Pluto's Atmosphere

1. The problem statement, all variables and given/known data

In 1988 telescopes viewed Pluto as it crossed in front of a distant star. As the star emerged from behind the planet, light from the star was slightly dimmed as it went through Pluto's atmosphere. The observations indicated that the atmospheric density at a height of 50 km above the surface of Pluto is about one-third the density at the surface. The mass of Pluto is known to be about 1.5 1022 kg, and its radius is about 1200 km. Spectroscopic data indicate that the atmosphere is mostly nitrogen (N2). Estimate the temperature of Pluto's atmosphere.

2. Relevant equations
No idea

3. The attempt at a solution
No idea... I don't even know where to start. I tried looking up the average density of Pluto and it turns out this question is completely bogus anyway because according to NASA Pluto's atmosphere is mainly methane.
No, I've never seen that before. I feel as though it's supposed to be easier than that. THe answer is supposedly 108K, but I'm not sure how to get it at all.

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