Lab_1_The_Rotating_Sky_William_Hanson
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The Rotating Sky
Remember to type your answers in blue text
I. Background Information
Work through the Main Content pages on The Observer
, Two Systems – Celestial,
Horizon
, Paths of the Stars, and Bands in the Sky
. All the concepts covered in these pages
are used in the Rotating Sky Explorer simulator and will be explored more fully there. II. Introduction to the Rotating Sky Simulator
Open the Rotating Sky Explorer
The Rotating Sky Explorer consists of a flat map of the Earth, Celestial Sphere, and a
Horizon Diagram that are linked together. The explanations below will help you fully
explore the capabilities of the simulator.
You may click and drag either the celestial sphere or the horizon diagram to
change your perspective.
A flat map of the earth is found in the lower left which allows one to control the
location of the observer on the Earth. You may either drag the map cursor to
specify a location, type in values for the latitude and longitude directly, or use the
arrow keys to make adjustments in 5
°
increments. You should practice dragging
the observer to a few locations (North Pole, intersection of the Prime Meridian
and the Tropic of Capricorn, etc.).
Note how the Earth Map, Celestial Sphere, and Horizon Diagram are linked
together. Grab the map cursor and slowly drag it back and forth vertically,
changing the observer’s latitude. Note how the observer’s location is reflected on
the Earth at the center of the Celestial Sphere (this may occur on the back side of
the earth out of view).
Continue changing the observer’s latitude and note how this is reflected on the
horizon diagram. When the observer is in the northern hemisphere the NCP is
seen above the north point on the horizon at an altitude equal to the
observer’s latitude.
When the observer is in the southern hemisphere the SCP is
seen above the south point at an altitude equal to the observer’s latitude.
The Celestial Sphere and Horizon Diagram are also linked such that any stars
added to the simulation are shown on both. There are many features related to
stars.
o
A star will be randomly created by clicking the add star randomly
button. o
A star may be created at a specific location on either sphere by shift-
clicking at that location. (Hold down the shift key on the keyboard while
clicking at that spot.)
o
You may move a star to any location by clicking and dragging on it. Note
that it moves on both spheres as you do this. NAAP – The Rotating Sky 1/9
o
Note that the celestial equatorial and horizon coordinates are provided for
the “active” star. Only one star (or none) may be active at a given time.
Simply click on a star to make it the active star. Click on any other
location to make no star active. o
If you wish to delete a star, you should delete-click on it. (Hold down the
delete key on the keyboard while clicking on the star.)
o
You may remove all stars by clicking the remove all stars
button. o
Note that stars are the means by which you make coordinate
measurements. If you want to make a measurement in either diagram,
place the active star at that location.
There are several modes of animation as well as a slider to control speed. o
You may turn on animate continuously or for preset time intervals: 1 hour,
3 hours, 6 hours, and 12 hours. o
If you click-drag a sphere to change its perspective while the simulator is
animating, the animation will cease. Once you release the mouse button
the present animation mode will continue.
This simulator has the ability to create star trails on the horizon diagram. o
A series of check boxes set the star trails option. No star trails
is self-
explanatory. Short star trails
creates a trail behind a star illustrating its
position for the past 3 hours. Long trails
will trace out a parallel of
declination in 1 sidereal day. o
Stars are created without trails regardless of the trail option checked. If
either short or long trails is checked, the trail will be drawn once the
simulator is animated. o
Existing star trails will be redrawn in response to changes – the star being
dragged on either sphere or changing the observer’s location. o
What’s not in this simulation? – the revolution of the Earth around the sun.
This simulator animates in sidereal time. One sidereal day (one 360°
rotation of the earth) is 23 hours and 56 minutes long. You should think of
this simulator as showing the Earth isolated in space as opposed to
revolving around the sun. III. Horizon Coordinates
Question 1:
The first column in the following table lists the description of a point in the
sky, as seen from an observer on Earth. The second column lists the observer’s latitude
on Earth. From these two pieces of information, you should be able to determine the
azimuth and altitude of that point in the sky. Try to predict the answers first, and then
NAAP – The Rotating Sky 2/9
use the simulator to check them. You can check (and correct) your answer by creating an
active star and entering the altitude and azimuth you think is correct.
Description
Latitude
Azimuth
Altitude
East point on the horizon
Any
90.0
0.0
Zenith
Any
Any
90.0
NCP (North Celestial Pole)
15ºN
360.0
15.0
NCP
48ºN
360.0
48.0
SCP (South Celestial Pole)
45ºS
180.0
45.0
SCP
50ºS
180.0
50.0
Intersection of CE (Celestial
Equator) and Meridian
48ºN
180.0
42.0
Intersection of CE and Meridian
35ºS
180.0
35.0
Question 2:
Assume that you are at latitude 48° N, which is
the approximate latitude of Spokane. When making
predictions about the future locations of stars A, B, and C,
use the diagram on the top of the next page that depicts a
“fish-eye” view of the sky. Remember that the sky appears
to rotate around the NCP, which is a point at altitude = 48°, azimuth = 0° in the diagram
(as seen from Spokane). Try making your predictions first, and then use an active star
within the horizon diagram view simulator to check (and correct) your answers. a)
Assume star A is at the specified coordinates at time t = 0 hrs. What will be the
alt/az coordinates of star A at t = 12 hours? At t = 24 hours? For what fraction of the day is star A visible (above the horizon)?
b)
Assume star B is at the specified coordinates at time t = 0 hrs. What will be the coordinates of star B at t = 6 hours? At t = 12 hours? For what fraction of the day is star B visible? c)
Assume star C is at the specified coordinates at time t = 0 hrs. What will be the coordinates of the star at t =12 hours? At t = 24 hours? NAAP – The Rotating Sky 3/9
Question 1: Alt – 15.0 Az – 360.0
Question 2: Alt – 81.0 Az
– 0.0
Question 4: 100% 1/1
Visible all day
Question 5: Alt – 42.0 Az – 180.0
Question 7: Alt - -0.0 Az – 270.0
Question 8: ½ of the day Question 9: Alt = -86.0 Az – 180.0 Question 10: Alt = -10.0 Az – 180.0
Star
Azimuth
Altitude
A
0°
15°
B
90°
0°
C
180°
-10°
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For what fraction of the day is star C visible?
Question 3:
For this question, assume you are in Spokane at latitude 48° N and you
want to determine the declination of a star that passes through your zenith. Try to predict
the answer first, and then use the simulator to verify your answer. If you go out at any
time of night in Spokane and see a star directly overhead, it will have this declination.
NAAP – The Rotating Sky 4/9
Question 11: 0 or 0 percent Question 12: Location of NCP, as seen
Question 13: from Question 14: 14.4 East
Remember that the declination of a star indicates how far north (or south) of the celestial
equator it is located.
Declination = IV. Declination Ranges
The area of an observer’s sky where stars can always be seen is called the circumpolar
region; the area where stars can sometimes be seen in the rise and set
region; and the
area where stars can never be seen is the never rise
region. Note that you can select
these three regions in the simulator by checking the appropriate boxes under Appearance
Settings
. For an observer at a specific location on Earth, it is the declination of the star
that determines which of the 3 regions it is found in. In this section you will be
investigating these different regions.
Question 4:
The two end stars of the Big Dipper are known as the “pointer stars” since a
line drawn through them points toward Polaris (an important marker in the sky since it is
located very near the NCP). Use the s
tar patterns
control to add the Big Dipper to the
celestial sphere. Now manipulate the observer's location on Earth to find a point (in
latitude) where the Big Dipper can always be seen (circumpolar), where it sometimes can
be seen (rise and set), and where it never can be seen (never rise). It will be helpful to
turn on the long star trails
when running the simulation to see whether or not the stars go
below the horizon. You only need to find the latitude of one location that satisfies the
given conditions, and record that latitude in the table below.
Star Pattern
Circumpolar
rise and set
never rise
Orion
N/A
46.9 N 113.3 W N/A
Big Dipper
54.1 n 113.5 W
9.1 N 10.7 E 83.5 S 7.6 W
Southern Cross
83.5 S 7.6 W
10.7 N 35 E
45.6 N 100.1 W
Repeat with Orion and the Southern Cross. All stars within the pattern must be visible
(above the horizon) to be counted as seen
.
Question 5:
In which of the 3 declination ranges (circumpolar, rise and set, or never rise)
Are the stars A, B, and C from question 2 found, assuming you are at latitude 48° N?
Star A
Circumpolar
NAAP – The Rotating Sky 5/9
Star B
Rise and Set
Star C
Never Rise
Question 6:
Let’s explore the boundaries of these 3 regions. Set the observer at latitude
40º N, create a random star, and set the coordinates of
this star so that it is on the north point of the horizon (0
Az, 0 Alt). Select the long star trails option and
animate for 24 hours so that a complete circle of
declination is made for the star. Note that a star with a
slightly smaller declination (further from the NCP)
would dip below the northern horizon while a star that
is closer to the NCP would be circumpolar. Thus, the
declination of the star that just touches the north point
on the horizon is the outer boundary of the circumpolar range. The declination of this
star is called the north point declination (+50º for an observer at 40º N). All stars from
this declination up to the NCP (+50º to +90º for an observer at 40º N) would be within
the circumpolar range. Now set the star to the south point on the horizon and read off the
star’s declination. This is the outer boundary of the never rise range, and is called the
south point declination (-50º for an observer at 40º N). The range of declinations between
the north point and south point declinations is the rise and set range (+50º to -50º for an
observer at 40º N). Complete the columns in the table below for each of the given latitudes. Note that the
coordinates for an observer at 40º N have already been provided from the above example.
Latitude
North Point
Declination
Circumpolar
Range
South Point
Declination
Rise and Set
Range
15º N
+75
+75 to +90
-75
+75 to -75
25º N
+65
+65 to 90
-65
+65 to -65
40º N
+50º
+50º to +90º
-50º
+50º to -50º
50º N
+40
+40 to +90
-40
+40 to -40
85º N
+5.0
+5.0 to +90
-5.0
+5.0 to -5.0
NAAP – The Rotating Sky 6/9
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Question 7:
Set up the simulator for an observer on the equator. Create some stars (~20)
in the simulator and set it to animate continuously. Describe the motion of the stars,
relative to the horizon
, as seen from the equator. Question 8:
Change the location of the observer to the North Pole and repeat the
animation. Describe the motion of the stars, relative to the horizon
, as seen from the
North Pole. V. Star Trails
Visualizing star trails is an important skill that is
very closely related to declination ranges. Again,
set up the simulator for latitude 48º N, create
about 20 stars randomly in the sky, turn on long
star trails, and set the simulator to animate
continuously. The view to the right illustrates the
NAAP – The Rotating Sky 7/9
Question 15: If the observer is on the equator no stars are located in the rise and set region due to the observer location directly on the equator. The stars move east to west relative to the observer.
Question 16: If the observer is at the north pole, the stars will be moving around the observer
in the circumpolar region. Some stars will never be seen by the observer. The stars also seem to be moving clockwise around the zenith/ncp.
region around the north celestial pole. Realize that we need to imagine what these trails
would look like from the stick figure’s perspective. Question 9:
Check the box in the simulator that shows the angle between the celestial
equator and the horizon. The angle will be nearly the same for all circles of declination
(i.e. star trails) near the east or west point of the horizon. Use the table below to record
the star trail angles for stars that rise and set at various latitudes. Latitude
Direction
Star Trail Angle
12º N
E
78
25º N
E
65
48º N
E
42
55º N
E
35
73º N
E
17
Question 10:
Notice the pattern between the latitude and star trail angle. Describe a
general rule for determining your latitude from looking at just
star trail angles. NAAP – The Rotating Sky 8/9
Question 17: When latitudes are closer to 0.0 degrees north, the star is 90 degrees which makes the stars seem to appear directly overhead, this is also is true when facing south at 0.0. As the observer’s latitude increases north the star angle changes to 0 degree, and most stars enter the never rise region. This also means the NCP is directly above the observer. If the latitude increases towards the south the star angle again shifts to 0.0 degrees and the stars appear to be around all around the observer and enter the rise and set region; also at this latitude the SCP is directly above the observer.
Summary/Conclusion (5 points):
Imagine watching the sky while taking a trip from the
equator to the North Pole. Describe how the location of each
of the following would change as you traveled from the equator to the North Pole: The
North celestial pole
, the celestial equator
, the circumpolar region
, and the star trail angles
.
NAAP – The Rotating Sky 9/9
Question 18: As I sit at the equator, we could see the NCP and the SCP they would be directly to the north and south, at this latitude the star trails would be sit above us running perpendicular to the north celestial pole and south celestial pole, the stars would also be in the rise and set region. Also, at this latitude the circumpolar region would not be visible to us at this latitude. When we stay at this latitude the celestial equator would run perpendicular to the North and South celestial poles running parallel with the star trail angles. As I start heading north from the equator things start to change, as I increase my latitude to 25° N we begin to see the circumpolar region appear along with the never rise region, it begins to appear in the north celestial pole region. At this latitude the north celestial pole will be the only visible pole to us, the South celestial pole will start to drop below our view of the horizon. Also, at this latitude the star angle and celestial equator will start decreasing and started moving to become parallel with the horizon. As I continue on my trip north my latitude again changes to 50° N, at this latitude we begin to see the circumpolar region get larger and it can be seen at the north celestial pole. Also, at this latitude we begin to see that the South celestial pole is falling deeper below the horizon and is now completely invisible on the horizon. At this latitude we can see the star trails and celestial equator begin their descent to start running parallel with the horizon instead of running perpendicular to the horizon. As I again venture further north inching closer to the North Pole, I again stop app latitude 75° N, the north celestial pole appears to be directly above my head and the sauce celestial pole is invisible to me on the horizon however it is almost directly under me. At this latitude the circumpolar region begins to completely take over the horizon. At this latitude the celestial equator and the star trails begin to align with the horizon just inching above it, this gives us an almost view unobstructed view of the sky. As we reach our destination the North Pole which is 90° latitude north, we can now see the north celestial pole directly above us and the South celestial pool directly below us, at this angle the circumpolar region encapsulates everything from the horizon to the zenith. Also, at
this point and our trip the celestial equator and the start trailer angle run parallel with the horizon giving us a clearer view of the north celestial pole, most stars are now located and then never rise region opposite of the circumpolar region. I think this latitude would give us the best clean and clear view of the night sky.
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