def spherical_velocity(x, y, z, vx, vy, vz):
"""Computes the projected angular velocity in spherical coordinates."""
d = sqrt(x ** 2 + y ** 2 + z ** 2)
r = sqrt(x ** 2 + y ** 2)
v_lon = degrees(1. / (kpc.to(km) * r) * (-y * vx + x * vy)) * year.to(second) * 1e6
v_lat = (degrees(vz / (sqrt(1 - (z / d) ** 2) * kpc.to(km) * d ) -
sqrt(vx ** 2 + vy ** 2 + vz ** 2) * z /
(kpc.to(km) * (sqrt(1 - (z / d) ** 2) * d ** 2))) * year.to(second) * 1e6)
return v_lon, v_lat
def motion_since_birth(x, y, z, v, age, theta, phi):
"""Takes x[kpc], y[kpc], z[kpc], v[km/s] and age[years] chooses an arbitrary direction
and computes the new position. Doesn't include any galactic potential modelation.
Returns the new position."""
vx = v * cos(phi) * sin(theta)
vy = v * sin(phi) * sin(theta)
vz = v * cos(theta)
age = year.to(second) * age
# Compute new positions
x = x + kpc.to(km) * vx * age
y = y + kpc.to(km) * vy * age
z = z + kpc.to(km) * vz * age
return x, y, z, vx, vy, vz