Source code for gammapy.utils.coordinates.other

# 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",
    "D_SUN_TO_GALACTIC_CENTER",
    "galactic",
    "motion_since_birth",
    "polar",
    "velocity_glon_glat",
]

# 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 an astrophysical object with a 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