The Moon State Vector Frame

The Moon state vector shown in this calculator gives the position and velocity of the Moon’s center measured from the Earth’s center.

Imagine placing the origin of a three-dimensional coordinate system at the center of the Earth. The Moon’s position is then described by three numbers: x, y, and z: the three components of one Earth-to-Moon vector.

\text{Earth center} \rightarrow \text{Moon center} = (x_{\text{Moon}},\,y_{\text{Moon}},\,z_{\text{Moon}})

What “J2000 ecliptic” means

The coordinates are expressed in the J2000 ecliptic reference frame.

That means the coordinate grid is tied to the orientation of Earth’s orbital plane at the standard epoch J2000.0, rather than the slowly changing ecliptic of the current date:

J2000 ecliptic: a fixed reference grid based on the position of the ecliptic at J2000.0.
Ecliptic of date: a slowly changing reference grid based on the ecliptic's position at the selected date.

This matters, because Earth’s equator, equinox, and ecliptic reference directions slowly drift over time due to precession and related long-term effects.

The calculator’s Moon state vector is therefore not using a coordinate grid that moves with the date; it is using a fixed J2000 reference grid, which makes the vector stable and suitable for comparison, storage, and later transformations.

The axis directions

In this J2000 ecliptic frame:

+x points toward the fixed zero-longitude direction, also called the J2000 vernal-equinox direction.
+y points 90° around the J2000 ecliptic from +x, in the direction of increasing ecliptic longitude. (This is also the Moon’s general prograde orbital direction.)
+z points north of the J2000 ecliptic plane.

So the displayed values are:

x_moon is how much of the Earth-to-Moon vector lies along the +x / −x direction.
y_moon is how much of the Earth-to-Moon vector lies along the +y / −y direction.
z_moon is how far the Moon is north or south of the J2000 ecliptic plane.

The same idea applies to the velocity (first derivative of position) components:

vx_moon is how fast the Moon’s x component is changing.
vy_moon is how fast the Moon’s y component is changing.
vz_moon is how fast the Moon’s z component is changing.

These position and velocity components are useful because many later quantities are built from them: distance, ecliptic longitude and latitude, right ascension and declination, shadow-axis geometry, and even fundamental-plane coordinates.

Distance and reverse direction

The Earth–Moon distance is the length of this vector:

D = \sqrt{ x_{\mathrm{Moon}}^2 + y_{\mathrm{Moon}}^2 + z_{\mathrm{Moon}}^2 }

The direction from the Moon back toward Earth is simply the opposite vector:

\text{Moon center} \rightarrow \text{Earth center} = (-x_{\text{Moon}},\,-y_{\text{Moon}},\,-z_{\text{Moon}})

That reversed vector is especially important for lunar libration: To find the sub-Earth point on the Moon, the calculator must determine the position of Earth from the Moon’s point of view. That requires the Moon-to-Earth direction.

The state vector shown here is the basic geometric starting point. It tells where the Moon is relative to Earth in a fixed space frame, and the calculator transforms that same geometry into other frames when needed.