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4

Partial problem with Anders' answer: 730K is a "hot Jupiter", which I think are usually kept hot by stellar insolation, which would also heat the proposed moon. Removing that heat-source: Shortly after Jupiter formed, assuming it orbited at its present distance from the Sun, at some point it might have had a surface radiation temperature of 730K, ...


6

Consider a planet with effective temperature $T$ radiating as a blackbody, emitting a total luminosity $L=4 \pi \sigma R^2 T^4$. At distance $a$ the power per square meter will be $$P = \frac{L}{4\pi a^2} = \sigma \left(\frac{R}{a}\right)^2 T^4.$$ If we demand a sun-like energy flow of $P_{required}$, we get a necessary temperature $$T=\left[\frac{P_{...


0

Say that you have an image with $N \times N$ pixels that covers a region of sky of $\theta \times \theta$ steradians. For each pixel $i$ you have a value of flux density $J_i$, expressed in Jy/sr. The image contains a galaxy and you want to calculate its the total flux. If this were a continuum problem, you would need to do an integral $$F = \int_{\Omega_{...


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