Saturday 22 December 2012

Power saturn radiates


$$P_{saturn} = 4\pi R_{Saturn}^{2}\sigma T_{Saturn}^{4}$$

First calculate with T as 76K:

$$P_{Saturn}^{T=76K} = 4\pi×57500^2×5.6703*10^{−8}×(76)^4$$
$$ = 7.8596*10^{10} W$$

Now T as 93K:

$$P_{Saturn}^{T=93K} = 4\pi×57500^2×5.6703*10^{−8}×(93)^4$$
$$ = 1.7623*10^{11}W$$

We have our two powers one $P_{Saturn}^{T=93K}$ and one $P_{Saturn}^{T=76K}$ so now we find the difference:

$$P_{difference} = P_{Saturn}^{T=76K} - P_{Saturn}^{T=93K} = 9.7634*10^{10}W$$

So Saturn radiates 0.554 times the power that saturn absorbes by sun which increases the temp to 93K.

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