The Heliocentric Julian Date (HJD) is the
Julian Date (JD) corrected for differences in the
Earth's position with respect to the
Sun. When timing events that occur beyond the
Solar System, due to the finite
speed of light, the time the event is observed depends on the changing position of the observer in the Solar System. Before multiple observations can be combined, they must be reduced to a common, fixed, reference location. This correction also depends on the direction to the object or event being timed.
Magnitude and limitations
The correction is zero (HJD = JD) for objects at the poles of the
ecliptic. Elsewhere, it is approximately an annual sine curve, and the highest amplitude occurs on the ecliptic. The maximum correction corresponds to the time in which light travels the distance from the Sun to the Earth, i.e. ±8.3 min (500 s, 0.0058 days).
JD and HJD are defined independent of the
time standard. Rather, JD can be expressed as e.g.
UTC, UT1,
TT or
TAI. The differences between these time standards are of the order of a minute, so that for minute accuracy of timings the standard used has to be stated. The HJD correction involves the heliocentric position of the Earth, which is expressed in TT. While the practical choice may be UTC, the natural choice is TT.
Since the Sun itself orbits around the
barycentre of the Solar System, the HJD correction is not actually to a fixed reference. The difference between correction to the heliocentre and to the barycentre is up to ±4 s. For second accuracy, the
Barycentric Julian Date (BJD) should be calculated instead of the HJD.
The common formulation of the HJD correction assumes that the object is at infinite distance, certainly beyond the Solar System. The resulting error for
Edgeworth-Kuiper Belt objects would be 5 s, and for objects in the
main asteroid belt it would be 100 s. In this calculation, the
Moon – which is closer than the Sun – can be wrongly placed on the far side of the Sun, resulting in an error of about 15 min.
Calculation
In terms of the vector
from the heliocentre to the observer, the unit vector
from the observer toward the object or event, and the speed of light
:
When the
scalar product is expressed in terms of the
right ascension
Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the earth.
When paired w ...
and
declination
In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of the ...
of the Sun (index
) and of the extrasolar object this becomes: