Return Earth’s heliocentric Keplerian elements at a given epoch.
Evaluates a linear secular model for Earth’s orbital elements
in the J2000 ecliptic and equinox frame. The model coefficients
are from JPL’s "Keplerian Elements for Approximate Positions of
the Major Planets" (Standish 1992, Table 1), valid for
3000 BC -- 3000 AD.
Parameters
----------
epoch_mjd : float, optional
Epoch as Modified Julian Date. Default is 51544.5
(J2000.0 = 2000 Jan 1.5 TDB).
Returns
-------
EarthElements
A namedtuple with fields:
``a_AU``
Semi-major axis in AU.
``e``
Eccentricity.
``inc_deg``
Inclination to the ecliptic in degrees. Set to a small
nonzero value (0.00005°) to avoid singularities in
rotation matrices; the true value is ~0 by definition
since the ecliptic *is* Earth’s mean orbital plane.
``Omega_deg``
Longitude of the ascending node in degrees. Zero by
definition in the ecliptic frame.
``omega_deg``
Argument of perihelion in degrees. Since Omega = 0 in
the ecliptic frame, this equals the longitude of
perihelion (ϖ).
Notes
-----
The linear model for each element is::
element(T) = element_0 + element_dot * T
where T is Julian centuries from J2000.0. The coefficients are:
====== =============== =================
Param Value at J2000 Rate (per century)
====== =============== =================
a 1.00000261 AU +0.00000562 AU
e 0.01671123 -0.00004392
ϖ 102.93768193° +0.32327364°
====== =============== =================
Inclination and Omega are fixed at ~0 (ecliptic frame).
MOID is a purely geometric quantity (no mean anomaly / phase
dependence), but the *shape and orientation* of Earth’s orbit
do evolve slowly. Evaluating at the asteroid’s osculating
element epoch ensures the two orbits are compared at a
consistent time.
References
----------
Standish, E.M. (1992). "Keplerian Elements for Approximate
Positions of the Major Planets." Solar System Dynamics Group,
JPL. https://ssd.jpl.nasa.gov/planets/approx_pos.html
Definition at line 28 of file moid.py.
1.13.2