The surface gravity of titan, the largest moon of saturn, is 0.135that of earth.

Question

The surface gravity of titan, the largest moon of saturn, is 0.135that of earth. The atmospheric pressure on Titan's surface is 1.6bar; mostly composed of Nitrogen (N2). The ground surface isbelieved to be mostly water ice ( the surface temperture is 95kelvin). The Huygens probe, part of the Cassini mission to thesaturn system, landed on Titan in early 2005. The probe wasapproximatly a cylinder 1.5 m in diameter and 0.5m tall, with amass of 320 kg.

It was suspected that there are bodies of liquid methane and ethaneon Titan's surface; this liquid is likely to have a density of 500kg m(^-3). The ability to survive landing in such a body of liquidhad to be designed into the probe. (We know it did not land inliquid, because there was no "splash" recorded by the onboardaccelerometer, but the pebbles in the image of the landing site arerounded, suggesting they have shaped by erosion by running liquid,as in a stream or on a beach.)

1. assuming the vertical extent of Titan's atmosphere is the sameas Earth's, how does the density of titan's atmosphere compare tothat of earth?

2. what is the total pressure at the bottom of Titanianmethane/ethane "lake" 15 m deep?

3. Would the Huygens probe have floated if it had landed in such a"lake"?

Explanation / Answer

Pressure = density x depth x g(planet)

1.6 = ratio of density x 1 x 0.135

density = 1.85 times that of earth's atm = 1.85x1.225 = 2.266 kg/m^3

Pressure at bottom of lake = 1.6 bar + 15 x 500 x (0.135*9.8) Pa = 2.49925 bar

Density of probe = Mass/ Volume = 320 / (PI*1.5*1.5*0.5/4) = 362 kg/m^3

so the huygen's probe did not land in methane (or else it would go down and splash out just as a can pushed into water jumps out)

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