def test_center_of_mass():
t = np.linspace(0, 100, 1000)
m_planet = np.array([0.5, 0.1])
m_star = 1.45
orbit = KeplerianOrbit(
m_star=m_star,
r_star=1.0,
t0=np.array([0.5, 17.4]),
period=np.array([100.0, 37.3]),
ecc=np.array([0.1, 0.8]),
omega=np.array([0.5, 1.3]),
Omega=np.array([0.0, 1.0]),
incl=np.array([0.25 * np.pi, 0.3 * np.pi]),
m_planet=m_planet,
)
planet_coords = theano.function([], orbit.get_planet_position(t))()
star_coords = theano.function([], orbit.get_star_position(t))()
com = np.sum(
(m_planet[None, :] * np.array(planet_coords) +
m_star * np.array(star_coords)) / (m_star + m_planet)[None, :],
axis=0,
)
assert np.allclose(com, 0.0)
def test_flip_circular():
t = np.linspace(0, 100, 1000)
m_planet = 0.1
m_star = 1.3
orbit1 = KeplerianOrbit(
m_star=m_star,
r_star=1.1,
t0=0.5,
period=100.0,
Omega=1.0,
incl=0.25 * np.pi,
m_planet=m_planet,
)
orbit2 = orbit1._flip(0.7)
x1, y1, z1 = theano.function([], orbit1.get_star_position(t))()
x2, y2, z2 = theano.function([], orbit2.get_planet_position(t))()
assert np.allclose(x1, x2, atol=1e-5)
assert np.allclose(y1, y2, atol=1e-5)
assert np.allclose(z1, z2, atol=1e-5)
x1, y1, z1 = theano.function([], orbit1.get_planet_position(t))()
x2, y2, z2 = theano.function([], orbit2.get_star_position(t))()
assert np.allclose(x1, x2, atol=1e-5)
assert np.allclose(y1, y2, atol=1e-5)
assert np.allclose(z1, z2, atol=1e-5)
def test_velocity():
t_tensor = tt.dvector()
t = np.linspace(0, 100, 1000)
m_planet = 0.1
m_star = 1.3
orbit = KeplerianOrbit(
m_star=m_star,
r_star=1.0,
t0=0.5,
period=100.0,
ecc=0.1,
omega=0.5,
Omega=1.0,
incl=0.25 * np.pi,
m_planet=m_planet,
)
star_pos = orbit.get_star_position(t_tensor)
star_vel = theano.function([], orbit.get_star_velocity(t))()
star_vel_expect = np.empty_like(star_vel)
for i in range(3):
g = theano.grad(tt.sum(star_pos[i]), t_tensor)
star_vel_expect[i] = theano.function([t_tensor], g)(t)
assert np.allclose(star_vel, star_vel_expect)
planet_pos = orbit.get_planet_position(t_tensor)
planet_vel = theano.function([], orbit.get_planet_velocity(t))()
planet_vel_expect = np.empty_like(planet_vel)
for i in range(3):
g = theano.grad(tt.sum(planet_pos[i]), t_tensor)
planet_vel_expect[i] = theano.function([t_tensor], g)(t)
assert np.allclose(planet_vel, planet_vel_expect)
pos = orbit.get_relative_position(t_tensor)
vel = np.array(theano.function([], orbit.get_relative_velocity(t))())
vel_expect = np.empty_like(vel)
for i in range(3):
g = theano.grad(tt.sum(pos[i]), t_tensor)
vel_expect[i] = theano.function([t_tensor], g)(t)
assert np.allclose(vel, vel_expect)
def test_light_delay_shape_two_planets_single_t():
orbit = KeplerianOrbit(period=[1.0, 2.0])
x, y, z = orbit.get_planet_position([1.0], light_delay=False)
xr, yr, zr = orbit.get_planet_position([1.0], light_delay=True)
assert np.array_equal(x.shape.eval(), xr.shape.eval())
def test_light_delay_shape_scalar_t():
orbit = KeplerianOrbit(period=1.0)
x, y, z = orbit.get_planet_position(1.0, light_delay=False)
xr, yr, zr = orbit.get_planet_position(1.0, light_delay=True)
assert np.array_equal(x.shape.eval(), xr.shape.eval())
def test_light_delay_shape_two_planets_vector_t():
orbit = KeplerianOrbit(period=[1.0, 2.0])
t = np.linspace(0, 10, 50)
x, y, z = orbit.get_planet_position(t, light_delay=False)
xr, yr, zr = orbit.get_planet_position(t, light_delay=True)
assert np.array_equal(x.shape.eval(), xr.shape.eval())
def test_light_delay():
# Instantiate the orbit
m_star = tt.scalar()
period = tt.scalar()
ecc = tt.scalar()
omega = tt.scalar()
Omega = tt.scalar()
incl = tt.scalar()
m_planet = tt.scalar()
t = tt.scalar()
orbit = KeplerianOrbit(
m_star=m_star,
r_star=1.0,
t0=0.0,
period=period,
ecc=ecc,
omega=omega,
Omega=Omega,
incl=incl,
m_planet=m_planet,
)
# True position
get_position = theano.function(
[t, m_star, period, ecc, omega, Omega, incl, m_planet],
orbit.get_planet_position([t], light_delay=False),
)
# Retarded position
get_retarded_position = theano.function(
[t, m_star, period, ecc, omega, Omega, incl, m_planet],
orbit.get_planet_position([t], light_delay=True),
)
# Retarded position (numerical)
def get_exact_retarded_position(t, *args):
def loss(params):
(ti, ) = params
xr, yr, zr = get_position(ti, *args)
delay = (zr * u.Rsun / c).to(u.day).value
return (ti - delay - t)**2
tr = minimize(loss, t).x[0]
return get_position(tr, *args)
# Compare for 100 different orbits
np.random.seed(13)
for i in range(100):
m_star = 0.1 + np.random.random() * 1.9
period = np.random.random() * 500
ecc = np.random.random()
omega = np.random.random() * 2 * np.pi
Omega = np.random.random() * 2 * np.pi
incl = np.random.random() * 0.5 * np.pi
m_planet = np.random.random()
t = np.random.random() * period
args = (m_star, period, ecc, omega, Omega, incl, m_planet)
assert np.allclose(
np.reshape(get_retarded_position(t, *args), (-1, )),
np.reshape(get_exact_retarded_position(t, *args), (-1, )),
)