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School
Eastern Michigan University *
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Course
105
Subject
Astronomy
Date
Dec 6, 2023
Type
Pages
5
Uploaded by diontaelt
Horizon Coordinate System
This activity will teach us how to use the observer-centered
Horizon Coordinate System
. Unlike
the
Equatorial Coordinate System
, which allows observers to measure the same coordinates for
any celestial object from any location on the Earth, the coordinates of every celestial object
measured in this coordinate system will have coordinates that change with time and also
change with location on the Earth. While this coordinate system is not very useful for
communicating the location of celestial objects to other astronomers around the world, it is
useful for communicating with people you are observing with and attaining a better
understanding of how the sky moves from your perspective on the Earth.
The
Horizon Coordinate System
has two coordinates,
azimuth
and
altitude
. The azimuthal
coordinate tells the observer the direction that they need to face to locate an object in the sky.
Once facing the correct direction, the altitude coordinate tells the observer how high to look
above the theoretical horizon.
Open the ‘Rotating Sky Explorer’ simulation
(
https://astro.unl.edu/naap/motion2/animations/ce_hc.html
). Make sure the only checked
boxes in the ‘Appearance Settings’ panel (bottom of simulation window) are ‘show labels’,
‘show celestial equator’, and ‘show underside of horizon diagram’.
The top-left panel shows the celestial sphere, the location where all celestial objects are
projected in the equatorial coordinate system. In this window we will be able to adjust the
declination and right ascension of stars to see how an observer at a specific location on the
Earth would perceive the motion of that star as the Earth rotates. The top-right panel shows
how the observer will perceive the celestial sphere in the horizon coordinate system. In this
window we will be able to adjust the altitude and azimuth of stars. Both windows can be
manipulated by clicking and dragging on the sphere.
Set the latitude of the observer to 42°N, 84°W. These are approximately the GPS coordinates
of EMU.
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1. Hold the shift key and click on the sphere in the top-right window to add a star to the
northern point directly along the horizon (the star should be centered on the northern point
right on the line where the ground meets the sky). Record the altitude and azimuth values (you
can estimate what the values should be if you are having difficulty putting the star exactly in the
right location). Drag the star to the eastern, southern, and western point directly along the
horizon and record the altitude and azimuth values.
*
All numbers in the table should be integers.
Cardinal
Direction
Azimuth
(°)
Altitude
(°)
North
0
0
East
90
0
South
180
0
West
270
0
2. What is the value of the altitude coordinate at the horizon?
-
0 degrees
3. Which direction from north must an observer rotate for the azimuth they are observing to
increase, east or west?
-
east
4. Drag the star to the zenith. Note that at the zenith, all azimuthal coordinates yield the same
location (you do not have to face a specific N/S/E/W direction in order to look “up”).
What is the maximum value of the altitude?
*It may be difficult to get the exact value, but it
should be a whole number.
-
90 degrees
5. Compare the declination of a star at the zenith to the latitude of the observer. Objects at this
declination always pass directly overhead.
a. What do you notice about these values?
-
the azimuth stays exactly the same while the altitude decreases towards the horizon
b. The sun’s maximum declination is 23.5. Can the sun ever pass directly overhead in
2
Michigan?
-
yes!
6. Drag the star to the north celestial pole (NCP).
a. What are the horizon coordinates of the NCP?
*It might be difficult to get the exact
value, but it should be a whole number.
-
If you are looking north, the azimuth would be 0 degrees and the altitude would be 90
degrees
b. What do you notice about the altitude compared to the latitude of the observer?
the altitude of the star is much higher than the latitude of the observer. To have the altitude be
eye level with the observer the number would have to basically be cut in half
7. Drag the star to various locations below the horizon. What do you notice about the altitude
coordinate at all locations below the horizon?
-
they are negative
8. In the star controls window, click the ‘add star randomly’ button 15 – 20 times. Make sure
the ‘long star trails’ option is selected. Set the latitude to N. Advance time to create star trails
and keep track of the motion of the stars through the sky.
*
You will need to look through the sphere to see the observer’s perspective.
a.
When facing north, how do the stars move from the perspective of the observer?
*When you are writing your descriptions, you can focus on details like whether stars are
rising or setting, whether they rise/set at an angle, or if they are traveling across the sky
in a certain direction/pattern (instead of rising/setting).
-
the stars are not rising or setting, the travel in circles around the NCP and stay at the same
altitude. They move from north to east going right.
b. When facing east, how do the stars move from the perspective of the observer?
-
When facing east, the stars are setting and going from east to west like going overhead the
observer. If not, then they are traveling along the horizon from east to south
c. When facing south, how do the stars move from the perspective of the observer?
-
When facing south the stars are rising in the east and setting in the west. They are going
3
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overhead and moving to the right (facing south)
d. When facing west, how do the stars move from the perspective of the observer?
-
When facing west, the stars are rising in the east and setting in the west, traveling directly
above. They are going to the right still, traveling north to make another rotation
e. Set the latitude to 0. Face east and advance time. It looks awesome! Check out the
north pole as well 90. (There isn’t a question that you need to answer here.)
9. Head to
https://stellarium-web.org
in your web browser. Turn off the atmosphere by clicking
the “atmosphere” button if you can’t see any stars. Click the “Azimuthal Grid” button at the
bottom of the screen to put the horizon coordinate system on the screen. Look in the simulated
sky and choose any single star above the horizon. Notice the altitude and azimuth of the star in
the pop-up window.
Advance time so the star moves in the sky (you can hold down the arrows in the time box or use
the slider-bar to advance time).
What happens to the altitude and azimuth values of that star?
-
the azimuth decreased along with the altitude, buy they end up higher up again and the
numbers increase
Do the gridlines representing the horizon coordinate system move relative to the ground, or are
they fixed to the ground?
-
the are fixed to the ground
Do the objects in the sky move relative to the coordinate system?
-
the coordinate system is fixed to the horizon. The objects in the sky move relative to it, they
will all return to the same spot throughout rotation.
Summary of Findings:
In the horizon coordinate system, the azimuth is measured from north (0°) and increases
toward the east (90°) with a maximum value of 360° when the observer has rotated back to
north. The altitude coordinate is measured from the horizon (0°) and increases towards its
maximum value, the zenith (90°). The coordinate decreases towards its minimum value, the
nadir (-90°). All stars with negative altitudes are located below the horizon.
4
The horizon coordinates of an object in the sky depend on the location of the observer. The
coordinate system is used the same way, no matter where the observer is located on the Earth,
so the altitude and azimuth of the cardinal directions (N, S, E, W), the horizon, the zenith, etc.
are the same for any observer.
The altitude and azimuth coordinates of any celestial object will change over time, because the
horizon coordinate system is fixed relative to the Earth’s horizon (so the gridlines stay in the
same place while the celestial objects in the background move). At northern latitudes, stars that
are further north stay in the sky longer (with any circumpolar stars that never set being located
most to the north).
5