Below are the radial velocity profiles of several different star-planet systems.

Posted: March 18th, 2022

Below are the radial velocity profiles of several different star-planet systems. What is shown is the radial velocity of the star as a function of time “phase,” the relative point in the planet’s orbit (one panel is an exception; see if you can identify it). Though it is the radial velocity of the stars being shown, the labels of the system are by planet name, with a “b.” For example, the top left is labeled HD 209458 b, which is the planet orbiting star HD 209458. In each panel, there are several actual data points representing the measured radial velocities of the stars, sometimes with error bars, along with a dotted, theoretically-determined curve that is a fit to the data points. Some other data is listed in on the panels.
Each panel is labeled, but for your convenience, from left to right, the systems are:
Top row: HD 209458 b, HD 80606 b, WASP-3 b
Middle row: HAT-P-2 b, HD 189733 b, XO-1 b
Bottom row:
And b, HD 20782 b, HD 37605 b
RV_all.png
Based on the above plots, answer the following questions. Be sure to explain your answers (your explanations need not be more than a sentence or so).
(1) Which of these stars experiences the largest range in radial velocities due to its planet? Explain.
(2) Which of these stars experiences the smallest range in radial velocities due to its planet? Explain.
(3) Which planets have roughly circular orbits, and which do not? Explain.
(4) Which planet has the longest orbital period? Look closely at the plots to ascertain this information and explain your answer.
Below are the radial velocity curves for (some of) the planets around the star 55 Cnc. The signal for each planet has been separated out, so each panel shows only the effect on the star from a single corresponding planet. Based on the information in these plots, and knowing that these planets are around the same star, answer the following questions.
RV_55_Cnc.png
(5) Order the four planets by the sizes of their orbits, from closest to the star to furthest out. Explain your answer.
(6) if you had to guess, which planet would you say is the most massive? Why do you think that? NOTE: Figuring this out is a lot harder than all of the other questions in this assignment, so I do not necessarily expect you to get it right. I am hoping you will give a reasonable answer that demonstrates some good physical reasoning behind it. There is one right answer, one wrong answer that’s a better guess than the others, and two pretty clearly wrong answers. If your reasoning is well-thought out I will give you full credit for the “best wrong” answer.

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