def test_cycle_BLCartesianDifferential(bl_coords):
M = 1e24
a = 0.75
bl_diff = bl_coords
cart_diff = bl_diff.convert_cartesian(M=M, a=a)
bl_diff2 = CartesianConversion(*cart_diff).convert_bl(M=M, a=a)
assert_allclose(bl_diff2, bl_diff.values(), rtol=0.0, atol=1e-6)
def cartesian_coords():
return CartesianConversion(t=0.,
x=10 / np.sqrt(2),
y=10 / np.sqrt(2),
z=0.,
v_x=-190 / np.sqrt(2),
v_y=210 / np.sqrt(2),
v_z=200.)
def test_calculate_trajectory0_kerrnewman():
# Based on the revolution of earth around sun
# Data from https://en.wikipedia.org/wiki/Earth%27s_orbit
# Initialized with cartesian coordinates
# Function returning cartesian coordinates
t = 0.
M = 1.989e30
a = 0.
Q = 0.
q = 0.
distance_at_perihelion = 147.10e9
speed_at_perihelion = 30290
x_sph = CartesianConversion(distance_at_perihelion / np.sqrt(2),
distance_at_perihelion / np.sqrt(2), 0.,
-speed_at_perihelion / np.sqrt(2),
speed_at_perihelion / np.sqrt(2),
0.).convert_spherical()
x_vec = x_sph[:3]
v_vec = x_sph[3:]
mkn_cov = KerrNewman(coords="BL", M=M, a=a, Q=Q, q=q)
x_4vec = four_position(t, x_vec)
mkn_cov_mat = mkn_cov.metric_covariant(x_4vec)
init_vec = stacked_vec(mkn_cov_mat, t, x_vec, v_vec, time_like=True)
end_lambda = 3.154e7
geod = Geodesic(
metric=mkn_cov,
init_vec=init_vec,
end_lambda=end_lambda,
step_size=end_lambda / 1.5e3,
)
ans = geod.trajectory
# velocity should be 29.29 km/s at aphelion(where r is max)
R = np.sqrt(ans[:, 1]**2 + ans[:, 2]**2 + ans[:, 3]**2)
i = np.argmax(R) # index where radial distance is max
v_aphelion = ((np.sqrt(ans[i, 5]**2 + ans[i, 6]**2 + ans[i, 7]**2) *
(u.m / u.s)).to(u.km / u.s)).value
assert_allclose(v_aphelion, 29.29, rtol=0.01)
def test_calculate_trajectory3_schwarzschild():
# same test as with test_calculate_trajectory2_schwarzschild(),
# but initialized with cartesian coordinates
# and function returning cartesian coordinates
t = 0.
M = 1.989e30
distance_at_perihelion = 147.10e9
speed_at_perihelion = 30290
x_sph = CartesianConversion(distance_at_perihelion / np.sqrt(2),
distance_at_perihelion / np.sqrt(2), 0.,
-speed_at_perihelion / np.sqrt(2),
speed_at_perihelion / np.sqrt(2),
0.).convert_spherical()
x_vec = x_sph[:3]
v_vec = x_sph[3:]
ms_cov = Schwarzschild(M=M)
x_4vec = four_position(t, x_vec)
ms_cov_mat = ms_cov.metric_covariant(x_4vec)
init_vec = stacked_vec(ms_cov_mat, t, x_vec, v_vec, time_like=True)
end_lambda = 3.154e7
geod = Geodesic(
metric=ms_cov,
init_vec=init_vec,
end_lambda=end_lambda,
step_size=end_lambda / 2e3,
)
ans = geod.trajectory
# velocity should be 29.29 km/s at aphelion(where r is max)
R = np.sqrt(ans[:, 1]**2 + ans[:, 2]**2 + ans[:, 3]**2)
i = np.argmax(R) # index where radial distance is max
v_aphelion = ((np.sqrt(ans[i, 5]**2 + ans[i, 6]**2 + ans[i, 7]**2) *
(u.m / u.s)).to(u.km / u.s)).value
assert_allclose(v_aphelion, 29.29, rtol=0.01)
def cartesian_coords():
return CartesianConversion(
10 / np.sqrt(2), 10 / np.sqrt(2), 0, -190 / np.sqrt(2), 210 / np.sqrt(2), 200.0
)