We use the term **epoch** (of a given date) to refer to the actual measured coordinates of a star that takes into account precession, nutation, and proper motion. The term **equinox** means that the coordinates have been precessed to a given date, but that other factors affecting a star’s position have not been applied. So, equinox 2000.0 is not the same as epoch 2000.0.

**Example: Barnard’s Star**

Epoch 2000.0 coordinates: α = 17^{h} 57^{m} 48.49803^{s}, δ = +4° 41′ 36.2072″ (the actual position of Barnard’s Star at 0^{h} UT on January 1, 2000, accounting for precession, nutation, and proper motion)

Equinox 2017.1 coordinates: α = 17^{h} 58^{m} 39.20689^{s}, δ = +4° 41′ 33.5614″ (coordinates have been precessed from epoch 2000.0 above to today’s date, but nutation and proper motion have not been applied)

Epoch 2017.1 coordinates: α = 17^{h} 58^{m} 37.85^{s}, δ = +4° 44′ 37.8″ (the actual position of Barnard’s Star on January 19, 2017, accounting for precession, nutation, and proper motion)

Sometimes, the epochal coordinates are further adjusted to account for aberration and atmospheric refraction. The latter tends to “lift” stars towards the zenith—the closer to the horizon the greater the lift.

Please,

Where did you get the decimal part of the equinox and epoch dates?

How is this calculated in each case?

Much obliged.

Regards,

Patrick

Hi Patrick,

The decimal part of the equinox and epoch dates is the fractional portion of a year that has occurred by a given date. In the example above, 0 hours UT on January 19, 2017 is 0.049 of the way between 0 hours UT January 1, 2017 and 0 hours UT January 1, 2018, so rounding to one decimal place, 0.0, I should have written 2017.0 instead of 2017.1.

It may be helpful to look at a day-of-the-year calendar, such as this one:

https://www.esrl.noaa.gov/gmd/grad/neubrew/Calendar.jsp

Here’s another example. Since there are 366 days in 2020 (a leap year), and tomorrow will be February 20, if we wanted to calculate coordinates for February 20, 2020, the epoch or equinox date would be 2020 + (51-1)/366 = 2020.1 (or 2020.137 to be more precise), since the interval between January 1st and February 20th is 50 days and it is 366 days between January 1, 2020 and January 1, 2021. So the equinox or epoch date is just a label. Make sense?

Thanks for your question!

David,

Very nice.

Thank you.

Patrick