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Why do RA and DEC change so much?


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Why do the RA and DEC of stars change so much? Is it related to the equation of time?

Example  - Polaris today is RA 02h 52m but on 1 Jan 2000 it was 02h 31m. Twenty minutes is quite a lot when trying to calculate where it should be in a polar finder.

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Hi Neil,

That's entirely down to precession of the nodes (i.e. the roughly 26,000 year period over which the Earth's rotation axis "wobbles", like a spinning top wobbles). If you're unfamiliar with that, see e.g.

https://en.wikipedia.org/wiki/Precession

In the Equatorial coordinate system, RA coordinates are measured with respect to the vernal equinox (the point in space where the Sun appears to cross from the southern to the northern hemisphere), so as precession progresses, the orientation of the Earth's axial tilt changes, and with it the reference grid.

Imagine looking at an all-sky map with the RA and Dec grids printed on it. 0° Dec corresponds to the Celestial Equator, i.e. the projection of the Earth's equator on the sky. RA=0.0 hrs corresponds to the Vernal equinox - the location in the sky where (if we take a geocentric view!) the Sun appears to cross the celestial equator from south to north. 

As the Earth's rotation axis precesses, the angular tilt of the rotation axis remains approximately unchanged, but the orientation of the axis doesn't. So the orientation of the celestial equator and the position of the vernal equinox "slips" around the map. Hence the position of the stars, measured with respect to that grid, also changes.

There's a nice tool, called "NED", which allows you to calculate this for any pair of dates - here:

https://ned.ipac.caltech.edu/forms/calculator.html

This is why star maps come out with specific epochs listed - currently the epoch is 2000, before that the most commonly quoted epoch was 1950, and eventually we'll start to see coordinates quoted in Epoch 2050. But with less reliance on printed media, intermediate epochs are encountered more frequently now. For some very high precision measurements, it's not uncommon for the researcher to "precess the coordinates" to match the current date or some other desired epoch.

Hope that's clear-ish...

 

Nigel

 

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One other point to mention - it's particularly noticeable in the case of Polaris' coordinates, because Polaris is close to the north celestial pole, where the lines of Right Ascension converge. So a large change in the RA coordinate doesn't correspond to a large absolute change in the angular position. It's just like standing at the north pole, where you could walk around through 360 degrees of longitude in a few small steps - or have one foot in the eastern hemisphere and the other in the west...

N.

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I understand precession, but at that rate of movement (21 minutes in 16 years) Polaris will make a full circuit in 68 years - there must be something else at work?

I wondered about nutation, but at 17" minutes of arc that has only a maximum impact of about one minute on longitude.

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I take that back:

 

"The Earth's axis rotates slowly westward about the poles of the ecliptic, completing one circuit in about 26,000 years. This effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. Therefore, equatorial coordinates (including right ascension) are inherently relative to the year of their observation, and astronomers specify them with reference to a particular year, known as an epoch. Coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch.[7] Right ascension for "fixed stars" near the ecliptic and equator increases by about 3.3 seconds per year on average, or 5.5 minutes per century, but for fixed stars further from the ecliptic the rate of change can be anything from negative infinity to positive infinity. The right ascension of Polaris is increasing quickly. The North Ecliptic Pole in Draco and the South Ecliptic Pole in Dorado are always at right ascension 18h and 6h respectively."

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Well, Polaris is veritably scudding across the sky, and speeding up! From Stellarium, ignoring arc-seconds:

Polaris_RA.jpg

A three and a half hour change over a century has to be taken into account for polar finder calculators!

Here's my bodge for rapid calculation using simple microcontroller maths:

Year RA Minutes Calculated RA
1990 140 140
2000 151 150
2010 163 162
2020 177 176
2030 191 192
2040 209 209
2050 228 228
2060 249 249
2070 273 272
2080 298 296
2090 325 322
2100 353 350
2110 382 380

This close fitting equation uses only right-shift division (by powers of 2) and integer multiplication. YR is the year number from -10 to 110.

RA = 150 + YR + YR/8 + ((YR+YR/8) * YR/64)

The quick witted will notice the term YR+YR/8 is fortuitously repeated, so it can be as simple as:

RA = 150 + (YR+YR/8)*(1+YR/64)

A result within three minutes should be good enough for polar alignment!

 

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