NMSUAstronomy

I have created an adaptive online tutor for general astronomy, one that allows students to learn about astronomy and to hone their problem-solving skills. This 12,000+ question self-review library has been used successfully in the classroom since 2006, and in distance education mode since 2011. A recent in-class cohort of 80 students took over 26,000 5-question quizzes. This corresponds to an average of 325 quizzes (or over 1,600 questions) per student (versus the five hand-graded quizzes per student which were offered in the past). Students cite the immediate feedback (24/7), with worked solutions for all math problems, the ability to focus repeatedly on a single difficult concept, and the wide breadth of topics covered as extremely helpful aspects of the tutor.

Questions are designed to give experience in a variety of problem-solving modes. There is an emphasis on quantification and on extrapolation, and drawing on physical evidence and theory to deduce logical properties and patterns found in the physical universe. Question types include the following:

1. Extrapolation: How can our knowledge of the biodiversity found on Earth enable us to estimate the probability of finding life in the oceans of Europa?

2. Scaling: If different galaxy components have different spectral energy distributions (emitted flux as a function of wavelength), how should optical and infrared images of the bulge or disk of a spiral galaxy like the Milky Way differ from each other?

3. Visualization: Given a physical model of the Sun–Earth–Moon system, what is the observed phase of the Moon at a certain position in the sky at a certain time of day?

4. Figure analysis: What is the frequency of a displayed light wave?

5. Computation: If the Sun burns its reservoir of hydrogen at a certain rate, how long can it exist in the hydrogen-burning phase?

6. Algebra: If the Hertzsprung-Russell diagram shows us the specific relationship between the luminosity, temperature, and radius of a star, how can one calculate one quantity from the other two variables?

Students work to complete sets of five questions at a time. Each such quiz contains links within each question to a hint (?) and to a relevant lecture page (i), as well as to an audio recording of the lecture. Students can thus refresh the connection between the question and general topics, or receive guidance on how to set up or think about the problem. A sample quiz is offered below.

#1. This figure shows the location of the Moon in the sky as we look from our position in the northern hemisphere toward the southern sky, with the horizon stretching from east (on the left) to west (on the right). If the figure shows the location of the Moon in the evening (9 pm), what phase must it exhibit?

      

#2. Which piece of evidence suggests that the Earth and the Moon formed at similar locations in the solar system?

      

#3. The plot drawn below shows the decay of a radioactive sample of a certain element with time. Which of the following statements about it are true?

The amount of the original element which remains in the sample, as a function of time.

      

#4. If a star has a temperature of 6810 K (recall that the temperature of the Sun is 5800 K), and is 109 times as large as the Sun, how bright is it? The luminosity, in solar units, is:

Write your answer in the box, using a standard format for numbers. For example, if the luminosity is one hundred and twenty five times brighter than that of the Sun type "125" or "1.25e2". If the luminosity is eight times fainter than that of the Sun type "0.125" or "1.25e-1".

      

#5. Because of the finite speed of light, when we observe the most distant galaxies we see them           .

      

Once students have submitted their answers, they are given a solution set with worked answers to all of the questions. A sample solution set is shown below.

Summary of results:

Your score was

#1. If the figure drawn below shows the location of the Moon in the evening (9 pm), what phase must it exhibit?

#2. Which piece of evidence suggests that the Earth and the Moon formed at similar locations in the solar system?

#3. The plot drawn below shows the decay of a radioactive sample of a certain element with time. Which of the following statements about it are true?

#4. If a star has a temperature of 6810 K and is 109 times as large as the Sun, how bright is it?

#5. Because of the finite speed of light, when we observe the most distant galaxies we see them ...

Elapsed Time: minutes

#1. This figure shows the location of the Moon in the sky as we look from our position in the northern hemisphere toward the southern sky, with the horizon stretching from east (on the left) to west (on the right). If the figure shows the location of the Moon in the evening (9 pm), what phase must it exhibit?

      

#2. Which piece of evidence suggests that the Earth and the Moon formed at similar locations in the solar system?

The ratios between different isotopes of oxygen found in the Earth and Moon are identical. Since these ratios are determined by the environmental richness, temperature, pressure, and such (conditions that are determined by location in the solar system), the Earth and the Moon must have formed at the same place.

      

#3. The plot drawn below shows the decay of a radioactive sample of a certain element with time. Which of the following statements about it are true?

The amount of the original element which remains in the sample, as a function of time.

Our sample begins with 100 counts, and we know that over the course of each half-life 50% of the remaining atoms of the radioactive element will decay. Over the course of one half-life, the first 100 counts drop to 50 counts. Measuring on the plot, we see that the time (measured along the x-axis) over which the amount of the original sample (measured along the y-axis) drops from a level of 100 to 50 is a bit less than 6,000 years.

We know that in each half-life, 50% of the remaining atoms of the radioactive element will decay. Over the first half-life, we begin with 100 counts and decay to 50 (losing 50). Over the second, we begin with 50 counts and decay to 25 (losing 25). Twice as many atoms do indeed decay during the first half-life as the second, because the sample is so much larger when it starts.

      

#4. If a star has a temperature of 6810 K (recall that the temperature of the Sun is 5800 K), and is 109 times as large as the Sun, how bright is it? The luminosity, in solar units, is:

We can use Stefan's Law to relate the luminosity L, temperature T, and radius R of the star. Because we know the values of R and T, we will express the relation in terms of L as a function of R and T.

The radius R is 109 times that of the Sun, and the temperature T is 6810 K. We need to rewrite T in terms of the temperature of the Sun (which has a temperature of 5800 K).

We now insert the values of R and T (in solar units) into the equation to find the value of L.

To check our numerical answer, we can estimate the location of the star on the Hertzsprung-Russell diagram shown in the lecture slide linked to below (i). At the intersection of a temperature of 6810 (roughly 6800) on the x-axis and a diagonal line representing a radius of 109 (roughly 100), we can draw a horizontal line to the left over to the y-axis to find that stars located here should have a luminosity of roughly 20,000 in solar units. Our answer has been verified!

What kind of stars inhabit this region of the Hertzsprung-Russell diagram? With a roughly solar temperature and a radius 100 times that of the Sun, we are in the regime of the giant stars (far above the Main Sequence where the Sun is found).

      

#5. Because of the finite speed of light, when we observe the most distant galaxies we see them           .

Light takes a finite amount of time to travel through space, and so light from the most distant objects takes the most time to reach us. When we observe the most distant galaxies, we see them not as they are today, but as they were in the distant past (billions and billions of years ago, when the Universe was young).

      

Please don't hesitate to contact me if you would like to explore the other 12,401 questions in the library, by yourself or with a group of your students. Project GEAS would love to hear from you!

I also offer topical tutorials, such as this one focused on the lunar phases.

This material is based upon work supported by the National Science Foundation (NSF) under Grant No. AST-0349155 and the National Aeronautics and Space Administration (NASA) under Grant No. NNX09AV36G. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF or NASA.