Heliocentric Julian Day
Encyclopedia
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.
. 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.
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
and declination
of the Sun (index 
) and of the extrasolar object this becomes:
where
is the distance between Sun and observer. The same equation can be used with any astronomical coordinate system. In ecliptic coordinates
the Sun is at latitude zero, so that
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
's position with respect to the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
. When timing events that occur beyond the Solar System
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
, due to the finite speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
, 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 eclipticEcliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
. 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
Time standard
A time standard is a specification for measuring time: either the rate at which time passes; or points in time; or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. An example of a kind of time...
. Rather, JD can be expressed as e.g. UTC, UT1
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
, TT
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
or TAI
International Atomic Time
International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
. 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
Barycentric coordinates (astronomy)
In astronomy, barycentric coordinates are non-rotating coordinates with origin at the center of mass of two or more bodies.The barycenter is the point between two objects where they balance each other. For example, it is the center of mass where two or more celestial bodies orbit each other...
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
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
– 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
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
and declinationDeclination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
of the Sun (index ) and of the extrasolar object this becomes:where
is the distance between Sun and observer. The same equation can be used with any astronomical coordinate system. In ecliptic coordinatesEcliptic coordinate system
The ecliptic coordinate system is a celestial coordinate system that uses the ecliptic for its fundamental plane. The ecliptic is the path that the sun appears to follow across the celestial sphere over the course of a year. It is also the intersection of the Earth's orbital plane and the celestial...
the Sun is at latitude zero, so that
External links
- http://astroutils.astronomy.ohio-state.edu/time/: Online converter from UTC to BJDTDB, BJDTDB to UTC, or HJD (UTC or TT) to BJDTDB.