This is the best answer. The area of the plane is 0.0196 m^2, so the heating of 10^5 W/m^2 is actually around 2 x 10^3 W, which seems much more reasonable.
Also, I noticed that I missed that the plane is made from 4 sheets of A4 paper. Table 1 lists the mass as 4 grams, but 4 grams is typical for a single sheet of A4 paper, so the listed mass is probably for a single sheet. The actual plane mass is likely 16 grams. This means that the kinetic energy is likely closer to 480 kJ.
Thank you to afeuerstein for pointing out that I was missing the potential energy! However, that is not enough to make a huge difference. A quick estimate because I'm lazy is 9.8 m/s^2 * 480 km * 0.016 kg = 75.2 kJ. Yes, gravity decreases slightly as you get farther out, so this is an over-estimate.
So a total of around 550 kJ, and a power around 2 x 10^3 W gives a duration of 275 seconds or... a couple of minutes. I feel much better about the numbers now.
Also, I noticed that I missed that the plane is made from 4 sheets of A4 paper. Table 1 lists the mass as 4 grams, but 4 grams is typical for a single sheet of A4 paper, so the listed mass is probably for a single sheet. The actual plane mass is likely 16 grams. This means that the kinetic energy is likely closer to 480 kJ.
Thank you to afeuerstein for pointing out that I was missing the potential energy! However, that is not enough to make a huge difference. A quick estimate because I'm lazy is 9.8 m/s^2 * 480 km * 0.016 kg = 75.2 kJ. Yes, gravity decreases slightly as you get farther out, so this is an over-estimate.
So a total of around 550 kJ, and a power around 2 x 10^3 W gives a duration of 275 seconds or... a couple of minutes. I feel much better about the numbers now.