Epoch (astronomy) Totally Explained

Everything about Besselian Epoch totally explained

In astronomy, an epoch is a moment in time for which something is specified that can vary, such as the position or the orbital elements of a celestial body. Typically, the epoch is either the moment that the observations were made or the moment for which the predictions were calculated.

Epoch versus equinox

Coordinates are incomplete without a specification of the used coordinate system. The most common celestial coordinate systems (equatorial coordinates and ecliptic coordinates) are tied to the position of the vernal equinox, which itself is linked to the orientations of the rotation axis of the Earth and of the orbit of the Earth around the Sun. These orientations vary (though slowly, for example due to precession), so there's an infinite number of such coordinate systems, each defined by the moment at which the coordinate system really fits the orientations of the rotation axis of the Earth and the orbit of the Earth around the Sun. That moment is called the equinox.
The equinox defines (partly) which coordinate system is used, and the epoch defines (completely) at which moment the observations or predictions are valid. A particular coordinate system (equinox) could be used forever, but a set of predictions for a particular date (epoch) will be (approximately) valid for only a limited period of time.
For example, the boundaries of the IAU constellations are specified relative to an equinox from near the beginning of the year 1875. To find out in which constellation a particular comet stands today, the current position of that comet must be expressed in the coordinate system of 1875 (epoch = now, equinox = 1875). That coordinate system can still be used today, while hardly any predictions made originally for 1875 (epoch = 1875) are still useful today. Equinox of the date means that the equinox is the same as the epoch.

Why switch to another standard equinox and epoch?

Calculations of the visibility of celestial objects for an observer at a specific location on Earth require the equatorial coordinates of the objects, relative to the equinox of the date. If the coordinates relative to some other equinox are used, then that will cause errors in the results. The magnitude of those errors increases as the time difference compared to the equinox of the date increases, because of precession of the equinoxes. If the time difference is small, then fairly easy and small corrections for the precession suffice. If the time difference gets large, then tedious, complicated corrections must be applied. So, a stellar position read from a star atlas or catalog that's based on a sufficiently old equinox can't be used without tedious corrections, at least not if reasonable accuracy is required.
Additionally, star positions change even if the coordinate system does not, because the stars move relative to each other through space. The apparent motion along the sky relative to the other stars is called proper motion. Most stars have very small proper motions, but a few have proper motions that accumulate to noticeable distances after a few tens of years. So, some stellar positions read from a star atlas or catalog for a sufficiently old epoch can't be used without tedious corrections for proper motion, at least not if reasonable accuracy is required.
Because of precession and proper motion, star positions become less useful as their equinox and epoch get older. After a while, it's easier to switch to a newer epoch and equinox than to keep applying the corrections to the data from the older epoch and equinox.

Ways to specify an epoch or equinox

Epochs and equinoxes are moments in time, so they can be specified in the same way as moments that indicate other things than epochs and equinoxes. The following standard ways of specifying epochs and equinoxes seem most popular:

Julian Day Numbers, for example, JDN 2433282.4235 for 1950 January 0.9235 TT
Besselian years, for example, 1950.0 or B1950.0 for 1950 January 0.9235 TT
Julian years, for example, J2000.0 for 2000 January 1.5000 TT

All three of these are expressed in TT = Terrestrial Time.
Besselian and Julian years are not often used to specify an epoch, except for things that vary very slowly, such as star positions. For example, the Hipparcos catalog summary defines the 'catalog epoch' to be equal to J1991.25, which is in terms of Julian years.

Besselian years

A Besselian year is named after the German mathematician and astronomer Friedrich Bessel (1784 – 1846). Meeus defines the beginning of a Besselian year to be the moment at which the mean longitude of the Sun, including the effect of aberration and measured from the mean equinox of the date, is 280 degrees exactly. This moment falls near the beginning of the corresponding Gregorian year. Unfortunately, the orbit of the Earth around the Sun isn't entirely fixed, so the length of the Besselian year according to this definition isn't constant. This makes such Besselian years somewhat difficult to work with.
   Lieske says that a 'Besselian epoch' can be calculated from the Julian date according to ť B = 1900.0 + (Julian date − 2415020.31352) / 365.242198781

This relationship is included in the SOFA software library, which implies endorsement by the IAU.
   The definition by Lieske isn't consistent with the earlier definition in terms of the mean longitude of the Sun. When using Besselian years, specify which definition is being used.
   To distinguish between calendar years and Besselian years, it became customary to add '.0' to the Besselian years. Since the switch to Julian years in the mid-1980s, it has become customary to prefix 'B' to Besselian years. So, '1950' is the calendar year 1950, and '1950.0' = 'B1950.0' is the beginning of Besselian year 1950.

The IAU constellation boundaries are defined in the equatorial coordinate system relative to the equinox of B1875.0.

The Henry Draper Catalog uses the equinox B1900.0.

The classical star atlas Tabulae Caelestes used B1925.0 as its equinox. According to Meeus, and also according to the formula given above,

B1900.0 = JDE 2415020.3135 = 1900 January 0.8135 TT

B1950.0 = JDE 2433282.4235 = 1950 January 0.9235 TT

Julian years

A Julian year, named after Julius Caesar (100 BC — 44 BC), is a year of exactly 365.25 days. Julian year 2000 began on 2000 January 1 at exactly 12:00 TT. The beginning of Julian years are indicated with prefix 'J' and suffix '.0', for example 'J2000.0' for the beginning of Julian year 2000.
   Because Julian years have a fixed length, their beginning is far easier to calculate than the beginning of Besselian years.
   The IAU decided at their General Assembly of 1976 that the new standard equinox of J2000.0 should be used starting in 1984. (Before that, the equinox of B1950.0 seems to have been the standard.) If the past is a good guide, then we may expect to switch to J2050.0 in the mid-2030s.
   Julian epochs are calculated according to:
ť J = 2000.0 + (Julian date − 2451545.0)/365.25

J2000.0

J2000.0 is precisely Julian date 2451545.0 TT (Terrestrial Time), or January 1, 2000, noon TT. This is equivalent to January 1, 2000, 11:59:27.816 TAI or January 1, 2000, 11:58:55.816 UTC.

Further Information

Get more info on 'Besselian Epoch'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://epoch__astronomy.totallyexplained.com">Epoch (astronomy) Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.