# Coverage for pySDC/implementations/problem_classes/FullSolarSystem.py: 100%

## 43 statements

, created at 2024-09-20 17:10 +0000

1import numpy as np

3from pySDC.implementations.datatype_classes.particles import particles, acceleration

4from pySDC.implementations.problem_classes.OuterSolarSystem import outer_solar_system

7# noinspection PyUnusedLocal

8class full_solar_system(outer_solar_system):

9 r"""

10 The :math:N-body problem describes the mutual influence of the motion of :math:N bodies. Formulation of the problem is

11 based on Newton's second law. Therefore, the :math:N-body problem is formulated as

13 .. math::

14 m_i \frac{d^2 {\bf r}_i}{d t^2} = \sum_{j=1, i\neq j}^N G \frac{m_i m_j}{|{\bf r}_i - {\bf r}_j|^3}({\bf r}_i - {\bf r}_j),

16 where :math:m_i is the :math:i-th mass point with position described by the vector :math:{\bf r}_i, and :math:G

17 is the gravitational constant. If only the sun influences the motion of the bodies gravitationally, the equations become

19 .. math::

20 m_i \frac{d^2 {\bf r}_i}{d t^2} = G \frac{m_1}{|{\bf r}_i - {\bf r}_1|^3}({\bf r}_i - {\bf r}_1).

22 This class implements the full solar system containing all planets including Earth's moon, i.e., :math:N=10. Initial conditions

23 are taken from [1]_, and masses relative to the sun taken from [2]_.

25 Parameters

26 ----------

27 sun_only : bool, optional

28 If False, only the sun is taken into account for the influence of the motion.

30 Attributes

31 ----------

32 G : float

33 Gravitational constant.

35 References

36 ----------

37 .. [1] https://www.aanda.org/articles/aa/full/2002/08/aa1405/aa1405.right.html

38 .. [2] https://en.wikipedia.org/wiki/Planetary_mass#Values_from_the_DE405_ephemeris

39 """

41 dtype_u = particles

42 dtype_f = acceleration

44 def __init__(self, sun_only=False):

45 """Initialization routine"""

47 super().__init__(sun_only)

48 self.init = ((3, 10), None, np.dtype('float64'))

50 def u_exact(self, t):

51 r"""

52 Routine to compute the exact/initial trajectory at time :math:t. Values here are taken from [1]_, [2]_.

54 Parameters

55 ----------

56 t : float

57 Time of the exact/initial trajectory.

59 Returns

60 -------

61 me : dtype_u

62 Exact/initial position and velocity.

63 """

64 assert t == 0.0, 'error, u_exact only works for the initial time t0=0'

65 me = self.dtype_u(self.init)

67 me.pos[:, 0] = [0.0, 0.0, 0.0]

68 me.pos[:, 1] = [-2.503321047836e-01, +1.873217481656e-01, +1.260230112145e-01]

69 me.pos[:, 2] = [+1.747780055994e-02, -6.624210296743e-01, -2.991203277122e-01]

70 me.pos[:, 3] = [-9.091916173950e-01, +3.592925969244e-01, +1.557729610506e-01]

71 me.pos[:, 4] = [+1.203018828754e00, +7.270712989688e-01, +3.009561427569e-01]

72 me.pos[:, 5] = [+3.733076999471e00, +3.052424824299e00, +1.217426663570e00]

73 me.pos[:, 6] = [+6.164433062913e00, +6.366775402981e00, +2.364531109847e00]

74 me.pos[:, 7] = [+1.457964661868e01, -1.236891078519e01, -5.623617280033e00]

75 me.pos[:, 8] = [+1.695491139909e01, -2.288713988623e01, -9.789921035251e00]

76 me.pos[:, 9] = [-9.707098450131e00, -2.804098175319e01, -5.823808919246e00]

78 me.vel[:, 0] = [0.0, 0.0, 0.0]

79 me.vel[:, 1] = [-2.438808424736e-02, -1.850224608274e-02, -7.353811537540e-03]

80 me.vel[:, 2] = [+2.008547034175e-02, +8.365454832702e-04, -8.947888514893e-04]

81 me.vel[:, 3] = [-7.085843239142e-03, -1.455634327653e-02, -6.310912842359e-03]

82 me.vel[:, 4] = [-7.124453943885e-03, +1.166307407692e-02, +5.542098698449e-03]

83 me.vel[:, 5] = [-5.086540617947e-03, +5.493643783389e-03, +2.478685100749e-03]

84 me.vel[:, 6] = [-4.426823593779e-03, +3.394060157503e-03, +1.592261423092e-03]

85 me.vel[:, 7] = [+2.647505630327e-03, +2.487457379099e-03, +1.052000252243e-03]

86 me.vel[:, 8] = [+2.568651772461e-03, +1.681832388267e-03, +6.245613982833e-04]

87 me.vel[:, 9] = [+3.034112963576e-03, -1.111317562971e-03, -1.261841468083e-03]

89 me.m[0] = 1.0 # Sun

90 me.m[1] = 0.1660100 * 1e-06 # Mercury

91 me.m[2] = 2.4478383 * 1e-06 # Venus

92 me.m[3] = 3.0404326 * 1e-06 # Earth+Moon

93 me.m[4] = 0.3227151 * 1e-06 # Mars

94 me.m[5] = 954.79194 * 1e-06 # Jupiter

95 me.m[6] = 285.88600 * 1e-06 # Saturn

96 me.m[7] = 43.662440 * 1e-06 # Uranus

97 me.m[8] = 51.513890 * 1e-06 # Neptune

98 me.m[9] = 0.0073960 * 1e-06 # Pluto

100 return me