pymeeus.Pluto — PyMeeus 0.5.11 documentation

# Source code for pymeeus.Pluto

    # -*- coding: utf-8 -*-

    # PyMeeus: Python module implementing astronomical algorithms.
    # Copyright (C) 2018  Dagoberto Salazar
    #
    # This program is free software: you can redistribute it and/or modify
    # it under the terms of the GNU Lesser General Public License as published by
    # the Free Software Foundation, either version 3 of the License, or
    # (at your option) any later version.
    #
    # This program is distributed in the hope that it will be useful,
    # but WITHOUT ANY WARRANTY; without even the implied warranty of
    # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    # GNU Lesser General Public License for more details.
    #
    # You should have received a copy of the GNU Lesser General Public License
    # along with this program.  If not, see <https://www.gnu.org/licenses/>.

    from math import sin, cos, sqrt, asin, atan2

    from pymeeus.Angle import Angle
    from pymeeus.Epoch import Epoch, JDE2000
    from pymeeus.Sun import Sun

    """
    .. module:: Pluto
       :synopsis: Class to model Pluto minor planet
       :license: GNU Lesser General Public License v3 (LGPLv3)

    .. moduleauthor:: Dagoberto Salazar
    """

    PLUTO_ARGUMENT = [
        (0.0, 0.0, 1.0),
        (0.0, 0.0, 2.0),
        (0.0, 0.0, 3.0),
        (0.0, 0.0, 4.0),
        (0.0, 0.0, 5.0),
        (0.0, 0.0, 6.0),
        (0.0, 1.0, -1.0),
        (0.0, 1.0, 0.0),
        (0.0, 1.0, 1.0),
        (0.0, 1.0, 2.0),
        (0.0, 1.0, 3.0),
        (0.0, 2.0, -2.0),
        (0.0, 2.0, -1.0),
        (0.0, 2.0, 0.0),
        (1.0, -1.0, 0.0),
        (1.0, -1.0, 1.0),
        (1.0, 0.0, -3.0),
        (1.0, 0.0, -2.0),
        (1.0, 0.0, -1.0),
        (1.0, 0.0, 0.0),
        (1.0, 0.0, 1.0),
        (1.0, 0.0, 2.0),
        (1.0, 0.0, 3.0),
        (1.0, 0.0, 4.0),
        (1.0, 1.0, -3.0),
        (1.0, 1.0, -2.0),
        (1.0, 1.0, -1.0),
        (1.0, 1.0, 0.0),
        (1.0, 1.0, 1.0),
        (1.0, 1.0, 3.0),
        (2.0, 0.0, -6.0),
        (2.0, 0.0, -5.0),
        (2.0, 0.0, -4.0),
        (2.0, 0.0, -3.0),
        (2.0, 0.0, -2.0),
        (2.0, 0.0, -1.0),
        (2.0, 0.0, 0.0),
        (2.0, 0.0, 1.0),
        (2.0, 0.0, 2.0),
        (2.0, 0.0, 3.0),
        (3.0, 0.0, -2.0),
        (3.0, 0.0, -1.0),
        (3.0, 0.0, 0.0)
    ]
    """This table contains Pluto's argument coefficients according to Table 37.A in
    Meeus' book, page 265."""

    PLUTO_LONGITUDE = [
        (-19799805.0, 19850055.0),
        (897144.0, -4954829.0),
        (611149.0, 1211027.0),
        (-341243.0, -189585.0),
        (129287.0, -34992.0),
        (-38164.0, 30893.0),
        (20442.0, -9987.0),
        (-4063.0, -5071.0),
        (-6016.0, -3336.0),
        (-3956.0, 3039.0),
        (-667.0, 3572.0),
        (1276.0, 501.0),
        (1152.0, -917.0),
        (630.0, -1277.0),
        (2571.0, -459.0),
        (899.0, -1449.0),
        (-1016.0, 1043.0),
        (-2343.0, -1012.0),
        (7042.0, 788.0),
        (1199.0, -338.0),
        (418.0, -67.0),
        (120.0, -274.0),
        (-60.0, -159.0),
        (-82.0, -29.0),
        (-36.0, -29.0),
        (-40.0, 7.0),
        (-14.0, 22.0),
        (4.0, 13.0),
        (5.0, 2.0),
        (-1.0, 0.0),
        (2.0, 0.0),
        (-4.0, 5.0),
        (4.0, -7.0),
        (14.0, 24.0),
        (-49.0, -34.0),
        (163.0, -48.0),
        (9.0, -24.0),
        (-4.0, 1.0),
        (-3.0, 1.0),
        (1.0, 3.0),
        (-3.0, -1.0),
        (5.0, -3.0),
        (0.0, 0.0)
    ]
    """This table contains the periodic terms to compute Pluto's heliocentric
    longitude according to Table 37.A in Meeus' book, page 265"""

    PLUTO_LATITUDE = [
        (-5452852.0, -14974862),
        (3527812.0, 1672790.0),
        (-1050748.0, 327647.0),
        (178690.0, -292153.0),
        (18650.0, 100340.0),
        (-30697.0, -25823.0),
        (4878.0, 11248.0),
        (226.0, -64.0),
        (2030.0, -836.0),
        (69.0, -604.0),
        (-247.0, -567.0),
        (-57.0, 1.0),
        (-122.0, 175.0),
        (-49.0, -164.0),
        (-197.0, 199.0),
        (-25.0, 217.0),
        (589.0, -248.0),
        (-269.0, 711.0),
        (185.0, 193.0),
        (315.0, 807.0),
        (-130.0, -43.0),
        (5.0, 3.0),
        (2.0, 17.0),
        (2.0, 5.0),
        (2.0, 3.0),
        (3.0, 1.0),
        (2.0, -1.0),
        (1.0, -1.0),
        (0.0, -1.0),
        (0.0, 0.0),
        (0.0, -2.0),
        (2.0, 2.0),
        (-7.0, 0.0),
        (10.0, -8.0),
        (-3.0, 20.0),
        (6.0, 5.0),
        (14.0, 17.0),
        (-2.0, 0.0),
        (0.0, 0.0),
        (0.0, 0.0),
        (0.0, 1.0),
        (0.0, 0.0),
        (1.0, 0.0)
    ]
    """This table contains the periodic terms to compute Pluto's heliocentric
    latitude according to Table 37.A in Meeus' book, page 265"""

    PLUTO_RADIUS_VECTOR = [
        (66865439.0, 68951812.0),
        (-11827535.0, -332538.0),
        (1593179.0, -1438890.0),
        (-18444.0, 483220.0),
        (-65977.0, -85431.0),
        (31174.0, -6032.0),
        (-5794.0, 22161.0),
        (4601.0, 4032.0),
        (-1729.0, 234.0),
        (-415.0, 702.0),
        (239.0, 723.0),
        (67.0, -67.0),
        (1034.0, -451.0),
        (-129.0, 504.0),
        (480.0, -231.0),
        (2.0, -441.0),
        (-3359.0, 265.0),
        (7856.0, -7832.0),
        (36.0, 45763.0),
        (8663.0, 8547.0),
        (-809.0, -769.0),
        (263.0, -144.0),
        (-126.0, 32.0),
        (-35.0, -16.0),
        (-19.0, -4.0),
        (-15.0, 8.0),
        (-4.0, 12.0),
        (5.0, 6.0),
        (3.0, 1.0),
        (6.0, -2.0),
        (2.0, 2.0),
        (-2.0, -2.0),
        (14.0, 13.0),
        (-63.0, 13.0),
        (136.0, -236.0),
        (273.0, 1065.0),
        (251.0, 149.0),
        (-25.0, -9.0),
        (9.0, -2.0),
        (-8.0, 7.0),
        (2.0, -10.0),
        (19.0, 35.0),
        (10.0, 3.0)
    ]
    """This table contains the periodic terms to compute Pluto's heliocentric
    radius vector according to Table 37.A in Meeus' book, page 265"""

    class Pluto(object):
        """
        Class Pluto models that minor planet.
        """

        @staticmethod
        def geometric_heliocentric_position(epoch):
            """This method computes the geometric heliocentric position of planet
            Pluto for a given epoch.

            :param epoch: Epoch to compute Pluto position, as an Epoch object
            :type epoch: :py:class:`Epoch`

            :returns: A tuple with the heliocentric longitude and latitude (as
                :py:class:`Angle` objects), and the radius vector (as a float,
                in astronomical units), in that order
            :rtype: tuple
            :raises: TypeError if input value is of wrong type.
            :raises: ValueError if input epoch outside the 1885-2099 range.

            >>> epoch = Epoch(1992, 10, 13.0)
            >>> l, b, r = Pluto.geometric_heliocentric_position(epoch)
            >>> print(round(l, 5))
            232.74071
            >>> print(round(b, 5))
            14.58782
            >>> print(round(r, 6))
            29.711111
            """

            # First check that input value is of correct types
            if not isinstance(epoch, Epoch):
                raise TypeError("Invalid input type")
            # Check that the input epoch is within valid range
            y = epoch.year()
            if y < 1885.0 or y > 2099.0:
                raise ValueError("Epoch outside the 1885-2099 range")
            t = (epoch - JDE2000) / 36525.0
            jj = 34.35 + 3034.9057 * t
            ss = 50.08 + 1222.1138 * t
            pp = 238.96 + 144.96 * t
            # Compute the arguments
            corr_lon = 0.0
            corr_lat = 0.0
            corr_rad = 0.0
            for n, argument in enumerate(PLUTO_ARGUMENT):
                iii, jjj, kkk = argument
                alpha = Angle(iii * jj + jjj * ss + kkk * pp).to_positive()
                alpha = alpha.rad()
                sin_a = sin(alpha)
                cos_a = cos(alpha)
                a_lon, b_lon = PLUTO_LONGITUDE[n]
                corr_lon += a_lon * sin_a + b_lon * cos_a
                a_lat, b_lat = PLUTO_LATITUDE[n]
                corr_lat += a_lat * sin_a + b_lat * cos_a
                a_rad, b_rad = PLUTO_RADIUS_VECTOR[n]
                corr_rad += a_rad * sin_a + b_rad * cos_a
            # The coefficients in the tables were scaled up. Let's scale them down
            corr_lon /= 1000000.0
            corr_lat /= 1000000.0
            corr_rad /= 10000000.0
            lon = Angle(238.958116 + 144.96 * t + corr_lon)
            lat = Angle(-3.908239 + corr_lat)
            radius = 40.7241346 + corr_rad
            return lon, lat, radius

        @staticmethod
        def geocentric_position(epoch):
            """This method computes the geocentric position of Pluto (right
            ascension and declination) for the given epoch, for the standard
            equinox J2000.0.

            :param epoch: Epoch to compute geocentric position, as an Epoch object
            :type epoch: :py:class:`Epoch`

            :returns: A tuple containing the right ascension and the declination as
                Angle objects
            :rtype: tuple
            :raises: TypeError if input value is of wrong type.
            :raises: ValueError if input epoch outside the 1885-2099 range.

            >>> epoch = Epoch(1992, 10, 13.0)
            >>> ra, dec = Pluto.geocentric_position(epoch)
            >>> print(ra.ra_str(n_dec=1))
            15h 31' 43.7''
            >>> print(dec.dms_str(n_dec=0))
            -4d 27' 29.0''
            """

            # First check that input value is of correct types
            if not isinstance(epoch, Epoch):
                raise TypeError("Invalid input type")
            # Check that the input epoch is within valid range
            y = epoch.year()
            if y < 1885.0 or y > 2099.0:
                raise ValueError("Epoch outside the 1885-2099 range")
            # Compute the heliocentric position of Pluto
            ll, b, r = Pluto.geometric_heliocentric_position(epoch)
            # Change angles to radians
            ll = ll.rad()
            b = b.rad()
            # Values corresponding to obliquity of ecliptic (epsilon) for J2000.0
            sine = 0.397777156
            cose = 0.917482062
            x = r * cos(ll) * cos(b)
            y = r * (sin(ll) * cos(b) * cose - sin(b) * sine)
            z = r * (sin(ll) * cos(b) * sine + sin(b) * cose)
            # Compute Sun's J2000.0 rectacngular coordinates
            xs, ys, zs = Sun.rectangular_coordinates_j2000(epoch)
            # Compute auxiliary quantities
            xi = x + xs
            eta = y + ys
            zeta = z + zs
            # Compute Pluto's distance to Earth
            delta = sqrt(xi * xi + eta * eta + zeta * zeta)
            # Get the light-time difference
            tau = 0.0057755183 * delta
            # Repeat the computations using the light-time correction
            ll, b, r = Pluto.geometric_heliocentric_position(epoch - tau)
            # Change angles to radians
            ll = ll.rad()
            b = b.rad()
            x = r * cos(ll) * cos(b)
            y = r * (sin(ll) * cos(b) * cose - sin(b) * sine)
            z = r * (sin(ll) * cos(b) * sine + sin(b) * cose)
            # Compute auxiliary quantities
            xi = x + xs
            eta = y + ys
            zeta = z + zs
            # Compute Pluto's distance to Earth
            delta = sqrt(xi * xi + eta * eta + zeta * zeta)
            # Compute right ascension and declination
            alpha = Angle(atan2(eta, xi), radians=True)
            dec = Angle(asin(zeta / delta), radians=True)
            return alpha.to_positive(), dec

    def main():

        # Let's define a small helper function
        def print_me(msg, val):
            print("{}: {}".format(msg, val))

        # Let's show some uses of Pluto class
        print("\n" + 35 * "*")
        print("*** Use of Pluto class")
        print(35 * "*" + "\n")

        # Let's now compute the heliocentric position for a given epoch
        epoch = Epoch(1992, 10, 13.0)
        lon, lat, r = Pluto.geometric_heliocentric_position(epoch)
        print_me("Geometric Heliocentric Longitude", lon.to_positive())
        print_me("Geometric Heliocentric Latitude", lat)
        print_me("Radius vector", r)

        print("")

        # Compute the geocentric position for 1992/10/13:
        epoch = Epoch(1992, 10, 13.0)
        ra, dec = Pluto.geocentric_position(epoch)
        print_me("Right ascension", ra.ra_str(n_dec=1))
        print_me("Declination", dec.dms_str(n_dec=1))

    if __name__ == "__main__":

        main()