Solved: Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the... [IB Physics]

Question

SLPaper 2

Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.

Show that the intensity of the solar radiation at the location of Titan is 16 Wm⁻².

[1]

Verified

Solution

incident intensity $\frac{1360}{9.3^2}$ OR $15.7 \approx 16$ «W m $^{-2}$ » $\checkmark$

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 Wm⁻².

[3]

Verified

Solution

exposed surface is $1/4$ of the total surface $\checkmark$ absorbed intensity $=(1-0.22) \times$ incident intensity $\checkmark$ $0.78 \times 0.25 \times 15.7$ OR 3.07 «W m $^{-2}$ » $\checkmark$

Show that the equilibrium surface temperature of Titan is about 90 K.

[1]

Verified

Solution

$\sigma T^4=3.07$ OR $T=86$ «K»

The orbital radius of Titan around Saturn is R and the period of revolution is T. Show that T² = (4π²R³)/(GM) where M is the mass of Saturn.

[2]

Verified

Solution

correct equating of gravitational force / acceleration to centripetal force / acceleration $\checkmark$ correct rearrangement to reach the expression given $\checkmark$

The orbital radius of Titan around Saturn is 1.2 × 10⁹ m and the orbital period is 15.9 days. Estimate the mass of Saturn.

[2]

Verified

Solution

$T=15.9 \times 24 \times 3600$ $\checkmark$ $M=\frac{4\pi^2(1.2 \times 10^9)^3}{6.67 \times 10^{-11} \times (15.9 \times 24 \times 3600)^2}=5.4 \times 10^{26}$ «kg» $\checkmark$

Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.

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