Which
stars are on your local meridian?
It depends on the time at which
you observe.
In fact, it depends on both the date and the
(clock) time,
because the Earth is in orbit around the Sun.
Consider the Earth at position E1 on the
diagram.
The star shown is on the meridian at midnight by the
clock.
But three months later, when the Earth reaches position E2
,
the same star is on the meridian at 6 p.m. by the clock.
Our clocks are set to run (approximately) on solar
time (sun time).
But for astronomical observations, we need to
use sidereal time (star time).
Consider the rotation of the Earth relative to the
stars.
We define one rotation of Earth as one sidereal
day,
measured
as the time between two successive meridian passages of the same
star.
Because of the Earth's orbital motion, this is a little
shorter than a solar day.
(In one year, the Earth rotates 365
times relative to the Sun,
but 366 times relative to the stars.
So the sidereal day is about 4 minutes shorter than the solar
day.)
We define Local Sidereal Time (LST) to be 0
hours
when the vernal equinox
is on the observer's local meridian.
One hour later,
the
local Hour Angle (LHA) of the equinox is +1h (by the definition of
Hour Angle),
and the Local Sidereal Time is 1h.
So at any
instant, Local Sidereal Time = Local Hour Angle of the vernal
equinox.
Here's an alternative definition:
suppose that
LST = 1h.
This means that the vernal equinox has moved 15°
(1h) west of the meridian,
and now some other star X is on the
meridian.
But the Right Ascension of star X is the angular
distance from the vernal equinox to X = 1h = LST.
So at any
instant, Local Sidereal Time = Right Ascension of whichever stars
are on the meridian.
And in general, the Local Hour Angle of a star = Local Sidereal Time - RA of the star.
However, at any instant,
different observers, to
the east or west, will have different stars on their local
meridians.
We need to choose one particular meridian to act as a
reference point; we choose Greenwich.
We define the Greenwich Hour Angle of X
as
the Hour Angle of X relative to the celestial meridian at
Greenwich.
Then we can define Greenwich Sidereal Time
(GST)
as the Greenwich Hour Angle of the vernal equinox.
This
gives the important relation
LST = GST - longitude west.
Recall that the Local Hour Angle (LHA) of a star = Local
Sidereal Time - RA of the star.
In particular, the Greenwich Hour
Angle (GHA) of a star = Greenwich Sidereal Time - RA of the star.
Combining these, we find
LHA(star) = GHA(star) - longitude
west.
Exercise:
At midnight on 1998 February
4th,
Local Sidereal Time at St.Andrews was 8h45m.
St.Andrews
has longitude 2°48'W.
What was the Local Hour Angle of
Betelgeuse (R.A. = 5h55m) at midnight?
At what time was Betelgeuse on the meridian at St.Andrews?
At what time was Betelgeuse on the meridian at Greenwich?
Click here for the answer.
For a more detailed discussion of Sidereal Time and related topics, see Chapter 2 of
USNO
Circular No.179.
Previous section: Coordinate
systems: the second equatorial or "RA-dec" system
Next section: Conversion between
horizontal and equatorial systems
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