Pluto's Atmosphere: Estimating Temp

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Pluto's atmosphere was analyzed using observations from 1988, which showed that atmospheric density at 50 km is one-third of that at the surface. The atmosphere is primarily composed of nitrogen, despite some claims that methane is the main component. Participants expressed confusion about how to estimate the temperature, with one suggesting the use of the barometric formula for density calculations. A temperature estimate of 108K was mentioned, but the method to derive this value remained unclear to the discussants. The conversation highlights the challenges in accurately modeling Pluto's atmospheric conditions.
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Homework Statement



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.

Homework Equations


No idea

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.
 
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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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