Return canonical heliocentric Keplerian orbital elements for the Earth,
suitable for MOID computations, in the J2000 mean ecliptic and equinox
reference frame.
The elements describe a *fixed Keplerian ellipse* that approximates the
Earth's mean orbit at epoch J2000. This is the standard convention used
in MOID literature and software (e.g., Milani & Gronchi, NEODyS, JPL)
when computing the MOID between small bodies and the Earth.
Returns
-------
EarthElements
A namedtuple with fields:
- a_AU : float
Semi-major axis in astronomical units (AU).
Canonical value: 1.00000011 AU
- e : float
Eccentricity (dimensionless).
Canonical value: 0.01671022
- inc_deg : float
Inclination to the ecliptic in degrees.
Canonical value: 0.00005 deg
Note: by definition the ecliptic plane is the Earth's mean orbital
plane, so the true inclination is ~0. A very small non-zero value
is used in practice to avoid singularities in rotation matrices
and angle definitions.
- Omega_deg : float
Longitude of the ascending node in degrees, measured in the
ecliptic plane from the J2000 vernal equinox.
Canonical value: -11.26064 deg (equivalent to 348.73936 deg)
- omega_deg : float
Argument of perihelion in degrees, measured from the ascending
node along the Earth's orbital plane.
Canonical value: 102.94719 deg
Notes
-----
* These values are the widely used J2000 "mean elements" of the Earth’s
heliocentric orbit, compatible with VSOP87-style low-order models and
with the orbital elements quoted in many celestial mechanics references.
* They are intended for *geometric* computations such as MOID, where one
wants a fixed Keplerian ellipse representing the Earth's orbit, rather
than the true, time-varying perturbed Earth orbit.
* If you are using the MOIDSolver defined above, you can plug this
directly into the solver as the Earth orbit, e.g.:
earth = earth_orbit_J2000()
result = solver.compute(asteroid_elements, earth)
or reverse the order depending on which way you want to label the
"orbit 1" quantities.
* The epoch associated with these elements is J2000.0; MOID is a purely
geometric quantity, so there is no mean anomaly / phase dependence.
References
----------
These values (or very close variants) are quoted in many sources, e.g.:
- Explanatory Supplement to the Astronomical Almanac
- VSOP87/IAU-style mean orbital element lists for planets
- Milani, A., & Gronchi, G. F., "Theory of Orbit Determination"
- Online resources summarizing J2000 planetary elements
Definition at line 28 of file moid.py.
1.13.2