The Rotating Sky Lab - Allison Price
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Spokane Falls Community College *
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Course
101
Subject
Astronomy
Date
Jan 9, 2024
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docx
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Uploaded by JudgeQuail4016
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.)
NAAP – The Rotating Sky 1/9
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.
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
90º
0º
Zenith
Any
Any
90º
NCP (North Celestial Pole)
15ºN
.8º
15.1º
NCP
48ºN
1.2º
48.1º
SCP (South Celestial Pole)
45ºS
180º
44.4º
SCP
50ºS
180º
49.4º
Intersection of CE (Celestial
Equator) and Meridian
48ºN
183.6º
41.9º
Intersection of CE and Meridian
35ºS
355.8º
54.9º
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?
Question 2:
At t = 24 hours?
Question 3:
For what fraction of the day is star A visible (above the horizon)?
NAAP – The Rotating Sky 3/9
alt 81°, az 0°
alt 15°,az 0°
It's visible all day.
Star
Azimuth
Altitude
A
0°
15°
B
90°
0°
C
180°
-10°
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a)
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?
b)
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?
For what fraction of the day is star C visible?
NAAP – The Rotating Sky 4/9
alt 42°, az 180°
alt -0°, az 270°
1/2 of the day
alt -86°, az 180°
alt -10°, az 180°
It is not 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.
Remember that the declination of a star indicates how far north (or south) of the celestial
equator it is located.
NAAP – The Rotating Sky 5/9
Location of NCP, as seen
from Spokane, WA
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
The Orion cannot
always be seen.
48°N
90°N
Big Dipper
48°N
2.3°S
55.2°S
Southern Cross
90°S
5°N
90°N
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 6/9
48.9°
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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°
+5° to +90°
-5°
+5° to -5°
NAAP – The Rotating Sky 7/9
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 8/9
They are setting in the west and rising in the east.
The stars in the northern hemisphere are circumpolar, the stars in the southern hemisphere are
never seen.
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.
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
The higher the star trail angle, the lower your latitude.
The NCP changed from being at the same latitude as me which is 0° at the equator, to
directly 90° above me.
The celestial equator when I am at the equator is an imaginary line directly above me
running east to west. As I travel to the North Pole the celestial equator moves south so by the
time I reach the North Pole, it will be even with the horizon.
The circumpolar region is non existent when I am at the equator, but as I travel north it
grows visible as a dome from the NCP.
When I start at the equator, the star trail angles are 90° and as I travel to the North Pole, it
slowly decreases with my latitude to reach 0° when I arrive there.
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