Resources: Sample Student Activities and Exercises

These are real assignments I’ve created and given to my students over the years. Solutions are available by contacting me.

Topic 1 The Celestial Sphere

The Angular Size of a Distant Object

On his very first attempt at astrophotography, Jeff Field of New Hampshire took the photo below which I have reproduced from the October 2000 edition of Sky and Telescope magazine with permission both from the photographer and from the magazine. The picture shows a Lockheed-Martin C-5 “Galaxy” transport aircraft (on the right) being refueled in mid-air against the backdrop of the waxing crescent Moon.

The Lockheed-Martin Corporation web site gives the true length of a C-5 as 75.53 meters. See the C-5 spec sheet at: http://www.lmaeronautics.com/products/airmobility/c5/specs.html

The goal here is to determine the distance (in kilometers) between the C-5 aircraft and the photographer.

Hints: You will need a ruler marked out in millimeters for this question. Recall that the angular diameter of the full Moon is about 0.5 degrees. Use this information to determine a “scale factor” in millimeters per degree for the photograph first. You do not need to know the true distance to the Moon or the true size of the Moon. Assume that, even though this is not a first quarter Moon, the distance between the “horns” of the crescent is a good estimate of the Moon’s diameter on the photograph.

Topic 2 Seasons and the Motion of the Sun

Using the Solar Motion Demonstrator

The exercise given below is just one of many possible ways students can use the SMD to help them appreciate the seasonal changes occurring on the different parts of the Earth throughout the year. It is easy to vary the particular locations. I try to choose three or four that represent low-, mid-, and high-latitudes so the students can see the a wide variation in their answers. You can even make the exercise more challenging by throwing in a southern-hemisphere city

To use the Solar Motion Demonstrator, pivot the green compass disk along the north-south axis so that the right hand side of the disk moves away from you through 90 degrees. Line up the slot in the compass disk with the edge of the frame where it is labeled "Latitude". Slip the slot in the compass disk over the frame and align it with the latitude of the location of interest. The compass disk must be perpendicular to the frame. The head of the metal fastener represents the Sun. Slide the "Sun" along the outer rim of the frame to the approximate day and month desired.

The edge of the compass disk represents the visible horizon for some imaginary person standing at the black dot in the center of the disk. To see the path the Sun makes across the sky for that particular latitude and time of year, swing the month portion of the frame completely from the "East" to the "West" as shown on the compass disk. The perimeter of the compass disk is marked in 10 degree increments. You can read the direction to the point on the horizon where the Sun sets (or rises) directly from the compass disk. For example, if you are at 40 degrees latitude and it is late June, the Sun will set about 30 degrees to the north of west. Comparing the location of the sunrise and sunset points at different times of the year is just one of the many things you can do! Note: you will also need a protractor along with the SMD to measure noontime altitude

1. Complete Table 1 on the next page by answering the following questions.

a) Use an atlas of the world to determine the latitude, longitude and country of the North American city of Tuktoyaktuk. For an observer in Tuktoyaktuk, determine at what directions along the horizon the Sun rises and sets for the various days of the year given in the table. State your sunrise answers as "X degrees north (or south) of due East"; state your sunset answers as "X degrees north (or south) of due West". Use a protractor to help you estimate what is the maximum angle above the southern horizon reached by the noontime Sun on each of these days. Record all of your answers in the table.

b) Repeat for an observer in the European city of Nice.

c) Repeat for an observer in the African city of Dakar.

d) Write a paragraph discussing your results for Tuktoyaktuk, Nice and Dakar. Do your answers make sense for what you know or have read/seen about the climate conditions at each location? Consider things like climate, the lengths of daylight and nighttime, and the noontime altitude of the Sun.

e) Does the term “midnight sun” have any connection to any of these places? Which one? How and why?

Table 1: Data for Tuktoyaktuk, Nice and Dakar

Tuktoyaktuk: __________________ latitude __________________ longitude __________________ country

Nice: __________________ latitude __________________ longitude __________________ country

Dakar: __________________ latitude __________________ longitude __________________ country

Reference for above data:

City Feb 1 Apr 15 Jun 20

Rise Max Noon Set Rise Max Noon Set Rise Max Noon Set

Altitude Altitude Altitude

Tuktoyaktuk

Nice

Dakar

City Sept 1 Nov 15 Dec 20

Rise Max Noon Set Rise Max Noon Set Rise Max Noon Set

Altitude Altitude Altitude

Tuktoyaktuk

Nice

Dakar

Topic 10 Small Solar System Bodies

Using Lowell Observatory Near-Earth Object Search (LONEOS) Data

Attached is a series of three photographs of the night sky taken with the 21-inch telescope of the LOwell Near-Earth Object Search in Flagstaff, Arizona. Compare the photographs carefully. Somewhere in the photographed patch of sky is a near-Earth object (NEO) called 1999CW7, an asteroid with an orbit that could bring it very close to (or in contact with!) the Earth. The only way such an object can be discovered is if someone notices its movement against the background stars. So, one photograph alone is not sufficient—you need to look at a series of pictures taken over a span of time. The purpose of the LONEOS survey is to find as many of these objects as possible and figure out their orbital characteristics so we can keep track of them and predict their movements. For more information about the project and the telescope, check out the LONEOS web page at http://asteroid.lowell.edu/asteroid/loneos/loneos_disc.html

Locate and carefully circle 1999CW7 on each photograph. Place a transparent grid over each of the photos one by one. For each photo, use a marker to carefully record the position of the object. Use a ruler to very accurately measure the distance in millimeters between the initial and final positions of the NEO. If the photographs have a scale of 2.81 seconds of arc per millimeter, how far has 1999CW7 moved on the sky in the time span between the first and last photos? With what angular speed (in seconds of arc per minute) is it apparently moving across the sky? If this asteroid takes about 1.5 years to orbit the Sun, what must be its average distance from the Sun (hint: remember Kepler's third law)?

Picture #1 -- Taken on Feb 13, 1999 at 08^h 56^m 40^s

(photograph courtesy of Lowell Observatory)

Picture #2 -- Taken on Feb 13, 1999 at 09^h 29^m 45^s

(photograph courtesy of Lowell Observatory)

Picture #3 -- Taken on February 13, 1999 at 10^h 02^m 50^s

(photograph courtesy of Lowell Observatory)

Topic 10 Small Solar System Bodies

A Near-Earth Passage of the Asteroid Toutatis

Let's look at NEO's from another perspective. In the recent past, a 5-mile wide asteroid named Toutatis made a very close pass by the Earth--it came almost as close to the Earth as the Moon does! And on the cosmic scale, that's CLOSE!

The object of this exercise is to see if you can determine exactly when that close passage occurred. You will need a ruler and a transparent protractor. Attached is a view of the inner Solar System showing the orbits of the Earth and other well-known objects. You know that the distance from the Sun to the Earth is 1 Astronomical Unit; measure this distance in millimeters on the diagram and record this number on the line below. Now you know how many millimeters are necessary to make 1 AU on this diagram.

Below is a table of distance and angle information for Toutatis for a series of days; you are going to use this information to plot part of the orbit of this asteroid to see when it came closest to Earth. For each day, convert the distance between Toutatis and the Sun from AU's to millimeters using your conversion number and write these distances into the table.

Center your protractor on the Sun with the zero degree line horizontal as indicated. For each day in the table, locate its angle along the edge of the protractor and make a small tickmark on the chart. Then draw a faint line from the Sun along your tickmark to represent the distance of Toutatis on that day. Use an "x" to mark the location of Toutatis on that day. Label the x with the day number. Draw a smooth (i.e not bumpy!) curved line through all of the x's. Look at the locations where the orbit of Toutatis crosses the orbit of the Earth. Are there any days when the Earth and Toutatis are in the same place at the same time?

1 Astronomical Unit = _______________ millimeters

Day Number Date Angle Distance in AU Distance in mm

1	Sept 21, 1992	339^o	1.18
2	Oct 1, 1992	349^o	1.09
3	Oct 10, 1992	359^o	1.02
4	Oct 20, 1992	11^o	0.96
5	Oct 30, 1992	22^o	0.96
6	Nov 10, 1992	38^o	0.89
7	Nov 20, 1992	51^o	0.91
8	Nov 30, 1992	66^o	0.92
9	Dec 9, 1992	80^o	0.98
10	Dec 19, 1992	92^o	1.03