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
With the initial parameters as set (Rstar = 1.27 RSun; Rplanet = 1.75 RJ; Porb = 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 Rplanet.
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 Rplanet = 2.40 RJ. What is the value of the transit depth now?
Adjust the planetary radius to Rplanet = 1.20 RJ. What is the new value of the transit depth?
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 Rp, i.e. Rp2. 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 Rplanet, and check that the transit depths you obtain always behave as predicted by Equation 3.