Crate vsop87

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This library implements the VSOP87 solutions to calculate the positions of the planets in the solar system.

The main module calculates heliocentric ecliptic orbital elements for the equinox J2000.0 for the planets in the solar system, the basic VSOP87 solution. There is one module per other VSOP87 implementation: VSOP87A, VSOP87B, VSOP87C, VSOP87D and VSOP87E. More information can be found here and here.

Each module has its own documentation, and here is the documentation on the base VSOP87 solution. The VSOP87 algorithm has great precission (under 1“) for 4,000 years before and after J2000 epoch for Mercury, Venus, Earth-Moon barycenter and Mars, for 2,000 years in the case of Jupiter and Saturn and for 6,000 years for Uranus and Neptune.

The base VSOP87 solution calculates the orbital elements of the planets arount the Sun. The returned elements are a special VSOP87 orbital elements, that can be converted into usual keplerian elements using the Into trait. These elements are ideal to get an idea on how the orbits are changing over time. It can also be used for other complex orbital computations.

Example

As an example, here we calculate the orbital parameters for Mercury on the January 1st, 2000. The VSOP87 algorithm requires dates to be entered as Julian Day (JD). In our case, that date is 2451545.0.

We first calculate the VSOP87 elements:

let vsop87_elts = vsop87::mercury(2451545.0);

assert!(vsop87_elts.a > 0.3870982121 && vsop87_elts.a < 0.3870982123);
assert!(vsop87_elts.l > 4.4026057778 && vsop87_elts.l < 4.4026057780);
assert!(vsop87_elts.k > 0.0446647517 && vsop87_elts.k < 0.0446647519);
assert!(vsop87_elts.h > 0.2007208957 && vsop87_elts.h < 0.2007208959);
assert!(vsop87_elts.q > 0.0406161540 && vsop87_elts.q < 0.0406161542);
assert!(vsop87_elts.p > 0.04563512 && vsop87_elts.p < 0.04563588);

Note that the > and < comparisons are there because floats should not be compared using ==. Those numbers are retrieved from the test data of the VSOP87 algorithm.

We can then convert them into keplerian elements, by using both KeplerianElements::from() or the into() function in the VSOP87 elements. This also works the other way around:

use vsop87::{KeplerianElements, VSOP87Elements};

let elements = KeplerianElements::from(vsop87_elts);
let convert_back: VSOP87Elements = elements.into();

assert!(elements.semimajor_axis() > 0.387097 && elements.semimajor_axis() < 0.387099);
assert!(elements.eccentricity() > 0.205629 && elements.eccentricity() < 0.205631);
assert!(elements.inclination() > 0.122260 && elements.inclination() < 0.122261);
assert!(elements.ascending_node() > 0.843525 && elements.ascending_node() < 0.843527);
assert!(elements.periapsis() > 1.35183 && elements.periapsis() < 1.35185);
assert!(elements.mean_anomaly() > 4.40259 && elements.mean_anomaly() < 4.40261);

As you can see, these numbers perfectly match those from NASA.

Modules

  • vsop87a
    VSOP87A algorithm: Heliocentric ecliptic rectangular coordinates for the equinox J2000.0.
  • vsop87b
    VSOP87B algorithm: Heliocentric ecliptic spherical coordinates for the equinox J2000.0.
  • vsop87c
    VSOP87C algorithm: Heliocentric ecliptic rectangular coordinates for the equinox of the day.
  • vsop87d
    VSOP87D algorithm: Heliocentric ecliptic spherical coordinates for the equinox of the day.
  • vsop87e
    VSOP87E algorithm: Barycentric ecliptic rectangular coordinates for the equinox J2000.0.

Structs

Functions

  • earth_moon
    Calculates VSOP87 solution for Earth - Moon barycenter.
  • jupiter
    Calculates VSOP87 solution for Jupiter.
  • mars
    Calculates VSOP87 solution for Mars.
  • mercury
    Calculates VSOP87 solution for Mercury.
  • neptune
    Calculates VSOP87 solution for Neptune.
  • saturn
    Calculates VSOP87 solution for Saturn.
  • uranus
    Calculates VSOP87 solution for Uranus.
  • venus
    Calculates VSOP87 solution for Venus.