def ccFromSCPVOff(pos, pm, parlax, radVel, offDir, offMag):
"""
Converts spherical to cartesian coordinates, including position, velocity
and and a local offset along a great circle from the position vector.
See also ccFromSCPV and ccFromSC.
Inputs:
- pos(2) spherical position (degrees);
pos[1] must be in the range [-90,90]
- pm(2) proper motion (arcsec per century)
- parlax parallax (arcsec)
- radVel radial velocity (km/s, positive receding)
- offDir offset direction (degrees):
dir. of increasing pos[0] = 0, pos[1] = 90
- offMag offset magnitude (degrees on the sky)
Returns:
- p(3) position vector (au)
- v(3) velocity (au per year)
- offP(3) offset position vector (au)
- atInf true if object is very far away (see Details)
Error Conditions:
- Raises ValueError if pos[1] is not in the range -90 to 90 deg
Warnings:
- Negative parallax is silently treated as zero parallax (object at infinity).
Details:
- See Sph.CCFromSCPV for more information.
History
2002-08-22 ROwen Converted to Python from the TCC's sph_SCPVOff2CC 6-1.
"""
# convert spherical position and velocity to cartesian
p, v, atInf = ccFromSCPV(pos, pm, parlax, radVel)
# compute spherical coordinates of the offset position;
# ignore the case of the offset position being at the pole,
# as the standard calculations work fine for that case
# (sets side_bb = 0 and ang_A = ang_C = 90)
ang_A, side_bb, ang_C, offPosAtPole = angSideAng(90.0 - pos[1],
90.0 - offDir, offMag)
offPos = (
pos[0] + ang_C,
90.0 - side_bb,
)
# convert the offset position to cartesian coordinates
# (the offset is assumed to be long a great circle,
# so the magnitude is exactly the same as the un-offset position)
magP = RO.MathUtil.vecMag(p)
offP = ccFromSC(offPos, magP)
return (p, v, offP, atInf)
def ccFromSCPVOff(pos, pm, parlax, radVel, offDir, offMag):
"""
Converts spherical to cartesian coordinates, including position, velocity
and and a local offset along a great circle from the position vector.
See also ccFromSCPV and ccFromSC.
Inputs:
- pos(2) spherical position (degrees);
pos[1] must be in the range [-90,90]
- pm(2) proper motion (arcsec per century)
- parlax parallax (arcsec)
- radVel radial velocity (km/s, positive receding)
- offDir offset direction (degrees):
dir. of increasing pos[0] = 0, pos[1] = 90
- offMag offset magnitude (degrees on the sky)
Returns:
- p(3) position vector (au)
- v(3) velocity (au per year)
- offP(3) offset position vector (au)
- atInf true if object is very far away (see Details)
Error Conditions:
- Raises ValueError if pos[1] is not in the range -90 to 90 deg
Warnings:
- Negative parallax is silently treated as zero parallax (object at infinity).
Details:
- See Sph.CCFromSCPV for more information.
History
2002-08-22 ROwen Converted to Python from the TCC's sph_SCPVOff2CC 6-1.
"""
# convert spherical position and velocity to cartesian
p, v, atInf = ccFromSCPV (pos, pm, parlax, radVel)
# compute spherical coordinates of the offset position;
# ignore the case of the offset position being at the pole,
# as the standard calculations work fine for that case
# (sets side_bb = 0 and ang_A = ang_C = 90)
ang_A, side_bb, ang_C, offPosAtPole = angSideAng (90.0 - pos[1], 90.0 - offDir, offMag)
offPos = (
pos[0] + ang_C,
90.0 - side_bb,
)
# convert the offset position to cartesian coordinates
# (the offset is assumed to be long a great circle,
# so the magnitude is exactly the same as the un-offset position)
magP = RO.MathUtil.vecMag(p)
offP = ccFromSC(offPos, magP)
return (p, v, offP, atInf)
def dcFromSC(pos):
"""Convert spherical coordinates to direction cosines, i.e. a unit vector.
Inputs:
- pos(2) spherical coordinates (deg):
longitude (increasing x to y), latitude,
e.g. (RA, Dec), (-HA, Dec) or (Az, Alt)
Returns:
- dc(3) direction cosines (rad), as a numpy.array
Error Conditions:
(none)
"""
return ccFromSC(pos, 1.0)
def dcFromSC(pos):
"""Convert spherical coordinates to direction cosines, i.e. a unit vector.
Inputs:
- pos(2) spherical coordinates (deg):
longitude (increasing x to y), latitude,
e.g. (RA, Dec), (-HA, Dec) or (Az, Alt)
Returns:
- dc(3) direction cosines (rad), as a numpy.array
Error Conditions:
(none)
"""
return ccFromSC(pos, 1.0)
def ccFromSCPV(
pos,
pm,
parallax,
radVel,
):
"""
Converts spherical position and velocity to cartesian coordinates.
Inputs:
- pos(2) spherical position
- pm(2) proper motion ("/century)
- parallax parallax (arcsec)
- radVel radial velocity (km/s, positive receding)
Returns a tuple consisting of:
- p cartesian position (au)
- v cartesian velocity (au/year)
- atInf true if object is very far away(see Details)
Error Conditions:
- Raises ValueError if pos[1] is not in the range -90 to 90 deg
Warnings:
- Negative parallax is silently treated as zero parallax (object at infinity).
Details:
- Proper motion is dPos/dt, not rate on the sky; in other words,
pm[0] gets large near the pole.
- If the star is very far away (parallax < _MinParallax), atInf is set true,
the distance is set to that limit and radial velocity is treated as zero.
- We could handle any range of pos[1] by checking to see if it's
in quadrants ii or iii, and if so, adding 180 degrees to offDir
and possibly negating pm[0] and pm[1]. However, it's not certain that's
what the user wanted, so for now avoid all that math and just complain.
History
2002-07-08 ROwen Converted from TCC's sph_SCPV2CC 1-1.
2002-12-23 ROwen Cosmetic change to make pychecker happy.
"""
# handle case of parallax too small ("at infinity")
if (parallax >= _MinParallax):
atInf = 0
else:
atInf = 1
parallax = _MinParallax
radVel = 0.0
# compute distance in au; note that distance (parsecs) = 1/parallax (")
distAU = RO.PhysConst.AUPerParsec / parallax
# compute p
p = ccFromSC (pos, distAU)
# compute useful quantities
sinP0 = RO.MathUtil.sind(pos[0])
cosP0 = RO.MathUtil.cosd(pos[0])
sinP1 = RO.MathUtil.sind(pos[1])
cosP1 = RO.MathUtil.cosd(pos[1])
# change units of proper motion from "/cy to au/year
# (multiply by distance and fix the units)
# pm(au/year) = pm ("/cy) distAU(au) (rad/year) / ("/cy)
pmAUPerYr = [x * distAU * _RadPerYear_per_ASPerCy for x in pm]
# change units of radial velocity from km/sec to au/year
radVelAUPerYr = radVel * _AUPerYear_per_KMPerSec
# compute velocity vector in au/year
v = (
- pmAUPerYr[0]*cosP1*sinP0 - pmAUPerYr[1]*sinP1*cosP0 + radVelAUPerYr*cosP1*cosP0,
pmAUPerYr[0]*cosP1*cosP0 - pmAUPerYr[1]*sinP1*sinP0 + radVelAUPerYr*cosP1*sinP0,
pmAUPerYr[1]*cosP1 + radVelAUPerYr*sinP1,
)
return (p, v, atInf)
def ccFromSCPV(
pos,
pm,
parallax,
radVel,
):
"""
Converts spherical position and velocity to cartesian coordinates.
Inputs:
- pos(2) spherical position
- pm(2) proper motion ("/century)
- parallax parallax (arcsec)
- radVel radial velocity (km/s, positive receding)
Returns a tuple consisting of:
- p cartesian position (au)
- v cartesian velocity (au/year)
- atInf true if object is very far away(see Details)
Error Conditions:
- Raises ValueError if pos[1] is not in the range -90 to 90 deg
Warnings:
- Negative parallax is silently treated as zero parallax (object at infinity).
Details:
- Proper motion is dPos/dt, not rate on the sky; in other words,
pm[0] gets large near the pole.
- If the star is very far away (parallax < _MinParallax), atInf is set true,
the distance is set to that limit and radial velocity is treated as zero.
- We could handle any range of pos[1] by checking to see if it's
in quadrants ii or iii, and if so, adding 180 degrees to offDir
and possibly negating pm[0] and pm[1]. However, it's not certain that's
what the user wanted, so for now avoid all that math and just complain.
History
2002-07-08 ROwen Converted from TCC's sph_SCPV2CC 1-1.
2002-12-23 ROwen Cosmetic change to make pychecker happy.
"""
# handle case of parallax too small ("at infinity")
if (parallax >= _MinParallax):
atInf = 0
else:
atInf = 1
parallax = _MinParallax
radVel = 0.0
# compute distance in au; note that distance (parsecs) = 1/parallax (")
distAU = RO.PhysConst.AUPerParsec / parallax
# compute p
p = ccFromSC(pos, distAU)
# compute useful quantities
sinP0 = RO.MathUtil.sind(pos[0])
cosP0 = RO.MathUtil.cosd(pos[0])
sinP1 = RO.MathUtil.sind(pos[1])
cosP1 = RO.MathUtil.cosd(pos[1])
# change units of proper motion from "/cy to au/year
# (multiply by distance and fix the units)
# pm(au/year) = pm ("/cy) distAU(au) (rad/year) / ("/cy)
pmAUPerYr = [x * distAU * _RadPerYear_per_ASPerCy for x in pm]
# change units of radial velocity from km/sec to au/year
radVelAUPerYr = radVel * _AUPerYear_per_KMPerSec
# compute velocity vector in au/year
v = (
-pmAUPerYr[0] * cosP1 * sinP0 - pmAUPerYr[1] * sinP1 * cosP0 +
radVelAUPerYr * cosP1 * cosP0,
pmAUPerYr[0] * cosP1 * cosP0 - pmAUPerYr[1] * sinP1 * sinP0 +
radVelAUPerYr * cosP1 * sinP0,
pmAUPerYr[1] * cosP1 + radVelAUPerYr * sinP1,
)
return (p, v, atInf)
