# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Other coordinate and distance-related functions"""
from __future__ import absolute_import, division, print_function, unicode_literals
import numpy as np
from astropy.units import Unit, Quantity
__all__ = [
'cartesian', 'galactic', 'luminosity_to_flux', 'flux_to_luminosity',
'radius_to_angle', 'angle_to_radius', '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')
[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 (deg) and distance (kpc)
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 luminosity_to_flux(luminosity, distance):
"""Distance is assumed to be in kpc"""
return luminosity / (4 * np.pi * distance ** 2)
[docs]def flux_to_luminosity(flux, distance):
"""Distance is assumed to be in kpc"""
return flux * 4 * np.pi * distance ** 2
[docs]def radius_to_angle(radius, distance):
"""Radius (pc), distance(kpc), angle(deg)"""
return np.arctan(radius / distance)
[docs]def angle_to_radius(angle, distance):
"""Radius (pc), distance(kpc), angle(deg)"""
return np.tan(angle * distance)
[docs]def velocity_glon_glat(x, y, z, vx, vy, vz):
"""
Compute projected angular velocity in galactic coordinates.
Parameters
----------
x : `~astropy.units.Quantity`
Position in x direction
y : `~astropy.units.Quantity`
Position in y direction
z : `~astropy.units.Quantity`
Position in z direction
vx : `~astropy.units.Quantity`
Velocity in x direction
vy : `~astropy.units.Quantity`
Velocity in y direction
vz : `~astropy.units.Quantity`
Velocity in z direction
Returns
-------
v_glon : `~astropy.units.Quantity`
Projected velocity in Galactic longitude
v_glat : `~astropy.units.Quantity`
Projected velocity in Galactic latitude
"""
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 : `~astropy.units.Quantity`
Angular direction of the velocity.
phi : `~astropy.units.Quantity`
Angular direction of the velocity.
Returns
-------
dx : `~astropy.units.Quantity`
Displacement in x direction
dy : `~astropy.units.Quantity`
Displacement in y direction
dz : `~astropy.units.Quantity`
Displacement in z direction
vx : `~astropy.units.Quantity`
Velocity in x direction
vy : `~astropy.units.Quantity`
Velocity in y direction
vz : `~astropy.units.Quantity`
Velocity in 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