Lab 5 Extrasolar Planets

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Dec 6, 2023

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Extrasolar Planets - Leah Andersen Remember to type your answers in blue text Background Material Complete the following after reviewing everything in the links under Background Materials. Question 1: The left side of the diagram below depicts the radial velocity curve of a star that is orbited by an extrasolar planet. The right side is a top-down view of the orbital motion of the star and planet. The small circle represents the star’s motion, and the larger circle represents the planet’s motion as both objects move around a common center of mass. The view from Earth is in the plane of the page, so we are viewing the system edge-on from the left side of the page. Radial velocity is positive when the star is moving away from Earth and negative when the star is moving towards Earth. In the boxes provided, label the positions on the star’s orbit with the letters corresponding to the labeled positions of the radial velocity curve. NAAP – ExtraSolar Planets 1/9 B + - C D A
Question 2: Label the positions on the planet’s orbit with the letters corresponding to the labeled positions of the radial velocity curve. Part I: Exoplanet Radial Velocity Simulator Introduction Open up the exoplanet radial velocity simulator. You should note that there are several distinct panels: a 3D Visualization panel in the upper left where you can see the star and the planet (magnified considerably). Note that the orange arrow labeled earth view shows the perspective from which we view the system. o The Visualization Controls panel allows one to check show multiple views . This option expands the 3D Visualization panel so that it shows the system from three additional perspectives. a Radial Velocity Curve panel in the upper right where you can see the graph of radial velocity versus phase for the system. The graph has show theoretical curve in default mode. A readout lists the system period and a cursor allows you to measure radial velocity and thus the curve amplitude (the maximum value of radial velocity) on the graph. The scale of the y-axis renormalizes as needed and the phase of perihelion (closest approach to the star) is assigned a phase of zero. Note that the vertical red bar indicates the phase of the system presently displayed in the 3D Visualization panel. This bar can be dragged and the system will update appropriately. There are three panels which control system properties. o The Star Properties panel allows you to control the mass of the star. Note that the star is constrained to be on the main sequence – so the mass selection also determines the radius and temperature of the star. o The Planet Properties panel allows you to select the mass of the planet, the semi- major axis, and the eccentricity of the orbit. o The System Orientation panel controls the two perspective angles. Inclination is the angle between the Earth’s line of sight and the plane of the orbit. Thus, an inclination of 0º corresponds to looking directly down NAAP – ExtraSolar Planets 2/9 C - + B D A
on the plane of the orbit and an inclination of 90º is viewing the orbit edge on. Longitude is the angle between the line of sight and the long axis of an elliptical orbit. Thus, when eccentricity is zero, longitude will not be relevant. There are also panels for Animation Controls (start/stop, speed, and phase) and Presets (preconfigured values of the system variables). NAAP – ExtraSolar Planets 3/9
Exercises Select the preset labeled Option A and click set . This will configure a system with the following parameters – inclination: 90º, longitude: 0º, star mass: 1.00 M sun , planet mass: 1.00 M jup , semimajor axis: 1.00 AU, eccentricity: 0 (effectively Jupiter in the Earth’s orbit). Question 3: What is the amplitude of the radial velocity curve? Remember that the amplitude in this case is the speed of the star. What is the orbital (system) period? Increase the planet mass to 2.0 M jup and note the effect on the system. Now increase the planet mass to 3.0 M jup and note the effect on the system. Question 4: In general, how does the amplitude of the radial velocity curve change when the mass of the planet is increased? Explain why the amplitude changes. Return the simulator to the values of Option A . Increase the mass of the star to 1.2 M sun and note the effect on the system. Now increase the star mass to 1.4 M sun and note the effect on the system. Question 5 : How is the amplitude of the radial velocity curve affected by increasing the star’s mass? Explain why the amplitude changes. Return the simulator to the values of Option A . Question 6: How is the amplitude of the radial velocity curve affected by decreasing the semi- major axis of the planet’s orbit? How is the period of the system affected? Explain why these values change. NAAP – ExtraSolar Planets 4/9 It looks like the orbital period is 365 days. The amplitude of the radial velocity curve is 28.5. We can see that the planet mass is increased, the amplitude of the radial velocity increases as well. This happens because the mass of the planet is greater the center of the mass moves closer to the planet so the star moves more which increases velocity. This produces the opposite effect than increasing the mass of the planet. Because the suns mass is greater, it takes a greater force to move it at such speeds. The amplitude of the radial velocity is changed as the planet’s orbits changed. The decreasing of the semi-major axis of the planets orbit causes the amplitude of the radial velocity to increase. When you decrease the semi-major axis of the planets orbit the period of the system decreases.
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