question about ICRF/J2000 equinox orientation The DE406 ephemeris data and the NASA Horizons website all report the Earth's current coordinates on 2014 Sep 27, a few days after the Fall equinox, as approximately [1,0,0] AU.
However every reference source I've found on the ICRF/J2000 coordinate system has stated that the x-axis points towards the Vernal equinox.
Shouldn't the Earth's ICRF/J2000 coordinates be [-1,0,0] now that we are furthest from the Vernal equinox, and shouldn't it be [1,0,0] in six months when we are at the Vernal equinox?
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The DE406 ephemeris data results can be seen here:
http://www.astro-phys.com/api/de406/states?date=2014-9-28&unit=au&bodies=earth
The NASA Horizons website results can be seen here http://ssd.jpl.nasa.gov/horizons.cgi with "ephemeris type" changed to "vectors", target body set to "399" (Earth Geocenter), and coordinate origin set to "@0" (Solar System Barycenter).
 A: TL;DR version
The ICRF +x axis is more or less the direction from the Earth to the Sun at the vernal equinox, or about March 20. Six months later, the direction from the Sun to the Earth is more or less along the +x axis.
Keep reading!
A bit of a taint of the ancient concept of a geocentric universe remains in modern astronomy. How astronomers specify right ascension (and your subsequent confusion) represents one of those ancient taints.
Thanks to the obliquity of the ecliptic, which is itself a very geocentric concept, the Sun as viewed from the Earth appears to be south of the Earth's equator in northern hemisphere autumn and winter, and north of the equator in northern hemisphere spring and summer. The dates at which the Sun appears to cross the equator, along with the dates at which the Sun appears to reach its northernmost and southernmost extremes form the basis of our calendar. This knowledge was known to the ancients across many cultures. It predates Aristotelian physics by millennia.
To make these very ancient concepts more scientific, Hipparchus (~190 to ~120 BCE) marked the vernal equinox as both a point in time and as a direction in space as special.  As a point in time, the vernal equinox is that time at which the mean fictitious Sun (another archaic concept that astronomers have not quite eliminated) as viewed from a geocentric perspective appears to cross the Earth's mean equator. As a direction in space, the vernal equinox, aka the first point in Ares, is the direction from the center of the Earth to the center of the mean fictitious Sun at the vernal equinox (as a point in time).
What this means is that at the vernal equinox, the ICRF cartesian coordinates of the Sun from an Earth-centered perspective is about (1 AU, 0, 0). The position of the Earth from a heliocentric perspective? That's simple: Negate that vector.
At the autumnal equinox, which is what you question addresses, the ICRF coordinates of the Sun from an Earth-centered perspective is about (-1 AU, 0, 0). The coordinates of the Earth from a heliocentric perspective? Negate that vector, or about (+1AU, 0, 0).
