Celestial Coordinate Systems
We can define a useful way to locate objects
on the celestial sphere by projecting onto the sky the latitude-longitude coordinate
system that we use on the surface of the Earth. As illustrated in the adjacent
figure, this allows us to define a north celestial pole and a
south celestial pole (the imaginary
points about which the daily rotation of the sky
appears to take place) and a celestial
equator. This
animation illustrates the
celestial coordinate system.
Angular Measure
Since the celestial coordinate system is defined in terms of angles, we must consider units of
angular measure. The circle can be divided equally
into 360 degrees. It is common to
subdivide the degree into minutes of arc (also denoted arc-min),
and
seconds of arc (also denoted arc-sec). There are 60 minutes of arc in one degree;
therefore, a minute of arc is 1 / 60 of a degree.
There are 60 seconds of arc in each minute of
arc and thus 60 x 60 = 3600 seconds of arc in a degree;
therefore, a second of arc is 1 / 60 of a minute of arc and is also 1 / 3600 of a degree. The
degree, minute, and second of angular measure are commonly denoted by the symbols
o, ', and ", respectively. For example, we may write
1o = 60' = 3600"
In applications that require trigonometry, it is more natural and therefore
common to measure angles in a unit called
a radian (denoted by rad). The conversion between degrees and radians is
1 radian = 180 / π = 57.296 degrees
where π = 3.1416. The relationships among these units of angular measure are summarized in
the following table.
|
Units of Angular Measure
|
| Angular
Measure |
Degrees |
Radians |
| One Degree ( 1o
) |
1 |
1 / 57.296 = 1.745 x
10-2
|
| One Minute ( 1'
) |
1 / 60 = 1.667 x 10-2 |
2.909 x 10-4
|
| One Second ( 1"
) |
1 / 3600 = 2.778 x
10-4 |
4.848 x 10-6
|
|
|
There are 180 / π = 57.296
degrees in one radian
|
In this table we have introduced the common practice of using scientific notation
to represent either large or small numbers. For example, we have expressed the number
0.01667 in the form 1.667 x 10-2. Since in astronomy
we frequently
encounter very large or very small numbers, we will use scientific notation often and it is
important that you be proficient with it.
If you are rusty on scientific notation, consult this
math tutorial for a review. Finally,
be careful not to confuse minutes and seconds of angular measure with minutes and seconds of
time.
Right Ascension and Declination
The celestial coordinates
that are analogous to the latitude and
longitude employed for the surface
of the Earth are illustrated in the following figure
(for which you should imagine the Earth to be a point at the center of the sphere).
The celestial
equivalent of latitude is called declination and is measured in degrees
north (positive numbers) or south (negative numbers) of the celestial equator.
The celestial equivalent of longitude is called right ascension. The
reference point from which right ascension is measured, which is
the analog of the point defining
the prime meridian on Earth, is called the vernal equinox. We will specify it
more precisely shortly.
Conversion between Time
and Angle Units
|
|
Time |
Angle
|
| 24 hours |
360 degrees
|
| 1 hour |
15 degrees
|
| 4 minutes |
1 degree
|
| 4 seconds |
1 arc minute
|
| 1 second |
15 arc
seconds |
|
Angle and Time
Right
ascension can be measured in degrees, but for historical reasons it is more
common to measure it in time (hours, minutes, seconds): the sky turns 360 degrees
in 24 hours and therefore it must turn 15 degrees every hour; thus, 1 hour of
right ascension is equivalent to 15 degrees of (apparent) sky rotation. The
adjacent table gives the relation between several times and the corresponding
angles through which the sky turns in that time.
Again, do not be confused by the use of
the terms "minutes" and "seconds" both as measures of angle and measures of time.
When there is potential danger of confusion we shall use the adjective "arc" to
make clear when seconds or minutes refer to angle measure rather than time measure.
