21N.2.SL.TZ0.6 Titan is a moon of Saturn

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

21N.2.SL.TZ0.6 Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance. a.i. Show that the intensity of the solar radiation at the location of Titan is

16\ \text{W m}^{-2}

. [1] a.ii. Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is

3.1\ \text{W m}^{-2}

. [3] a.iii. Show that the equilibrium surface temperature of Titan is about 90 K. [1] b.i. The orbital radius of Titan around Saturn is

R

and the period of revolution is

T

. Show that

T^2 = \frac{4\pi^2 R^3}{GM}

where

M

is the mass of Saturn. [2] b.ii. The orbital radius of Titan around Saturn is

1.2 \times 10^9

m and the orbital period is 15.9 days. Estimate the mass of Saturn. [2]

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