3.5 Planet size and transit depth
In the last activity you explored changing the orbital inclination. This time you will explore changing the planet size.
Activity 4 Planet size and transit depth
Allow about 15 minutes
With the initial parameters as set (R star = 1.27 RSun; R planet = 1.75 RJ; P orb = 10 days; i = 90°), you should see a 2% transit depth. Adjust the size of the planet using the slider. Observe how the graph changes as you choose larger and smaller values for R planet.
The slider for this application only allows planet sizes up to 2.5 RJ, which is larger than more than 99% of the exoplanets currently known.
Adjust the planetary radius to R planet = 2.40 RJ. What is the value of the transit depth now?
Answer
3.77%
Adjust the planetary radius to R planet = 1.20 RJ. What is the new value of the transit depth?
Answer
0.94%
Discussion
You reduced the size of the planet by a factor of two while keeping everything else the same. Let’s consider whether the transit depths you obtained agree with Equation 3 in Section 3.3.
The equation told us that the transit depth depends on the size of the planet, that is to say the square of its radius R p, i.e. R p 2. So if the size of the planet is reduced by a factor of 2, the equation tells us that the transit depth should decrease by a factor of 22 (= 2 × 2 = 4). If you divide the transit depth of 3.77% by 4 you get 0.9425%, which is 0.94% rounded to 2 decimal places, exactly as the interactive application showed.
Play with the values of R planet, and check that the transit depths you obtain always behave as predicted by Equation 3.
OpenLearn - An introduction to exoplanets
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