The orbital elements

The primary orbital elements are here denoted as:

N = longitude of the ascending node
i = inclination to the ecliptic (plane of the Earth's orbit)
w = argument of perihelion
a = semi-major axis, or mean distance from Sun
e = eccentricity (0=circle, 0-1=ellipse, 1=parabola)
M = mean anomaly (0 at perihelion; increases uniformly with time)

Related orbital elements are:

w1 = N + w = longitude of perihelion
L = M + w1 = mean longitude
q = a*(1-e) = perihelion distance
Q = a*(1+e) = aphelion distance
P = a ^ 1.5 = orbital period (years if a is in AU, astronomical units)
T = Epoch_of_M - (M(deg)/360_deg) / P = time of perihelion
v = true anomaly (angle between position and perihelion)
E = eccentric anomaly

One Astronomical Unit (AU) is the Earth's mean distance to the Sun, or 149.6 million km. When closest to the Sun, a planet is in perihelion, and when most distant from the Sun it's in aphelion. For the Moon, an artificial satellite, or any other body orbiting the Earth, one says perigee and apogee instead, for the points in orbit least and most distant from Earth.

To describe the position in the orbit, we use three angles: Mean Anomaly, True Anomaly, and Eccentric Anomaly. They are all zero when the planet is in perihelion:
Mean Anomaly (M): This angle increases uniformly over time, by 360 degrees per orbital period. It's zero at perihelion. It's easily computed from the orbital period and the time since last perihelion.
True Anomaly (v): This is the actual angle between the planet and the perihelion, as seen from the central body (in this case the Sun). It increases non-uniformly with time, changing most rapidly at perihelion.
Eccentric Anomaly (E): This is an auxiliary angle used in Kepler's Equation, when computing the True Anomaly from the Mean Anomaly and the orbital eccentricity.
Note that for a circular orbit (eccentricity=0), these three angles are all equal to each other.


Orbital elements of the Sun:

N = 0.0
i = 0.0
w = 282.9404 + 4.70935E-5 * d
a = 1.000000 (AU)
e = 0.016709 - 1.151E-9 * d
M = 356.0470 + 0.9856002585 * d

Orbital elements of the Moon:

N = 125.1228 - 0.0529538083 * d
i = 5.1454
w = 318.0634 + 0.1643573223 * d
a = 60.2666 (Earth radii)
e = 0.054900
M = 115.3654 + 13.0649929509 * d

Orbital elements of Mercury:

N = 48.3313 + 3.24587E-5 * d
i = 7.0047 + 5.00E-8 * d
w = 29.1241 + 1.01444E-5 * d
a = 0.387098 (AU)
e = 0.205635 + 5.59E-10 * d
M = 168.6562 + 4.0923344368 * d

Orbital elements of Venus:

N = 76.6799 + 2.46590E-5 * d
i = 3.3946 + 2.75E-8 * d
w = 54.8910 + 1.38374E-5 * d
a = 0.723330 (AU)
e = 0.006773 - 1.302E-9 * d
M = 48.0052 + 1.6021302244 * d

Orbital elements of Mars:

N = 49.5574 + 2.11081E-5 * d
i = 1.8497 - 1.78E-8 * d
w = 286.5016 + 2.92961E-5 * d
a = 1.523688 (AU)
e = 0.093405 + 2.516E-9 * d
M = 18.6021 + 0.5240207766 * d

Orbital elements of Jupiter:

N = 100.4542 + 2.76854E-5 * d
i = 1.3030 - 1.557E-7 * d
w = 273.8777 + 1.64505E-5 * d
a = 5.20256 (AU)
e = 0.048498 + 4.469E-9 * d
M = 19.8950 + 0.0830853001 * d

Orbital elements of Saturn:

N = 113.6634 + 2.38980E-5 * d
i = 2.4886 - 1.081E-7 * d
w = 339.3939 + 2.97661E-5 * d
a = 9.55475 (AU)
e = 0.055546 - 9.499E-9 * d
M = 316.9670 + 0.0334442282 * d

Orbital elements of Uranus:

N = 74.0005 + 1.3978E-5 * d
i = 0.7733 + 1.9E-8 * d
w = 96.6612 + 3.0565E-5 * d
a = 19.18171 - 1.55E-8 * d (AU)
e = 0.047318 + 7.45E-9 * d
M = 142.5905 + 0.011725806 * d

Orbital elements of Neptune:

N = 131.7806 + 3.0173E-5 * d
i = 1.7700 - 2.55E-7 * d
w = 272.8461 - 6.027E-6 * d
a = 30.05826 + 3.313E-8 * d (AU)
e = 0.008606 + 2.15E-9 * d
M = 260.2471 + 0.005995147 * d