[Space] How much does a Gas Giant heat it's moons?

[Kraydak]

Originally Posted by scc

OK, revisiting this, the idea has crawled back into my head so I decided to muck around with values from our solar system, using Jupiter and Ganymede. Now Jupiter is 5.2 AU from Sol, so I square that, and raise to -1 and multiply by Jupiter's albedo of ~0.5 tells me that Jupiter counts as a star of ~0.02 Luminosity. Is this the correct way to treat Jupiter?

Not quite, you need to calculate the fraction of the Sun's energy output that Jupiter captures.. Jupiter's radius is about 7 X 10^9 cm,
while its orbit is about 7.8 X 10^13 cm, so Jupiter intercepts about (pi(7X10^9 cm)^2)/(4pi(7.8X10^13 cm)^2) = 2X10^-9 of the solar energy. The factor of 4 is the difference between the area of a circle of radius r (the area that Jupiter covers), and the area of a shell of radius r (the area that the Sun is shining on). A few billionths of a solar luminosity don't really change things very much, and note that Jupiter's temperature isn't controlled by the Sun.