示例#1
0
def topo_posvels(xyz, toa):
    """
    topo_posvels(xyz, toa)

    This routine returns a PosVel instance , containing the positions
    (m) and velocities (m / UT1 s) at the time of the toa and
    referenced to the ITRF geocentric coordinates.  This routine is
    basically SOFA's pvtob() with an extra rotation from c2ixys.
    """
    # All the times are passed as TT
    tt = toa.mjd.tt.jd1, toa.mjd.tt.jd2

    # Get a floating-point MJD to use for interpolating IERS values
    mjd = toa.mjd.utc.mjd

    # Gets x,y coords of Celestial Intermediate Pole and CIO locator s
    X, Y, S = erfa.xys00a(*tt)
    # Get dX and dY from IERS A
    #dX = numpy.interp(mjd, iers_tab['MJD'], iers_tab['dX_2000A_B']) * u.arcsec
    #dY = numpy.interp(mjd, iers_tab['MJD'], iers_tab['dY_2000A_B']) * u.arcsec
    # Get dX and dY from IERS B
    dX = numpy.interp(mjd, iers_tab['MJD'], iers_tab['dX_2000A']) * u.arcsec
    dY = numpy.interp(mjd, iers_tab['MJD'], iers_tab['dY_2000A']) * u.arcsec
    # Get GCRS to CIRS matrix
    rc2i = erfa.c2ixys(X+dX.to(u.rad).value, Y+dY.to(u.rad).value, S)

    # Gets the TIO locator s'
    sp = erfa.sp00(*tt)
    # Get X and Y from IERS A
    #xp = numpy.interp(mjd, iers_tab['MJD'], iers_tab['PM_X_B']) * u.arcsec
    #yp = numpy.interp(mjd, iers_tab['MJD'], iers_tab['PM_Y_B']) * u.arcsec
    # Get X and Y from IERS B
    xp = numpy.interp(mjd, iers_tab['MJD'], iers_tab['PM_x']) * u.arcsec
    yp = numpy.interp(mjd, iers_tab['MJD'], iers_tab['PM_y']) * u.arcsec
    # Get the polar motion matrix
    rpm = erfa.pom00(xp.to(u.rad).value, yp.to(u.rad).value, sp)

    # Observatory XYZ coords in meters
    xyzm = [a.to(u.m).value for a in xyz]
    x, y, z = erfa.trxp(rpm, xyzm)

    # Functions of Earth Rotation Angle
    ut1 = toa.mjd.ut1.jd1, toa.mjd.ut1.jd2
    theta = erfa.era00(*ut1)
    s, c = math.sin(theta), math.cos(theta)

    # Position
    pos = numpy.asarray([c*x - s*y, s*x + c*y, z])
    pos = erfa.trxp(rc2i, pos) * u.m

    # Earth rotation rate in radians per UT1 second
    OM = 1.00273781191135448 * 2 * math.pi / erfa.DAYSEC

    # Velocity
    vel = numpy.asarray([OM * (-s*x - c*y), OM * (c*x - s*y), 0.0])
    vel = erfa.trxp(rc2i, vel) * u.m / u.s

    return utils.PosVel(pos, vel, obj=toa.obs, origin="EARTH")
def cirs_to_itrs_mat(time):
    # compute the polar motion p-matrix
    xp, yp = get_polar_motion(time)
    sp = erfa.sp00(*get_jd12(time, 'tt'))
    pmmat = erfa.pom00(xp, yp, sp)

    # now determine the Earth Rotation Angle for the input obstime
    # era00 accepts UT1, so we convert if need be
    era = erfa.era00(*get_jd12(time, 'ut1'))

    # c2tcio expects a GCRS->CIRS matrix, but we just set that to an I-matrix
    # because we're already in CIRS
    return erfa.c2tcio(np.eye(3), era, pmmat)
def tete_to_itrs_mat(time):
    # compute the polar motion p-matrix
    xp, yp = get_polar_motion(time)
    sp = erfa.sp00(*get_jd12(time, 'tt'))
    pmmat = erfa.pom00(xp, yp, sp)

    # now determine the greenwich apparent siderial time for the input obstime
    # we use the 2006A model for consistency with RBPN matrix use in GCRS <-> TETE
    ujd1, ujd2 = get_jd12(time, 'ut1')
    jd1, jd2 = get_jd12(time, 'tt')
    gast = erfa.gst06a(ujd1, ujd2, jd1, jd2)

    # c2tcio expects a GCRS->CIRS matrix, but we just set that to an I-matrix
    # because we're already in CIRS equivalent frame
    return erfa.c2tcio(np.eye(3), gast, pmmat)
def teme_to_itrs_mat(time):
    # Sidereal time, rotates from ITRS to mean equinox
    # Use 1982 model for consistency with Vallado et al (2006)
    # http://www.celestrak.com/publications/aiaa/2006-6753/AIAA-2006-6753.pdf
    gst = erfa.gmst82(*get_jd12(time, 'ut1'))

    # Polar Motion
    # Do not include TIO locator s' because it is not used in Vallado 2006
    xp, yp = get_polar_motion(time)
    pmmat = erfa.pom00(xp, yp, 0)

    # rotation matrix
    # c2tcio expects a GCRS->CIRS matrix as it's first argument.
    # Here, we just set that to an I-matrix, because we're already
    # in TEME and the difference between TEME and CIRS is just the
    # rotation by the sidereal time rather than the Earth Rotation Angle
    return erfa.c2tcio(np.eye(3), gst, pmmat)
示例#5
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def _polar_mot_matrix(obstime):
    """
    Form the matrix of polar motion for a given date, IAU 2000.

    The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning that
    it is the final rotation when computing the
    pointing direction to a celestial source.

    Parameters
    ----------
    obstime : Time
        time at which the polar motion should be calculated.
    Returns
    -------
        3x3 rotation matrix due to polar motion
    """
    # compute the polar motion p-matrix
    xp, yp = get_polar_motion(obstime)
    # noinspection PyArgumentList
    sp = erfa.sp00(*get_jd12(obstime, "tt"))
    polar_mot_mat = erfa.pom00(xp, yp, sp)

    return polar_mot_mat
def tete_to_itrs_mat(time, rbpn=None):
    """Compute the polar motion p-matrix at the given time.

    If the nutation-precession matrix is already known, it should be passed in,
    as this is by far the most expensive calculation.
    """
    xp, yp = get_polar_motion(time)
    sp = erfa.sp00(*get_jd12(time, 'tt'))
    pmmat = erfa.pom00(xp, yp, sp)

    # now determine the greenwich apparent siderial time for the input obstime
    # we use the 2006A model for consistency with RBPN matrix use in GCRS <-> TETE
    ujd1, ujd2 = get_jd12(time, 'ut1')
    jd1, jd2 = get_jd12(time, 'tt')
    if rbpn is None:
        # erfa.gst06a calls pnm06a to calculate rbpn and then gst06. Use it in
        # favour of getting rbpn with erfa.pnm06a to avoid a possibly large array.
        gast = erfa.gst06a(ujd1, ujd2, jd1, jd2)
    else:
        gast = erfa.gst06(ujd1, ujd2, jd1, jd2, rbpn)

    # c2tcio expects a GCRS->CIRS matrix, but we just set that to an I-matrix
    # because we're already in CIRS equivalent frame
    return erfa.c2tcio(np.eye(3), gast, pmmat)
示例#7
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ERA = erfa.era00(DJMJD0 + DATE, TUT)
print("Earth rotation angle")
print('ERA = %.17f radians' % ERA)
print("    = %.17f degrees" % math.degrees(ERA))
print("    = %s%dd%dm%d.%ds" % erfa.a2af(6, ERA))
print("    = %s%dh%dm%d.%ds" % erfa.a2tf(6, ERA))

# Form celestial-terrestrial matrix (no polar motion yet).
##RC2TI = erfa.cr(RC2I)
##RC2TI = erfa.rz(ERA, RC2TI)
RC2TI = erfa.rz(ERA, RC2I)
print("celestial to terrestrial matrix (no polar motion)")
pprint(RC2TI)

# Polar motion matrix (TIRS->ITRS, IERS 2003).
RPOM = erfa.pom00(XP, YP, erfa.sp00(DJMJD0, TT))

# Form celestial-terrestrial matrix (including polar motion).
RC2IT = erfa.rxr(RPOM, RC2TI)
print("celestial to terrestrial matrix (including polar motion)")
pprint(RC2IT)

##B = scipy.matrix(RC2IT)

print('''
================================================
IAU 2000A, equinox based, using classical angles
================================================
''')

# Nutation, IAU 2000A.
示例#8
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ERA = erfa.era00(DJMJD0+DATE, TUT)
print("Earth rotation angle")
print('ERA = %.17f radians'%ERA)
print("    = %.17f degrees"%math.degrees(ERA))
print("    = %s%dd%dm%d.%ds"%erfa.a2af(6, ERA))
print("    = %s%dh%dm%d.%ds"%erfa.a2tf(6, ERA))

# Form celestial-terrestrial matrix (no polar motion yet).
##RC2TI = erfa.cr(RC2I)
##RC2TI = erfa.rz(ERA, RC2TI)
RC2TI = erfa.rz(ERA, RC2I)
print("celestial to terrestrial matrix (no polar motion)")
pprint(RC2TI)

# Polar motion matrix (TIRS->ITRS, IERS 2003).
RPOM = erfa.pom00(XP, YP, erfa.sp00(DJMJD0,TT))

# Form celestial-terrestrial matrix (including polar motion).
RC2IT = erfa.rxr(RPOM, RC2TI)
print("celestial to terrestrial matrix (including polar motion)")
pprint(RC2IT)

##B = scipy.matrix(RC2IT)

print('''
================================================
IAU 2000A, equinox based, using classical angles
================================================
''')

# Nutation, IAU 2000A.
示例#9
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def old_gcrs_posvel_from_itrf(loc, toas, obsname="obs"):
    """Return a list of PosVel instances for the observatory at the TOA times.

    Observatory location should be given in the loc argument as an astropy
    EarthLocation object. This location will be in the ITRF frame (i.e.
    co-rotating with the Earth).

    The optional obsname argument will be used as label in the returned
    PosVel instance.

    This routine returns a list of PosVel instances, containing the
    positions (m) and velocities (m / s) at the times of the toas and
    referenced to the Earth-centered Inertial (ECI, aka GCRS) coordinates.
    This routine is basically SOFA's pvtob() [Position and velocity of
    a terrestrial observing station] with an extra rotation from c2ixys()
    [Form the celestial to intermediate-frame-of-date matrix given the CIP
    X,Y and the CIO locator s].
    """
    unpack = False
    # If the input is a single TOA (i.e. a row from the table),
    # then put it into a list
    if type(toas) == table.row.Row:
        ttoas = Time([toas["mjd"]])
        unpack = True
    elif type(toas) == table.table.Table:
        ttoas = toas["mjd"]
    elif isinstance(toas, Time):
        if toas.isscalar:
            ttoas = Time([toas])
            unpack = True
        else:
            ttoas = toas
    else:
        if np.isscalar(toas):
            ttoas = Time([toas], format="mjd")
            unpack = True
        else:
            ttoas = toas
    N = len(ttoas)
    if len(ttoas.shape) != 1:
        raise ValueError("At most one-dimensional array of times possible, "
                         "shape was {}".format(ttoas.shape))

    # Get various times from the TOAs as arrays
    tts = np.asarray([(t.jd1, t.jd2) for t in ttoas.tt]).T
    ut1s = np.asarray([(t.jd1, t.jd2) for t in ttoas.ut1]).T
    mjds = np.asarray(ttoas.mjd)

    iers_b = get_iers_b_up_to_date(mjds.max())

    # Get x, y coords of Celestial Intermediate Pole and CIO locator s
    X, Y, S = erfa.xys00a(*tts)

    # Get dX and dY from IERS A in arcsec and convert to radians
    # dX = np.interp(mjds, iers_tab['MJD'], iers_tab['dX_2000A_B']) * asec2rad
    # dY = np.interp(mjds, iers_tab['MJD'], iers_tab['dY_2000A_B']) * asec2rad
    # Get dX and dY from IERS B in arcsec and convert to radians
    dX = np.interp(mjds, iers_b["MJD"].to_value(u.d),
                   iers_b["dX_2000A"].to_value(u.rad))
    dY = np.interp(mjds, iers_b["MJD"].to_value(u.d),
                   iers_b["dY_2000A"].to_value(u.rad))

    # Get GCRS to CIRS matrices
    rc2i = erfa.c2ixys(X + dX, Y + dY, S)

    # Gets the TIO locator s'
    sp = erfa.sp00(*tts)

    # Get X and Y from IERS A in arcsec and convert to radians
    # xp = np.interp(mjds, iers_tab['MJD'], iers_tab['PM_X_B']) * asec2rad
    # yp = np.interp(mjds, iers_tab['MJD'], iers_tab['PM_Y_B']) * asec2rad
    # Get X and Y from IERS B in arcsec and convert to radians
    xp = np.interp(mjds, iers_b["MJD"].to_value(u.d),
                   iers_b["PM_x"].to_value(u.rad))
    yp = np.interp(mjds, iers_b["MJD"].to_value(u.d),
                   iers_b["PM_y"].to_value(u.rad))

    # Get the polar motion matrices
    rpm = erfa.pom00(xp, yp, sp)

    # Observatory geocentric coords in m
    xyzm = np.array([a.to_value(u.m) for a in loc.geocentric])
    x, y, z = np.dot(xyzm, rpm).T

    # Functions of Earth Rotation Angle
    theta = erfa.era00(*ut1s)
    s, c = np.sin(theta), np.cos(theta)
    sx, cx = s * x, c * x
    sy, cy = s * y, c * y

    # Initial positions and velocities
    iposs = np.asarray([cx - sy, sx + cy, z]).T
    ivels = np.asarray([OM * (-sx - cy), OM * (cx - sy), np.zeros_like(x)]).T
    # There is probably a way to do this with np.einsum or something...
    # and here it is .
    poss = np.empty((N, 3), dtype=np.float64)
    vels = np.empty((N, 3), dtype=np.float64)
    poss = np.einsum("ij,ijk->ik", iposs, rc2i)
    vels = np.einsum("ij,ijk->ik", ivels, rc2i)
    r = PosVel(poss.T * u.m, vels.T * u.m / u.s, obj=obsname, origin="earth")
    if unpack:
        return r[0]
    else:
        return r
示例#10
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for c,a in erfa.a2af(6, ERA):
    print("    = %s"%c, end='')
    print("%dd%dm%d.%ds"%tuple(a))
for c,a in erfa.a2af(6, ERA):
    print("    = %s"%c, end='')
    print("%dd%dm%d.%ds"%tuple(a))

# Form celestial-terrestrial matrix (no polar motion yet).
##RC2TI = erfa.cr(RC2I)
##RC2TI = erfa.rz(ERA, RC2TI)
RC2TI = erfa.rz(ERA, RC2I)
print("celestial to terrestrial matrix (no polar motion)")
pprint(RC2TI)

# Polar motion matrix (TIRS->ITRS, IERS 2003).
RPOM = erfa.pom00(np.array([XP]), np.array([YP]), erfa.sp00(DJMJD0,TT))

# Form celestial-terrestrial matrix (including polar motion).
RC2IT = erfa.rxr(RPOM, RC2TI)
print("celestial to terrestrial matrix (including polar motion)")
pprint(RC2IT)

##B = scipy.matrix(RC2IT)

print('''
================================================
IAU 2000A, equinox based, using classical angles
================================================
''')

# Nutation, IAU 2000A.