astro 2.0.0

Advanced algorithms for astronomy
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132

/*
Copyright (c) 2015, 2016 Saurav Sachidanand

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/

//! The four Galilean moons

/*

Meeus referrs to the moons as Satellites I, II, III and IV.
Wikipedia says satellite I is Io, II is Europa, III is Ganymede
and IV is Callisto. That mapping is used.

*/

/// Represents a Galilean moon
pub enum Moon {
    /// Io
    Io,
    /// Europa
    Europa,
    /// Ganymede
    Ganymede,
    /// Callisto
    Callisto
}

/**
Computes the apparent rectangular coordinates for a Galilean moon

This function implements the low accuracy method described in Meeus's
book, that is *"sufficient for identifying the satellites at the
telescope, or drawing a wavy-line diagram showing their positions with
respect to Jupiter"*

# Returns

`(X, Y)`

The rectangular coordinates returned give the apparent position of a moon,
with respect to Jupiter, as seen from Earth. The `X` and `Y`
coordinates are measured from the center of the disk of Jupiter, in units
of Jupiter's equatorial radius.

`X` is measured positively to the west of Jupiter, and negatively to the
east. The x-axis coincides with Jupiter's equator.

`Y` is measured positively to the north of Jupiter, and negatively to
the south. The y-axis coincides with Jupiter's axis of rotation.

# Arguments

* `JD`  : Julian (Ephemeris) day
* `moon`: The [Moon](./enum.Moon.html)
**/
pub fn apprnt_rect_coords(JD: f64, moon: &Moon) -> (f64, f64) {

    let d = JD - 2451545.0;
    let V = (172.74 + 0.00111588*d).to_radians();
    let M = (357.529 + 0.9856003*d).to_radians();
    let N = (20.02 + 0.0830853*d + 0.329*V.sin()).to_radians();
    let J = (66.115 + 0.9025179*d - 0.329*V.sin()).to_radians();
    let A = (1.915*M.sin() + 0.02*(2.0*M).sin()).to_radians();
    let B = (5.555*N.sin() + 0.168*(2.0*N).sin()).to_radians();
    let K = J + A - B;
    let R = 1.00014 - 0.01671*M.cos() - 0.00014*(2.0*M).cos();
    let r = 5.20872 - 0.25208*N.cos() - 0.00611*(2.0*N).cos();
    let delta = (r*r + R*R - 2.0*r*R*K.cos()).sqrt();

    let phi = (R*K.sin()/delta).asin();

    let d_minus_delta_by_173 = d - delta/173.0;
    let phi_minus_B = phi - B;

    let u1 = (163.8069 + 203.4058646*d_minus_delta_by_173).to_radians() + phi_minus_B;
    let u2 = (358.414  + 101.2916335*d_minus_delta_by_173).to_radians() + phi_minus_B;
    let u3 = (5.7176   + 50.234518*d_minus_delta_by_173).to_radians()   + phi_minus_B;

    let mut u = match moon {
        &Moon::Io       => u1,
        &Moon::Europa   => u2,
        &Moon::Ganymede => u3,
        &Moon::Callisto => (224.8092 + 21.48798*d_minus_delta_by_173).to_radians() + phi_minus_B,
    };

    let G = (331.18 + 50.310482*d_minus_delta_by_173).to_radians();
    let H = (87.45  + 21.569231*d_minus_delta_by_173).to_radians();

    u += (match moon {
        &Moon::Io       => 0.473 * (2.0*(u1 - u2)).sin(),
        &Moon::Europa   => 1.065 * (2.0*(u2 - u3)).sin(),
        &Moon::Ganymede => 0.165 * G.sin(),
        &Moon::Callisto => 0.843 * H.sin(),
    }).to_radians();

    let r_moon = match moon {
        &Moon::Io       => (5.9057  - 0.0244*(2.0*(u1 - u2)).cos()),
        &Moon::Europa   => (9.3966  - 0.0882*(2.0*(u2 - u3)).cos()),
        &Moon::Ganymede => (14.9883 - 0.0216*G.cos()),
        &Moon::Callisto => (26.3627 - 0.1939*H.cos()),
    };

    let lambda = (34.35 + 0.083091*d + 0.329*V.sin()).to_radians() + B;
    let Ds = (3.12 * (lambda + 42.8_f64.to_radians()).sin()).to_radians();
    let De = Ds - (
        2.22*phi.sin()*(lambda + 22_f64.to_radians()).cos()
        + 1.3*(r - delta)*(lambda - 100.5_f64.to_radians()).sin()/delta
    ).to_radians();

    let X =  r_moon * u.sin();
    let Y = -r_moon * u.cos() * De.sin();

    (X, Y)

}