr[0].to(u.km).value) - norm(r0),
dr_expected,
rtol=1e-2)
def test_altitude_crossing():
# Test decreasing altitude cross over Earth. No analytic solution.
R = Earth.R.to(u.km).value
orbit = Orbit.circular(Earth, 230 * u.km)
t_flight = 48.209538 * u.d
# Parameters of a body
C_D = 2.2 # Dimensionless (any value would do)
A_over_m = ((np.pi / 4.0) * (u.m**2) / (100 * u.kg)).to_value(
u.km**2 / u.kg) # km^2/kg
# Parameters of the atmosphere
rho0 = rho0_earth.to(u.kg / u.km**3).value # kg/km^3
H0 = H0_earth.to(u.km).value # km
tofs = [50] * u.d
thresh_alt = 50 # km
altitude_cross_event = AltitudeCrossEvent(thresh_alt, R)
events = [altitude_cross_event]
def f(t0, u_, k):
du_kep = func_twobody(t0, u_, k)
ax, ay, az = atmospheric_drag_exponential(t0,
u_,
k,
R=R,
C_D=C_D,
A_over_m=A_over_m,
H0=H0,
rho0=rho0)
du_ad = np.array([0, 0, 0, ax, ay, az])
return du_kep + du_ad
rr, _ = cowell(
Earth.k,
orbit.r,
orbit.v,
tofs,
events=events,
f=f,
)
assert_quantity_allclose(norm(rr[0].to(u.km).value) - thresh_alt, R)
assert_quantity_allclose(altitude_cross_event.last_t, t_flight, rtol=1e-2)
def setup(self):
from poliastro.twobody import Orbit
self.R = Earth.R.to(u.km).value
self.k = Earth.k.to(u.km**3 / u.s**2).value
self.orbit = Orbit.circular(Earth, 250 * u.km)
# parameters of a body
self.C_D = 2.2 # dimentionless (any value would do)
self.A_over_m = ((np.pi / 4.0) * (u.m**2) / (100 * u.kg)).to_value(
u.km**2 / u.kg) # km^2/kg
self.B = self.C_D * self.A_over_m
# parameters of the atmosphere
self.rho0 = rho0_earth.to(u.kg / u.km**3) # kg/km^3
self.H0 = H0_earth.to(u.km).value
self.tof = [60.0] * u.s
def test_atmospheric_demise():
# Test an orbital decay that hits Earth. No analytic solution.
R = Earth.R.to(u.km).value
orbit = Orbit.circular(Earth, 230 * u.km)
t_decay = 48.2179 * u.d
# parameters of a body
C_D = 2.2 # dimentionless (any value would do)
A = ((np.pi / 4.0) * (u.m**2)).to(u.km**2).value # km^2
m = 100 # kg
# parameters of the atmosphere
rho0 = rho0_earth.to(u.kg / u.km**3).value # kg/km^3
H0 = H0_earth.to(u.km).value # km
tofs = [365] * u.d # actually hits the ground a bit after day 48
lithobrake_event = LithobrakeEvent(R)
events = [lithobrake_event]
rr, _ = cowell(
Earth.k,
orbit.r,
orbit.v,
tofs,
ad=atmospheric_drag,
R=R,
C_D=C_D,
A=A,
m=m,
H0=H0,
rho0=rho0,
events=events,
)
assert_quantity_allclose(norm(rr[0].to(u.km).value), R,
atol=1) # below 1km
# last_t is not an analytic value
assert_quantity_allclose(lithobrake_event.last_t, t_decay, rtol=1e-2)
# adder = 2*np.pi * u.rad
# for i in range(1,len(lons)):
# if np.abs(lons[i].value-lons[i-1].value) > 1:
# sgn=np.sign(lons[i].value-lons[i-1].value)
# lons[i:] += -sgn*adder
#interpolation of manipulated and folded points
#flats = interp1d(tofs,lats)
#flons = interp1d(tofs,lons)
#tofs = np.linspace(0,T*3600*24*u.s,int(T*3600*24/dt))
#lats = flats(tofs) * u.rad
#lons = (lons.value) % (2*np.pi) * u.rad
return lons,lats
rho0 = rho0_earth.to(u.kg / u.km ** 3).value
H0 = H0_earth.to(u.km).value
@jit
def J2_and_drag(t0, state, k, J2, R, C_D, A_over_m, H0, rho0):
return J2_perturbation(t0, state, k, J2, R) + atmospheric_drag_exponential(
t0, state, k, R, C_D, A_over_m, H0, rho0
)
#C_D = 2.2 # dimentionless (any value would do)
#Min kommentar: ändrade från den betämda luftmotståndskonstanten C_D = 2 till att testa olika värden(värdena 1.02 till 2.0) i en vektor.
#Min kommentar: Dessutom lade jag till en for-loop för att programmet skulle ge mig svar för olika värden på C_D.
#C_D = np.array([1.22, 1.44, 1.66 ])
C_D = np.arange(
1.50, 1.6, 0.1
) #Min kommentar: Jag bytade från np.array till np.arange(börjar:1.5,slutar2.0,hoppar0.1)
for x in C_D:
A_over_m = ((np.pi / 4.0) * (u.m**2) / (100 * u.kg)).to_value(
u.km**2 / u.kg
) # km^2/kg #Min kommentar: Här tror jag vi antar att föremålet väger 100kg, men jag förstår inte area-beräkningen?
B = x * A_over_m #Min kommentar: Skrev in x istället för C_D
# parameters of the atmosphere
rho0 = rho0_earth.to(u.kg / u.km**3).value # kg/km^3
H0 = H0_earth.to(
u.km
).value #Min kommentar: Ändras atmosfärens egenskaper ju högre radien är i det här programmet?
#[<matplotlib.lines.Line2D at 0x7ffb5f511048>]
#Orbital Decay
#If atmospheric drag causes the orbit to fully decay, additional code is needed to stop the integration when the satellite reaches the surface.
#Please note that you will likely want to use a more sophisticated atmosphere model than the one in atmospheric_drag for these sorts of computations.
orbit = Orbit.circular(
Earth, 230 * u.km, epoch=Time(0.0, format="jd", scale="tdb")
) #Min kommentar: Här tror jag att jag kan ändra på värdet hos radien på omloppsbanan
tofs = TimeDelta(
np.linspace(0 * u.h, 100 * u.d, num=200)
) #Min kommentar: Här tror jag deltatiden beskrivs, att den mäter mellan noll timmar till ett max antal dagar, samt att den mäter 2000 gånger.