# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Other coordinate and distance-related functions"""
import numpy as np
from astropy.units import Quantity, Unit
__all__ = [
"cartesian",
"galactic",
"velocity_glon_glat",
"motion_since_birth",
"polar",
"D_SUN_TO_GALACTIC_CENTER",
]
# TODO: replace this with the default from the Galactocentric frame in astropy.coordinates
D_SUN_TO_GALACTIC_CENTER = Quantity(8.5, "kpc")
"""Default assumed distance from the Sun to the Galactic center (`~astropy.units.Quantity`)"""
[docs]def cartesian(r, theta):
"""Convert polar coordinates to cartesian coordinates."""
x = r * np.cos(theta)
y = r * np.sin(theta)
return x, y
[docs]def polar(x, y):
"""Convert cartesian coordinates to polar coordinates."""
r = np.sqrt(x ** 2 + y ** 2)
theta = np.arctan2(y, x)
return r, theta
[docs]def galactic(x, y, z, obs_pos=None):
"""Compute galactic coordinates lon, lat and distance.
For given position in cartesian coordinates (kpc).
"""
obs_pos = obs_pos or [D_SUN_TO_GALACTIC_CENTER, 0, 0]
y_prime = y + D_SUN_TO_GALACTIC_CENTER
d = np.sqrt(x ** 2 + y_prime ** 2 + z ** 2)
glon = np.arctan2(x, y_prime).to("deg")
glat = np.arcsin(z / d).to("deg")
return d, glon, glat
[docs]def velocity_glon_glat(x, y, z, vx, vy, vz):
"""
Compute projected angular velocity in galactic coordinates.
Parameters
----------
x, y, z : `~astropy.units.Quantity`
Position in x, y, z direction
vx, vy, vz : `~astropy.units.Quantity`
Velocity in x, y, z direction
Returns
-------
v_glon, v_glat : `~astropy.units.Quantity`
Projected velocity in Galactic sky coordinates
"""
y_prime = y + D_SUN_TO_GALACTIC_CENTER
d = np.sqrt(x ** 2 + y_prime ** 2 + z ** 2)
r = np.sqrt(x ** 2 + y_prime ** 2)
v_glon = (-y_prime * vx + x * vy) / r ** 2
v_glat = vz / (np.sqrt(1 - (z / d) ** 2) * d) - np.sqrt(
vx ** 2 + vy ** 2 + vz ** 2
) * z / (np.sqrt(1 - (z / d) ** 2) * d ** 2)
return v_glon * Unit("rad"), v_glat * Unit("rad")
[docs]def motion_since_birth(v, age, theta, phi):
"""
Compute motion of a object with given velocity, direction and age.
Parameters
----------
v : `~astropy.units.Quantity`
Absolute value of the velocity
age : `~astropy.units.Quantity`
Age of the source.
theta, phi : `~astropy.units.Quantity`
Angular direction of the velocity.
Returns
-------
dx, dy, dz : `~astropy.units.Quantity`
Displacement in x, y, z direction
vx, vy, vz : `~astropy.units.Quantity`
Velocity in x, y, z direction
"""
vx = v * np.cos(phi) * np.sin(theta)
vy = v * np.sin(phi) * np.sin(theta)
vz = v * np.cos(theta)
# Compute new positions
dx = vx * age
dy = vy * age
dz = vz * age
return dx, dy, dz, vx, vy, vz