Astrophysics Problem. Atmosperic calculations for Titan Titan has an atmosphere

Question

Astrophysics Problem. Atmosperic calculations for Titan

Titan has an atmosphere composed of >98% N2. In 2005, the Huygens lander reported a surface temperature of T0=94K and surface pressure of P0=147 kPa. The mass of Titan is 1.3452×1023 kg and its radius is 2575.5 km.

a. Compute the pressure scale height, H, of Titan’s atmosphere, in kilometers? How does it compare to the scale height of Earth’s atmosphere (be quantitative)?

b. Compute the mass of Titan’s atmosphere in kg? How does it compare to the mass of Earth’s atmosphere (be quantitative)?

c. The surface pressure, P0, of an atmosphere is related to its vertical column density, N, by P0 = mpgN where is the mean molecular weight, mp is the proton mass, and g is the surface gravity. Compute the vertical column density of Titan’s atmosphere in meters2?

d. The Rayleigh scattering cross-section for N2 is 5.1×1031 m2. What is the optical depth, , of Titan’s atmosphere looking out from the surface into space (or, conversely, looking vertically down through Titan’s atmosphere from outside)? Comment on your answer.

Explanation / Answer

Titan, the largest moon of Titan has 600 km height atmospheric layer.

Titan atmosphere height is much more than earth’s atmospheric height.

Earth’s atmosphere height is about 110 km consists of 5 layers troposphere, stratosphere, mesosphere, thermosphere and exosphere. But most of its atmosphere is within 16 km from the surface of the earth.

Saturn moon Titan atmosphere mass is 1.3452±0.0002 ×1023 kgs

Earth’s atmosphere mass is 5.1480×1018kgs

Titan’s mass of atmosphere is more than earth’s atmosphere mass

          Mean molar mass of the Titan = 28.6 gm/mol

          Surface temperature = 95K

          Atmosphere pressure =1.6

Then density = 28.6 x 1.6 x 0.0821 x 95 = 8.57 g/L

So the atmosphere density of Titan is 8.57 g/L

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