Is there life outside of Earth? Activity 2: Moving Stars and Their Planets Overview In this activity, students are introduced to the wobble-method (officially known as the radial velocity method) of detecting planets. The activity starts with an introduction to Newton s Third Law of Motion. Students use a model to explore the effects of a planet s mass on the star s motion. Students then explore how the wavelength of light that a star emits is apparently changed as the star moves towards and away from a telescope. Students use a model to discover the influence of orbiting angle on the ability to detect a planet with the wobble method. Students then use an integrated model to explore the effects of planetary mass and orbiting angle concurrently. Finally, students learn about telescope precision and noise in the data. Learning Objectives Students will be able to describe how an orbiting planet can cause a star to wobble. explore the effect of planetary mass on a star s wobble. explain how wavelength can describe the motion of a star. demonstrate how a planet s angle of orbit determines whether or not the planet might be found. explain how planets are found using the wobble method. make claims about the data and determine their own level of certainty with regard to their claims. Lesson Plan 1. Estimated Time This activity should take approximately 45 minutes. 2. Introduce the Activity In this activity, your students will explore several models of motion.
Page 1: The effect of mass on a star s wobble In this model, students will change the mass of planet using the planet-diameter slider and the Rocky-planet switch. A rocky planet is denser than a gaseous planet, so the mass of the rocky planet will be higher than a gaseous planet of the same size. The mass of the student-created planet is given in the upper right-hand corner of the model in multiples of Earth s mass. Encourage your students to test different combinations of rocky planet and planet diameter to understand rocky planets and gaseous planets of the same size can have different effects on the wobble of the star. Page 2: A star s movement can change its apparent wavelength In this model, students will move the star towards and away from a telescope to see how the apparent emitted wavelength changes. It is important that students understand that the overall color of the light emitted by the star it not dramatically changed as the star moves; the wavelength detected by the telescope changes because the star is either moving closer (compressing the waves) or moving farther away (decompressing the waves). Also be sure to discuss with your students the idea that the graph shows the light hitting the telescope. This means the graph changes only when the wavelength hitting the lens changes--not when the star motion is changed. Page 3: The importance of orbiting angle on being able to detect a star s wobble In this model, students change the angle of orbit of the planet by tilting the plane (by clicking and holding the mouse button down in the simulation window, then dragging the cursor). The telescopes that are used to detect a star s wobble detect movement towards and away from the telescope. Your students eyes are now the telescope, so to detect a star s wobble, they will need to detect movement of the star into and out of the screen. If the planet does not orbit the star in a way that makes the star move into and out of the screen (towards and away from the detection instrument), the planet will not be detected. Students should try out many different angles of orbit to determine what angles of orbit lead to planet detection with the wobble method. This model introduces another slider: the graph-time-window slider. This control allows students to increase or decrease the amount of data they see in the velocity graph window. Be sure to have students explore and get comfortable with this slider as it comes up when exploring future models in this investigation.
Page 4: Combinations of mass and angle that lead to planet detection with the wobble method In this model, students will make different combinations of mass and angle that result in the same velocity graph. Additionally, students can now explore with a list of preset planets in the Preset- Planets pull-down menu. They can also create their own custom planets. To do this, turn on the custom-planet switch when the model is running. Then set the Rocky-planet switch to choose a rocky planet or a gaseous planet and set the planet s diameter with the planet-diameter slider. To set the planet s velocity, move the arrow (vector) of the planet. To change the location of the planet drag the planet around. To start the simulation, turn off the custom-planet switch. It is easy to get an elliptical orbit this way; it is also easy to select a starting velocity that doesn t result in an orbit at all. If a circular orbit is desired, click on the make circular orbit button. The Distance-to-star button zooms the view in and out. It does not change the distance of the planet from its star, just your viewpoint. Hopefully, students will explore lots of variations, but be sure to get students to focus on solving the problem. With the entire class, discuss the different solutions students found and/or what difficulties students had with solving the problem. Students are challenged to match the graph. It is important to tell them that close enough is fine; the curriculum focuses on getting students to see how different variables affect how the data can be interpreted. Page 5: Limitations of Noise This page introduces students to the idea of noise and that the graphed data they have been viewing is too perfect to match real data. One way students interpret graphs with lots of noise is that there are lots of changes going on. In reality the noise is an artifact of either the environment through which the light passed (gases and other materials in space), as well as physical limitations of the sensors on the instrument. Most advances in science are a result of some advance in engineering. New more sensitive light sensors, or complex telescopic arrays launched into space, make possible less and less noisy signals.
Page 6: Impact of Noise on Angle of Orbit In this model, students will experience the data in a way more similar to how scientists get data about a star s wobble. Students will set up the model so that the planet is detectible with a perfect telescope, and then they will decrease the precision using the telescope-precision slider until they can no longer detect the planet. There is a new control in this model; students can now magnify the y-axis with the slider. This will allow them to see data that is very small or very large. It is important that students look at the values on the y-axis to determine the magnitude of the velocity change. Discuss with your students the importance of scale--similar-looking graphs with different y-axis scales are not equivalent. On this page students are asked to focus on how it can be difficult to spot a small signal inside noisy data, and to explore this through changing the angle of orbit for a planet. Regardless of the mass of the planet, when the tilt of the orbit is close to 90 degrees there will be little movement of the star toward and away from the observer. This produces a weak signal that can get lost in noise. It is important to talk about experimenter s bias at this point. Since they know that they have a planet in the model, some students may detect a planet in the noisy data that is undetectable. It is important to discuss that the noise in the data may obscure planets that are there or make scientists think that there may be planets present where there are not. Remind your students that scientists repeat their experiments many times and ask their colleagues to independently analyze the data so that the experimenter s bias is minimized. It is also important to focus on scientists certainty about their conclusions and what scientists can do to increase their certainty. Page 7: Impact of Noise via Planet Discovery via Star Motion This page is very similar to the previous one, except this time students are asked to explore how low mass planets, even when on the ideal orbital plane, may become undetectable if the data is noisy enough. This page ends with a challenge for students to determine if a particularly noisy graph indicates the presence of a planet.
3. Discuss the Activity Possible discussion questions: Using light to find planets How do scientists use light from distant stars to measure movement? What do scientists know about the motion of a star from the size of its wavelength? How is a star moving if its wavelength is shifted towards the red end of the spectrum (longer wavelengths)? How is a star moving if its wavelength is shifted towards the blue end of the spectrum (shorter wavelengths? Wobbling stars What is meant by the term star wobble? Is Earth s star (the Sun) wobbling? The graphs represent the velocity of the star, not the velocity of the planet. Why do scientists focus on a star s motion (and not the planet s motion)? How does the model help to explain star wobble? How does a planet s angle of orbit affect the ability of scientists to detect it? What would the velocity graph look like if there were multiple planets orbiting the star? Finding planets with indirect evidence The graphs represent the velocity of the star, not the velocity of the planet. Why do scientists focus on a star s motion? How can scientists be sure that they have found a new planet? How do technological innovations influence the process of science? 4. Answers to Questions Section 1: Finding Planets Using Star Motion Page 1: Gravity and Orbits Q. The motion of a star caused by an orbiting planet is referred to as a wobble. What does this wobble motion look like? A. The wobble motion looks like the star moving in a circle around the center of the graph. The planet is pulling on the star and the star is pulling on the planet. The planet tugs the star outward and the star tugs inward on the planet.
Q. What happens to the motion of the star when the planet has a very low mass? A. (A) The star moves around, but not enough for use to see it in the model. Q. Explain your choice in the previous question. A. Students should support their choice with evidence from the model. For example, when the planet s mass was very low, the star appeared to stop moving, but I know that it did not actually stop moving because every object has an effect on every other object. It must be too small for me to be able to see it in this model. Q. Based on your observations, what is the relationship between movement of the star and the mass of the planet? A. When the planet is more massive, the star moves more. When the planet is less massive, the star moves less. This is because a more massive planet exerts a stronger gravitational force. Page 2: The Doppler Effect Q. Place a snapshot of the model below that shows both short and long wavelengths in the same picture. Be sure to add text notes to the image that indicate which ones are short and which are long. A. Q. Imagine you are observing the star through the telescope pictured above. What happens to the wavelength of the star s light as it moves away from you? A. (B) It gets longer. Q. Imagine you are observing the star through the telescope pictured above. What happens to the wavelength of the star s light as it moves towards you? A. (A) It gets shorter.
Q. You observe light from a star that seems to be shifted toward the red end of the spectrum. What does that say about the motion of the star? Explain your reasoning. A. That means that the star is moving away from the telescope. The wavelengths will be spread out further if the star is moving away, making its light appear to be red. Page 3: The Importance of Angle Q. What orbital angle prevents you from seeing the motion of a star that does have an orbiting planet? A. (C) 90 degrees Q. Explain your choice in the previous question. A. When the telescope can t see the wobble, it can t record any movement. When the planet s orbiting angle is at 90 degrees relative to the telescope, the telescope can t see the star s wobble at all. It s at a right angle to the planet rather than a shallower (more detectable) angle. Q. A scientist looks for planets by studying the light from a newly discovered star. The GRAPH of the star's motion (based on shifting wavelengths) indicates no motion of the star toward or away from Earth. The scientist decides that the star doesn't have any planets. Do you agree with the scientist? A. Student answers will vary, but most should choose no. Q. Explain your choice in the previous question. A. The scientist may be right or may be wrong. It depends on the angle that any planets orbit the star and what their masses are. If the planets are very small or orbit at an angle close to 90, then they will not be detectable. Or there may not be any planets at all. What the scientist should say is that no planets were detected with those methods. Page 4: The Importance of Both Mass and Angle Q. Place a snapshot here of the first solution to the challenge above. A. Student answers will vary. The graph should look similar to the challenge graph. Q. Place a snapshot here of your solution to the challenge above. A. Student answers will vary. The graph should look similar to the challenge graph. Q. How do different combinations of planetary mass and orbiting angle create the same velocity graph? Explain. A. Both mass and orbiting angle affect how well a planet can be detected with the wobble method. If the planet is very massive, then it isn t necessary to have an optimal orbiting angle to be detected, but if the planet is not as massive, then it needs to orbit its star at an optimal viewing angle (from Earth) if it is going to be detected at all.
Q. To the right is a velocity graph that was recorded by pointing a telescope at a nearby star. What are the approximate mass and orbital angle of the planet orbiting the star? A. Student answers will vary. Answers should include a combination of mass and orbital angle. Q. Are you certain about your description of the mass and orbital angle of the planet that made the graph above? A. Student answers will vary. Q. Explain what influenced your certainty rating in the last question. A. Student answers will vary. Answers should include reference to the possibility of many combinations that result in the same graph. Page 5: Limitations of Noise Q. Does this graph show a planet orbiting a star? What is your prediction? A. There is a planet there, but it is hard to see, so any one could be correct. This question has a self check on it, so students can see the real answer and compare to their prediction. Page 6: Impact of Noise on Angle of Orbit Q. Most of the planets that have been discovered have an orbit that is tilted closer to zero degrees than to 90 degrees. Why? A. When the planet is orbiting closer to 0 degrees the effect of its pull is more prominent, so it is more detectable. If the orbital plane is closer to 90 degrees, then the signal will be weak and could be lost in the noise. Q. Why might noise cause a scientist to be unsure about having discovered a planet? A. Because noise caused the data on the graph to jump up and down, hiding what could be a faint signal in the data. Page 7: Impact of Noise on Planet Discovery via Star Motion Q. Most of the planets that have been found so far have been very massive. Why? A. Since the telescopes are not very precise, they are unable to detect small planets. The bigger planets cause bigger shifts in their stars, resulting in changes in the velocity graphs that can be seen even with all of the noise. Q. Based on the data to the right and considering both mass and angle, could there be a planet orbiting this star? A. Student answers will vary, but the graph does seem to indicate a wobble.
Q. Explain your answer in the previous question. A. Student answers will vary. Explanations should include an analysis of any perceived wobble. Q. Are you certain of your response? A. Student answers will vary. Q. Explain what influenced your certainty rating in the last question. A. Student answers will vary. Answers should include reference to the level of noise in the graph as well as instrument precision.