Download Astronomical Motions I: The Night Sky

AST-103L
Fall 2001: Astronomical Motions I.
The Night Sky
Early Greek observers viewed the sky as a transparent sphere which surrounded the Earth. They
divided the stars into six categories of brightness with the brightest stars called first magnitude,
the next brightest second magnitude, and so on down to the faintest stars visible to the naked eye,
sixth magnitude. The Greeks, as well as other peoples, arranged the stars into groupings which
we call constellations. Most of the names of the eighty-eight constellations we use today are
based on Greek mythology and their Latin translations. Modern astronomy uses the constellation
designation to map the sky. The boundaries between constellations, set by international
convention, are imaginary lines on the celestial sphere. With the invention of the telescope, many
fainter stars and objects were discovered. These are also measured on the magnitude system,
with a larger number denoting a fainter object. On maps, the size of the dot is usually related to
the brightness of the object (look on your planisphere). Most only show the brightest stars. They
are named from brightest to faintest using the Greek alphabet (α, β, γ, etc.; see the handout you
were given in the first class meeting) with the constellation name in the genitive form; e.g. alpha
Cygni is the brightest star in Cygnus. Many stars also have Arabic names such as Betelgeuse,
Algol, and Arcturus; α Cygni is named Deneb and α Ursa Minoris is more commonly known as
Polaris. Either designation is correct.
In the exercise “Angles and Parallax,” you made a cross-staff and quadrant and learned how
to use them to measure objects in and around the classroom. Now, we will use them to measure
objects in the night sky, much like Tycho Brahe did in the 1500’s. Remember to record the date,
time, and conditions (and optical instrument if other than naked-eye) when making any
astronomical observations!
Objectives:
! Measure angular sizes and altitudes of objects in the night sky with instruments
! Estimate angular sizes and altitudes of objects in the night sky with your hands
! Determine the direction and rate at which the sky appears to rotate
! Learn how to find the North Star
! Determine your latitude
Equipment:
! Cross-staff with meterstick
! Quadrant with weight
! Planisphere
! Red flashlight
! Timepiece
! Computer with Starry Night program
! Two different colored pens or pencils (for take-home part)
! Protractor (for take-home part)
Set-Up:
You do not have to work with anyone else, but if it helps you, by all means do so. Remember
to credit your collaborators in your write-up. Part of this exercise must be conducted outside
and part in the lab. Skim through the exercise before you begin and get familiar with what
you’ll be doing. Clearly mark answers to discussion questions.
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AST-103L
Fall 2001: Astronomical Motions I.
The Night Sky
I. THE CELESTIAL SPHERE
Above, we noted how the ancient Greeks viewed the heavens as a transparent sphere centered on
the earth. This sphere has several features that are analogous to features on Earth. For example,
the celestial sphere has an equator and poles, same as Earth. Each location on the Earth can be
described in terms of a pair of coordinates known as longitude and latitude. Astronomers use a
similar system to pinpoint locations on the sky. These coordinates are known as right ascension
(RA) and declination (DEC). Declination is measured in degrees, minutes, and seconds and can
be positive or negative. It is measured from the equator (0°0’0”). Right ascension is measured in
hours, minutes, and seconds and starts from the vernal equinox (point at which the Sun crosses
the celestial equator moving northward, i.e. intersection of the ecliptic and celestial equator).
Thus, the vernal equinox is 0h0m0s, or 00:00:00.
ANSWER THE FOLLOWING QUESTIONS IN YOUR LAB NOTEBOOK.
1. Draw a representation of the celestial sphere and label these features: celestial equator,
right ascension, north celestial pole, declination, south celestial pole. Now draw a
representation of the Earth and label the terrestrial analogs of the above celestial
features.
~18°
2°
Figure 1. Approximate angles subtended by various parts of the average human hand.
II. USING YOUR HAND AS A MEASURING DEVICE
You have learned to measure angles accurately with a cross-staff and quadrant. A less accurate,
but more convenient, method is to calibrate something which is always available for use – your
hand. If you extend your arm and make a fist, its angular size is about 10°. With your hand
spread, the angle subtended is about 18° while a finger viewed sideways subtends about 1°. The
distance between two knuckles is about 2°. See Figure 1. These measurements are only
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Fall 2001: Astronomical Motions I.
The Night Sky
approximations; if you like, you can calibrate your own hand using what you learned in the
“Angles and Parallax” lab.
ANSWER THE FOLLOWING QUESTIONS IN YOUR LAB NOTEBOOK.
2. Do you expect this method to work for everyone? Why or why not? If not, can you
think of a way to standardize or improve this method?
III. MEASURING ASTRONOMICAL OBJECTS: IN-CLASS ACTIVITY
Find a safe, dark place outside to observe on a reasonably clear night. Align yourself so that you
can easily match your planisphere to the sky. Locate the constellations Cygnus, Lyra, and Aquila
and the three stars that make up the Summer Triangle: Deneb, Vega, and Altair. Using your
cross-staff, measure the angular separation between Vega and Deneb five times. Use your hands
to repeat the measurements. You may find it useful to alternate one method with the other,
resetting your cross-staff each time, to obtain independent measurements. Record your data in a
table. Calculate the average separation and standard deviation for each method.
Now locate the constellation Boötes and the bright star Arcturus. Use your quadrant to
measure the angular height of Arcturus five times. Repeat the measurements using your hands.
Again, you may find it helpful to alternate methods to avoid biasing your observations. DO NOT
FORGET TO RECORD THE DATE AND TIME OF EACH OF YOUR OBSERVATIONS!
Record the information in a table (see Figure 2 for an example) and calculate the average and
standard deviation for both sets of measurements.
Angular Separation:
Vega-Deneb
CrossStaff
Time
Hand
Angular Height of Arcturus
Time
Quadrant
Time
Hand
Time
1
2
3
4
5
Average
Std. Dev.
from Starry Night:
Actual VegaDeneb separation:
Actual angular
height of Arcturus:
Figure 2. Sample layout of data table.
Once you have completed these measurements, you can return to the classroom for the next
part. Use the Starry Night program to determine how close your measurements are to the actual
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Fall 2001: Astronomical Motions I.
The Night Sky
angular separations and heights of the objects. Do not forget to set the date and time to match
those of your data or you will not be making a legitimate comparison. Record the actual
separation of Vega and Deneb and the actual height of Arcturus in your notebook. Use
appropriate units and make sure things are labeled clearly.
ANSWER THE FOLLOWING QUESTIONS IN YOUR LAB NOTEBOOK.
3. Which was more accurate: the cross-staff and quadrant or your hands? Explain why.
4. Calculate the percent error between the actual angular separation of Vega and Deneb
and your average measurements using the cross-staff and your hands.
5. Did you have any systematic error or were your measurements within a standard
deviation of the actual values? If you had systematic error, what were possible causes?
6. When should you use the cross-staff and quadrant and when can you use your hands?
IV. MEASURING ASTRONOMICAL OBJECTS: AT HOME ACTIVITY
We often refer to Polaris as the “North Star” despite the fact that it is neither due north nor
directly overhead (at the zenith). The truth is that Polaris is due north and directly overhead if
you live at the North Pole. Because Polaris is very nearly at the North Celestial Pole, “North
Star” is not really a misnomer. This key piece of information can allow us (and anyone else in
the northern hemisphere) to quite easily determine our latitude on the planet.
The diagrams in Figure 3 are intended to convince you that the altitude of the pole star
depends upon the observer’s location on the Earth. Each diagram shows the Earth, its equator,
and the line of sight to Polaris for an observer standing at a different latitude. The first diagram is
for an observer standing at the North Pole. In this case, Polaris would be at the zenith and its
to Polaris
to Polaris
to Polaris
horizon
equator
equator
equator
horizon
Figure 3. The altitude of Polaris and latitude of the observer.
altitude would be 90°. The second diagram shows an equatorial observer, for whom Polaris
would be right on the north horizon, at an altitude of zero degrees. Thus, in both cases, the
altitude of the pole star equals the latitude of the observer. The third diagram shows the situation
for an observer at an intermediate latitude. From studying these diagrams it should not be
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Fall 2001: Astronomical Motions I.
The Night Sky
difficult to convince yourself that the altitude of the pole star is equal to the latitude of the
observer. Notice that in each diagram the observer’s horizon is shown; it is represented by a
tangent plane to Earth’s surface at the point where the observer is standing. Objects below the
observer’s horizon are not visible. Notice also that the direction to the pole star is indicated as
being the same on each diagram, even though the observers are at different locations on Earth.
This is because the stars are so enormously distant compared to the size of the Earth that all
observers anywhere on the Earth see a particular star by looking in the same direction in space.
Alternately, the light from any given star falls in very closely parallel rays over the entire surface
of the Earth.
Note that if you happen to be going on a trip which involves travel either north or south, the
altitude of Polaris will change. If you take your quadrant and measure the change, and if you also
know (using an atlas or the car’s odometer) how far you have traveled north or south, you can
easily compute the circumference of the Earth! The change in altitude of Polaris would be the
same fraction of 360° as the distance you traveled was of the Earth’s circumference.
Use your quadrant and hands to measure the angular height of Polaris five times each way, just
as you did in class for Arcturus. Record your information (and dates and times) in your
notebook. Calculate the average and standard deviation for each method of determination.
Locate Cassiopeia and either Ursa Major (Big Dipper) or Ursa Minor (Little Dipper). Find
Polaris (the North Star). Using your planisphere, locate two bright stars to the east and two bright
stars to the west of Polaris. Clearly mark these stars on the starwheel page. Using your cross-staff
measure the angular separations between Polaris and each of these stars. Record this information
along with that of the date/time of the observations. Now use your quadrant to measure the
angular height of Polaris and the four stars you chose. Record these measurements. Wait at least
two hours. Again measure the angular separations between Polaris and the four stars and the
angular heights of all five stars. Record the information along with the dates/times of the
observations.
Analyze this data by plotting what you observed. This will be easier on graph paper (if your
notebook is not quadrille ruled, you can do the graph on a separate piece of graph paper and
fasten it into your notebook). Mark the paper off in degrees east and west of north. The vertical
axis of your graph should be degrees of altitude. It is very important that both axes have the same
scale; for example, if each square on your graph paper represents two degrees horizontally, it
must also represent two degrees vertically. Start by placing Polaris at the proper altitude near the
center of your graph. Plot the other four stars’ positions based on their positions relative to
Polaris. Use one color to plot the positions of the stars as given by the first set of observations
and use another color to distinguish the second set of observations. Mark both data sets on the
same graph!
ANSWER THE FOLLOWING QUESTIONS IN YOUR LAB NOTEBOOK.
7. Based on your observations, what is your latitude?
8. How did the sky change over the course of two or more hours?
9. Do you think you actually observed Polaris? Why or why not? What does this mean?
10. Use a protractor to determine how much rotation took place during the time interval
between your two sets of north polar observations and calculate the rate in degrees per
hour at which the sky moved.
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The Night Sky
11. Based on your answer to Question 10 above, how long will it take to rotate 360°°? You
most likely will not get the “expected” answer. Speculate as to why this is the case.
V. REFERENCES
Gay, P.L. & Tufts, J.R. AST 103L Observational Astronomy Course Handbook, University of
Texas, 2000.
Hemenway, M.K. & Robbins, R.R. Modern Astronomy: An Activities Approach, Revised
Edition, University of Texas Press, 1991.
Shaw, J.S., Dittman, M., & Magnani, L. Laboratory Textbook for Elementary Astronomy, 7th
Edition, Contemporary Publishing Company, 1996.
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The Night Sky
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