def _sun_north_angle_to_z(frame):
"""
Return the angle between solar north and the Z axis of the provided frame's coordinate system
and observation time.
"""
# Find the Sun center in HGS at the frame's observation time
sun_center = SkyCoord(0*u.deg, 0*u.deg, 0*u.km, frame=HGS, obstime=frame.obstime)
# Find the Sun north in HGS at the frame's observation time
# Only a rough value of the solar radius is needed here because, after the cross product,
# only the direction from the Sun center to the Sun north pole matters
sun_north = SkyCoord(0*u.deg, 90*u.deg, 690000*u.km, frame=HGS, obstime=frame.obstime)
# Find the Sun center and Sun north in the frame's coordinate system
sky_normal = sun_center.transform_to(frame).data.to_cartesian()
sun_north = sun_north.transform_to(frame).data.to_cartesian()
# Use cross products to obtain the sky projections of the two vectors (rotated by 90 deg)
sun_north_in_sky = sun_north.cross(sky_normal)
z_in_sky = CartesianRepresentation(0, 0, 1).cross(sky_normal)
# Normalize directional vectors
sky_normal /= sky_normal.norm()
sun_north_in_sky /= sun_north_in_sky.norm()
z_in_sky /= z_in_sky.norm()
# Calculate the signed angle between the two projected vectors
cos_theta = sun_north_in_sky.dot(z_in_sky)
sin_theta = sun_north_in_sky.cross(z_in_sky).dot(sky_normal)
angle = np.arctan2(sin_theta, cos_theta).to('deg')
return Angle(angle)
def _sun_north_angle_to_z(frame):
"""
Return the angle between solar north and the Z axis of the provided frame's coordinate system
and observation time.
"""
# Find the Sun center in HGS at the frame's observation time(s)
sun_center_repr = SphericalRepresentation(0 * u.deg, 0 * u.deg, 0 * u.km)
# The representation is repeated for as many times as are in obstime prior to transformation
sun_center = SkyCoord(sun_center_repr._apply('repeat', frame.obstime.size),
frame=HGS,
obstime=frame.obstime)
# Find the Sun north in HGS at the frame's observation time(s)
# Only a rough value of the solar radius is needed here because, after the cross product,
# only the direction from the Sun center to the Sun north pole matters
sun_north_repr = SphericalRepresentation(0 * u.deg, 90 * u.deg,
690000 * u.km)
# The representation is repeated for as many times as are in obstime prior to transformation
sun_north = SkyCoord(sun_north_repr._apply('repeat', frame.obstime.size),
frame=HGS,
obstime=frame.obstime)
# Find the Sun center and Sun north in the frame's coordinate system
sky_normal = sun_center.transform_to(frame).data.to_cartesian()
sun_north = sun_north.transform_to(frame).data.to_cartesian()
# Use cross products to obtain the sky projections of the two vectors (rotated by 90 deg)
sun_north_in_sky = sun_north.cross(sky_normal)
z_in_sky = CartesianRepresentation(0, 0, 1).cross(sky_normal)
# Normalize directional vectors
sky_normal /= sky_normal.norm()
sun_north_in_sky /= sun_north_in_sky.norm()
z_in_sky /= z_in_sky.norm()
# Calculate the signed angle between the two projected vectors
cos_theta = sun_north_in_sky.dot(z_in_sky)
sin_theta = sun_north_in_sky.cross(z_in_sky).dot(sky_normal)
angle = np.arctan2(sin_theta, cos_theta).to('deg')
# If there is only one time, this function's output should be scalar rather than array
if angle.size == 1:
angle = angle[0]
return Angle(angle)
def _sun_north_angle_to_z(frame):
"""
Return the angle between solar north and the Z axis of the provided frame's coordinate system
and observation time.
"""
# Find the Sun center in HGS at the frame's observation time(s)
sun_center_repr = SphericalRepresentation(0*u.deg, 0*u.deg, 0*u.km)
# The representation is repeated for as many times as are in obstime prior to transformation
sun_center = SkyCoord(sun_center_repr._apply('repeat', frame.obstime.size),
frame=HGS, obstime=frame.obstime)
# Find the Sun north in HGS at the frame's observation time(s)
# Only a rough value of the solar radius is needed here because, after the cross product,
# only the direction from the Sun center to the Sun north pole matters
sun_north_repr = SphericalRepresentation(0*u.deg, 90*u.deg, 690000*u.km)
# The representation is repeated for as many times as are in obstime prior to transformation
sun_north = SkyCoord(sun_north_repr._apply('repeat', frame.obstime.size),
frame=HGS, obstime=frame.obstime)
# Find the Sun center and Sun north in the frame's coordinate system
sky_normal = sun_center.transform_to(frame).data.to_cartesian()
sun_north = sun_north.transform_to(frame).data.to_cartesian()
# Use cross products to obtain the sky projections of the two vectors (rotated by 90 deg)
sun_north_in_sky = sun_north.cross(sky_normal)
z_in_sky = CartesianRepresentation(0, 0, 1).cross(sky_normal)
# Normalize directional vectors
sky_normal /= sky_normal.norm()
sun_north_in_sky /= sun_north_in_sky.norm()
z_in_sky /= z_in_sky.norm()
# Calculate the signed angle between the two projected vectors
cos_theta = sun_north_in_sky.dot(z_in_sky)
sin_theta = sun_north_in_sky.cross(z_in_sky).dot(sky_normal)
angle = np.arctan2(sin_theta, cos_theta).to('deg')
# If there is only one time, this function's output should be scalar rather than array
if angle.size == 1:
angle = angle[0]
return Angle(angle)