إحداثيات استوائية RA-Dec

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positional

إحداثيات استوائية (2) RA-Dec

{Note: If your browser does not distinguish between "a,b" and " α, β " (the Greek letters "alpha, beta") then I am afraid you will not be able to make much sense of the equations on this page.}

Coordinates in the first equatorial system (HA and declination)
still depend on the time of observation.
Now we change the zero-point for our coordinates.


We choose a fixed point on the celestial equator,
called the vernal equinox, or the First Point of Aries.
The symbol for this is the astrological symbol for Aries:


(The function of this point will become clearer later on.)

The declination (δ) of object X is measured in the same way as before.
The Right Ascension or RA (α) of object X
is the angle along the celestial equator measured eastwards
from the vernal equinox to the meridian of X.
Like HA, RA is measured in hours 0-24h, but it goes in the opposite direction.


Comparison of these celestial coordinate systems with the terrestrial system:

terrestrial alt-az HA-dec RA-dec
equator horizon celestial equator celestial equator
North Pole zenith North Celestial Pole North Celestial Pole
South Pole nadir South Celestial Pole South Celestial Pole
latitude altitude declination declination
co-latitude zenith distance North Polar Distance North Polar Distance
parallel of latitude parallel of altitude parallel of declination parallel of declination
meridian of longitude vertical circle meridian meridian
Greenwich Meridian Principal Vertical celestial meridian vernal equinox
longitude azimuth Hour Angle Right Ascension

تمرين:

The four stars at the corners of the “Great Square of Pegasus” are:

star

R.A.

declination

α And

00h 08m

+29°05'

β Peg

23h 04m

+28° 05'

α Peg

23h 05m

+15° 12'

γ Peg

00h 13m

+15° 11'

Calculate the lengths of the two diagonals of the “Square”.

الحل


It is necessary to plot the four stars, at least approximately,
to find out which pairs form the diagonals!


Then, to find the length of each diagonal, use the cosine rule:
cos S1S2 = cos S1P cos S2P + sin S1P sin S2P cos P


This gives {α And} to {α Peg} = 20.1°
and {β Peg} to {γ Peg} = 20.5°.

The Right Ascension and declination of a star do not normally change over short periods of time; but the Hour Angle changes constantly with time. Consequently we have to find a way of defining the time.

Equatorial System (2) RA-Dec

Arabic Index
positional

Equatorial System (2) RA-Dec

{Note: If your browser does not distinguish between "a,b" and " α, β " (the Greek letters "alpha, beta") then I am afraid you will not be able to make much sense of the equations on this page.}

Coordinates in the first equatorial system (HA and declination)
still depend on the time of observation.
Now we change the zero-point for our coordinates.
We choose a fixed point on the celestial equator,
called the vernal equinox, or the First Point of Aries.
The symbol for this is the astrological symbol for Aries:


(The function of this point will become clearer later on.)

The declination (δ) of object X is measured in the same way as before.
The Right Ascension or RA (α) of object X
is the angle along the celestial equator measured eastwards
from the vernal equinox to the meridian of X.
Like HA, RA is measured in hours 0-24h, but it goes in the opposite direction.


Comparison of these celestial coordinate systems with the terrestrial system:

terrestrial alt-az HA-dec RA-dec
equator horizon celestial equator celestial equator
North Pole zenith North Celestial Pole North Celestial Pole
South Pole nadir South Celestial Pole South Celestial Pole
latitude altitude declination declination
co-latitude zenith distance North Polar Distance North Polar Distance
parallel of latitude parallel of altitude parallel of declination parallel of declination
meridian of longitude vertical circle meridian meridian
Greenwich Meridian Principal Vertical celestial meridian vernal equinox
longitude azimuth Hour Angle Right Ascension

Exercise:

The four stars at the corners of the “Great Square of Pegasus” are:

star

R.A.

declination

α And

00h 08m

+29°05'

β Peg

23h 04m

+28° 05'

α Peg

23h 05m

+15° 12'

γ Peg

00h 13m

+15° 11'

Calculate the lengths of the two diagonals of the “Square”.

Answer


It is necessary to plot the four stars, at least approximately,
to find out which pairs form the diagonals!


Then, to find the length of each diagonal, use the cosine rule:
cos S1S2 = cos S1P cos S2P + sin S1P sin S2P cos P


This gives {α And} to {α Peg} = 20.1°
and {β Peg} to {γ Peg} = 20.5°.

The Right Ascension and declination of a star do not normally change over short periods of time; but the Hour Angle changes constantly with time. Consequently we have to find a way of defining the time.