Download Celestial Coordinate System

Celestial Coordinate System
Fall 2007
Updated 09/07/2007
Purpose
The purpose of this lab is to familiarize the student with determining sidereal time,
both through calculation and observation, and applying this system of time to locating
stars and other objects using the celestial coordinate system.
Introduction
Early in the history of astronomy it became necessary to devise a system for
describing the positions of the stars on the celestial sphere. The most obvious system was
one based on the local horizon and named simply the Horizon System. It gives the star’s
position in terms of the observer’s horizon pane, with one coordinate (azimuth) measured
in terms of compass directions along this plane. However, this system of coordinates has
disadvantages in that the azimuth and altitude of a star change both with the time of day
and the location of the observer.
It is desirable to have a system of coordinates permanently attached to the celestial
sphere. Such a system is the Celestial Equatorial System (Fig. 1). The polar axis of the
earth is projected outwards, defining the poles of the celestial sphere. The equatorial
plane of the earth is projected outward and it defines the celestial equator. The
coordinates of this system are right ascension (analogous to longitude on the earth),
measured along the celestial equator and declination (analogous to latitude), measured
north and south from the celestial equator. The coordinates of stars in this system are
constant rather than dependent on the observer’s time of day and place.
Figure 1.
Sidereal time
You are already familiar with solar time – you use it every day. The earth makes one
complete revolution in 24 hours, and the sun crosses the observer’s meridian at noon,
local mean time.
The sidereal day, however, is 3 minutes, 56 seconds shorter than the solar day.
Sidereal time is based on one rotation of the earth in relation to any star (other than the
sun), starting with the star on the observer’s meridian, and returning to the meridian one
earth rotation later. The reason for the star returning to the meridian in less than 24 hours
is that the earth orbits about the sun. The rate of this orbit is 360 degrees/ 365.25 days, or
about 1 degree per day. One degree per day is equal to 4 minutes of time and averages
two hours per month. (See Fig.2)
Figure 2
Application to Astronomy
Simply put, the sidereal time is equal to the right ascension of an astronomical object
lined up with the observer’s meridian. The sidereal day begins at 0 hours, a time when the
vernal equinox crosses the celestial meridian. On or about March 21, the sun is located at
the vernal equinox, and will be on the meridian at noon. We can therefore assume that the
sidereal time on March 21 is 0h at noon, local mean time. One sidereal hour later, stars
with a right ascension of 1 h will cross the meridian.
Sidereal time can be calculated for an observer’s location, using the formulas and
table provided with this lab. Once determined, the sidereal time will be used, in
conjunction with the celestial coordinate system, to locate astronomical objects with an
equatorially aligned telescope.
(Fig. 3)
Standard Time Zones
Terminology
Standard Time: is the mean time of a time zone, which is 15 degrees wide. At the central
meridian of a time zone, standard time coincides exactly with mean solar time. Simply,
this means the sun will be on the meridian at noon (or nearly so), as observed from the
central meridian of the time zone. Elsewhere in the time zone, the sun will be no more
than 30 minutes from the meridian.
Local Mean Time: This is the mean solar time applied to your exact location. L.M.T. is
calculated by applying a correction equal to four minutes for each degree you are away
from the central meridian of your time zone. The central meridian for the Eastern Time
zone is 75 degrees. Providence is located 71 degrees, 25 minutes longitude. This is about
3 ½ degrees east of the central meridian. (3 ½ degrees times 4 minutes = 14 minutes
times correction) Because we are east of the central meridian, we add this time correction
to standard time. This means that our watches, set to L.M.T., will read 14 minutes later
than Eastern Standard Time.
Local Sidereal Time (L.S.T.): Indicates how much time has passed since the vernal
equinox crossed the observer’s meridian. Sidereal time is also equal to the right ascension
of any star currently on the observer’s meridian. To calculate L.S.T. with an approximate
correction, use this formula: L.S.T.= L.M.T. + G.S.T at 0h next day (see table # 1 ). If
the answer is greater than 24 hours, subtract 24 hours for the answer.
For example, if it is 8:00 PM E.S.T. (remember to subtract 1 hour from daylight savings
time) on October 1st, then…
L.M.T. = E.S.T. + time correction (14 minutes) = 20h 14m (Providence, R.I.)
L.S.T.= L.M.T. + G.S.T at 0h next day
L.S.T. = 20:14 + 0h 41m (table 1)
L.S.T. = 20h 55m @ 8:00 P.M. (EST) on October 1, 2007
Sidereal Time (rounded to nearest minute) at 0h Greenwich Mean Time (G.M.T.)
October through December, 2007.
(Table 1)
Day
Oct
Nov
Dec
2h 40m
4h 38m
0h 37m
1
0h 41m
2
2h 44m
4h 42m
0h
45m
3
2h 48m
4h 46m
4
0h 49m
2h 51m
4h 50m
5
0h 53m
2h 55m
4h 54m
6
0h 57m
2h 59m
4h 58m
7
1h 1m
3h 3m
5h 2m
8
1h 5m
3h 7m
9
1h 9m
3h 11m
10
1h 13m
3h 15m
11
1h 17m
3h 19m
12
1h 21m
3h 23m
13
1h 25m
3h 27m
14
1h 29m
3h 31m
15
1h 33m
3h 35m
16
1h 37m
3h 39m
17
1h 40m
3h 43m
18
1h 44m
3h 47m
19
1h 48m
3h 51m
20
1h 52m
3h 55m
21
1h 56m
3h 58m
22
2h 0m
4h 2m
23
2h 4m
4h 6m
24
2h 8m
4h 10m
25
2h 12m
4h 14m
26
2h 16m
4h 18m
27
2h 20m
4h 22m
28
2h 24m
4h 26m
29
2h 28m
4h 30m
30
2h 32m
4h 34m
31
2h 36m
Equipment needed for this lab
Equatorially mounted telescope, equipped with setting circles.
Accurate time signal http://www.time.gov/timezone.cgi?Eastern/d/-5/java
Accurate watch set to L.S.T.
Star atlas and catalog.
Rotating Star Chart
Procedure (Indoors):
1)
The first thing you need to do is to determine the current sidereal time, and set
your watch to it. Although your watch will run slower than sidereal time, about
10 seconds per hour, it will be accurate enough for the duration of this lab. Refer
to table # 1 for G.S.T. at 0h, not for today’s date, but the following day. Use this
time in the formula above. Make sure to calculate the local mean time (LMT)
correction for the location you plan to do your observations from. The
coordinates for Providence are given above, and the coordinates for Jerimoth
Hill are 41 50 58N, 071 46 45W. Once you have your watch set to sidereal time,
you are ready for the next step.
2)
Sidereal time equals the RA of objects currently on the meridian. In this lab, we
will be trying to find objects throughout the sky. To do this, we will need to
determine the angular separation of the object from the meridian, measured in
hours, minutes and seconds. This is called the Hour Angle. 0 hours will define
the meridian, and objects will either east or west of the meridian.
3)
To determine the hour angle (HA) of an object, use the following equation:
HA=ST-RA
Let’s say it is December 1st at 11:00 PM, EST. Using the equation to determine sidereal
time, we come up with ST = 3h 56m.
We want to locate M42, the Orion Nebula. The coordinates for M42 are RA=5h 34m,
DEC= 5.4 degrees south.
HA=3h 56m – 5h 34m
HA= (-2h 22m)
A negative hour angle means M42 is east of the meridian.
If you were to try to locate M42 later in the evening, say at 6h (L.S.T.), then the equation
would read:
HA= 6h - 5h 34 m
HA= 0h 26m
A positive hour angle means M42 is west of the meridian.
(If the answer is greater than 12h, it must be subtracted from 24h to give the answer in negative hour angle.)
Orion on Dec 1st, at 3h LST and 6h LST
(Fig. 4)
4) Practice indoors, using “Starry Nights”
Determine the HA for the three objects in the table below, setting the time to 9:00PM this
evening. You will need to calculate the sidereal time.
Object
NGC 884
Alberio
M15
RA
2h 22.6m
19h 30.7m
21h 30.3m
Dec
+57 8m
+27 58’
+12 10’
ST
HA (east/west)
Using “Starry Nights”, select the following in the tool bar:
“View”
-“Alt/Az Guide”
- “Meridian”
“View”
-“Celestial Guides”
- “Equator”
- “Grid”
Verify that the calculations you entered in the table above are correct, by locating
the objects in the “Starry Night” program, and noting where the objects are located
on the celestial grid.
Which object most recently crossed the meridian? _______________________________
Which object is currently located in the eastern most part of the sky? ________________
Which object is currently located in the western most part of the sky? ________________
Doing the above exercise should help you to find your way around the sky, which
will be useful for the next, outdoor part of this lab.
Procedure (outdoors):
1) You will need to use a telescope with an equatorial mount, and align the mount
with the celestial pole. Please refer to “Polar Alignment Procedure for Meade
ETX” for directions on properly setting up the Meade telescope. If you are using a
telescope that is already aligned to the pole, you may skip this step.
2) You know the current local sidereal time, and the telescope is properly aligned to
the pole. Level the declination axis using a level (your TA will show you how to
do this); set the RA circle to the current sidereal time.
3) To locate an object in the table above, turn the telescope mount in RA to the RA
coordinates of the object sought. Then turn the telescope mount in DEC until the
circle matches the coordinates.
4) If the object you are looking for does not appear in the eyepiece, try looking in the
small finder telescope to see if the object is close by – then move the telescope to
center the object in the eyepiece. This might happen if the polar alignment is a
little off.
5) Note the appearance of each object in your notebook.
Answer the following questions: (This part will be done indoors, using “Starry
Nights”.)
(Providence is located at 71 degrees, 25 minutes west longitude; 41 degrees, 50 minutes north latitude)
I)
From our location on Earth, is it possible to locate an object more than 6 hours east
or west of the meridian? Are there any limitations on how many hours of RA can be
seen if you look in different directions (east, west, north and south)?
II)
How many hours of RA, east and west of the meridian could you see from the
earth’s equator, and from the poles?
III)
Looking due north, along the meridian, from our location, what is the declination of
the horizon? Looking due south, along the meridian, what would the southern most
declination be?
Polar Alignment Procedure for Meade ETX
Part of Celestial Coordinates Lab
Star trails around the celestial pole.
1) The ETX telescope is set-up, with telescope mounting
roughly pointing north. Note that the optical in the photo
is pointing towards the south.
2) Turn fork arms until the telescope is
pointing south. Check this with a level.
3) Turn RA circle (the moveable dial
located on the drive base of the mount)
until it reads the current local sidereal
time. Example shown is 3h, for January 1
at 8pm, EST.
4) Rotate mount until the RA circle reads the
coordinates for Polaris: 20h 30m. Turn the
telescope in declination until the setting circle (the
smaller dials located at the top of the fork arms)
reads 89 degrees N.
5) First, try to sight Polaris along the side of
one of the fork arms. Turn the adjustment
screws on the tripod head to align the mount
with Polaris. Once Polaris is close, look
through the eyepiece; continue to turn the
adjustment screws in azimuth and altitude
until Polaris is centered in the eyepiece.
6) Turn the mount back towards the south,
place a level across the fork arms, and continue
to turn the mount until the bubble is level.
7) Turn the RA circle until it reads the
current sidereal time. You are ready to
begin finding astronomical objects using
the setting circles on your telescope.
Follow the directions in the “Celestial
Coordinates” lab.