def test_calculate_trajectory2():
# based on the revolution of earth around sun
# data from https://en.wikipedia.org/wiki/Earth%27s_orbit
M = 1.989e30 * u.kg
distance_at_perihelion = 147.10e6 * u.km
speed_at_perihelion = 30.29 * u.km / u.s
angular_vel = (speed_at_perihelion / distance_at_perihelion) * u.rad
sph_obj = SphericalDifferential(
distance_at_perihelion,
np.pi / 2 * u.rad,
0 * u.rad,
0 * u.km / u.s,
0 * u.rad / u.s,
angular_vel,
)
end_lambda = ((1 * u.year).to(u.s)).value
cl = Schwarzschild.from_coords(sph_obj, M)
ans = cl.calculate_trajectory(
start_lambda=0.0,
end_lambda=end_lambda,
OdeMethodKwargs={"stepsize": end_lambda / 2e3},
)[1]
# velocity should be 29.29 km/s at apehelion(where r is max)
i = np.argmax(ans[:, 1]) # index whre radial distance is max
v_apehelion = (((ans[i][1] * ans[i][7]) * (u.m / u.s)).to(u.km / u.s)).value
assert_allclose(v_apehelion, 29.29, rtol=0.01)
def test_calculate_trajectory3():
# same test as with test_calculate_trajectory2(),
# but initialialized with cartesian coordinates
# and function returning cartesian coordinates
M = 1.989e30 * u.kg
distance_at_perihelion = 147.10e6 * u.km
speed_at_perihelion = 30.29 * u.km / u.s
cart_obj = CartesianDifferential(
distance_at_perihelion / np.sqrt(2),
distance_at_perihelion / np.sqrt(2),
0 * u.km,
-1 * speed_at_perihelion / np.sqrt(2),
speed_at_perihelion / np.sqrt(2),
0 * u.km / u.h,
)
end_lambda = ((1 * u.year).to(u.s)).value
cl = Schwarzschild.from_coords(cart_obj, M)
ans = cl.calculate_trajectory(
start_lambda=0.0,
end_lambda=end_lambda,
return_cartesian=True,
OdeMethodKwargs={"stepsize": end_lambda / 2e3},
)[1]
# velocity should be 29.29 km/s at apehelion(where r is max)
R = np.sqrt(ans[:, 1] ** 2 + ans[:, 2] ** 2 + ans[:, 3] ** 2)
i = np.argmax(R) # index whre radial distance is max
v_apehelion = (
(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_apehelion, 29.29, rtol=0.01)
def get_schwarz():
schwarz_obj = {}
schwarz_ans = {}
for object in bodies_list:
if object != 'sun':
schwarz_obj[object] = Schwarzschild.from_coords(
sd_obj[object], mass['sun'])
schwarz_ans[object] = schwarz_obj[object].calculate_trajectory(
end_lambda=end_lambda['earth'],
OdeMethodKwargs={"stepsize": stepsize['earth']},
return_cartesian=True)
return schwarz_obj, schwarz_ans
def test_calculate_trajectory_iterator(
coords, time, M, start_lambda, end_lambda, OdeMethodKwargs, return_cartesian
):
cl1 = Schwarzschild.from_coords(coords, M, time)
arr1 = cl1.calculate_trajectory(
start_lambda=start_lambda,
end_lambda=end_lambda,
OdeMethodKwargs=OdeMethodKwargs,
return_cartesian=return_cartesian,
)[1]
cl2 = Schwarzschild.from_coords(coords, M, time)
it = cl2.calculate_trajectory_iterator(
start_lambda=start_lambda,
OdeMethodKwargs=OdeMethodKwargs,
return_cartesian=return_cartesian,
)
arr2_list = list()
for _, val in zip(range(50), it):
arr2_list.append(val[1])
arr2 = np.array(arr2_list)
assert_allclose(arr1[:50, :], arr2, rtol=1e-10)
def test_calculate_trajectory(
coords, time, M, start_lambda, end_lambda, OdeMethodKwargs
):
cl = Schwarzschild.from_coords(coords, M, time)
ans = cl.calculate_trajectory(
start_lambda=start_lambda,
end_lambda=end_lambda,
OdeMethodKwargs=OdeMethodKwargs,
)
ans = ans[1]
testarray = list()
for i in ans:
g = schwarzschild_utils.metric(i[1], i[2], M.value)
testarray.append(
g[0][0] * (i[4] ** 2)
+ g[1][1] * (i[5] ** 2)
+ g[2][2] * (i[6] ** 2)
+ g[3][3] * (i[7] ** 2)
)
testarray = np.array(testarray, dtype=float)
comparearray = np.ones(shape=ans[:, 4].shape, dtype=float)
assert_allclose(testarray, comparearray, 1e-4)
def test_calculate_trajectory_iterator_RuntimeWarning2():
sph_obj = SphericalDifferential(
306 * u.m,
np.pi / 2 * u.rad,
np.pi / 3 * u.rad,
0 * u.m / u.s,
0.01 * u.rad / u.s,
10 * u.rad / u.s,
)
M = 1e25 * u.kg
start_lambda = 0.0
OdeMethodKwargs = {"stepsize": 0.4e-6}
cl = Schwarzschild.from_coords(sph_obj, M)
with warnings.catch_warnings(record=True) as w:
it = cl.calculate_trajectory_iterator(
start_lambda=start_lambda,
OdeMethodKwargs=OdeMethodKwargs,
stop_on_singularity=False,
)
for _, _ in zip(range(1000), it):
pass
assert len(w) >= 1
import numpy as np
from project import write_out
from astropy import units as u
from einsteinpy.coordinates import SphericalDifferential, CartesianDifferential
from einsteinpy.metric import Schwarzschild
M = 5.972e24 * u.kg
sph_coord = SphericalDifferential(306.0 * u.m, np.pi/2 * u.rad, -np.pi/6*u.rad,
1000*u.m/u.s, 0*u.rad/u.s, 1900*u.rad/u.s)
obj = Schwarzschild.from_coords(sph_coord, M , 0* u.s)
end_tau = 0.01 # approximately equal to coordinate time
stepsize = 0.3e-6
ans = obj.calculate_trajectory(end_lambda=end_tau, OdeMethodKwargs={"stepsize":stepsize})
x = []
y = []
z = []
for i in range(len(ans[1])):
x.append(ans[1][i][1])
y.append(ans[1][i][2])
z.append(ans[1][i][3])
write_out([ans[0]] + [x] + [y] + [z], 'spherical', "solveEinstein_randphi2.txt")
