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

[Anthony]

Originally Posted by Captain Joy

To bring this back on topic: it seems based on everything I'm hearing that you can safely ignore the heat given off by a gas giant for it's moons, unless your system is still in the process of forming.

And if it is, you have much bigger issues to worry about, as the massive cometary bombardment phase may not be over yet.

[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?

Now Ganymede is a little more the 1mil KM from Jupiter, or 0.007 AU. Now when I plug those numbers into the formula on page 113 it tells me that Jupiter would heat Ganymede to over 1,200 Kelvin ALONE, that can't be right, so what am I doing wrong?

[David Johnston2]

Originally Posted by scc

I've done a search of the forums (Via Google) and I can't seem to find anything that answers this question.

What sort of adjustment should I make to blackbody temperatures of moons of Gas Giants?

Don't bother. It would be a fraction of a degree.

[Nereidalbel]

For one, Jupiter's albedo is .343, not .5. Also, Space uses AU for measuring distances within solar systems, not kilometers. Try the math again and see what happens!

[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.

[malloyd]

Originally Posted by David Johnston2

Don't bother. It would be a fraction of a degree.

Mostly. In the limiting case after you could imagine the moon always sat exactly between the sun and the gas giant, and the gas giant was a perfect mirror and so much bigger than the moon you could treat it as a flat one. This completely ridiculous arrangement maximizes the amount of light falling on the moon. It doubles it, which raises its temperature by the fourth root of 2 (i.e. about 19%).

The heating gas giants do of their moons isn't radiant, it's tidal. Maybe occasionally there'll be some meaningful magnetic effects too, at least on the air temperature of something with an atmosphere, but reflected light isn't going to contribute very much.

[Donny Brook]

Considering various factors and aspects, I would estimate* that it would be about

{----------------------------this much------------------------}.





*Depending on the units you choose, and the frame of reference.

[scc]

Originally Posted by Kraydak

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.

That last bit is actually part of the thing that makes this interesting. If Jupiter was bigger how much would it heat things up? If it was about as far away from Sol as Mars is how much brighter would it be?

[Anthony]

As a rule of thumb (this fails at very short distances), you can take the surface temperature of the object and multiply by sqrt( 0.5 * radius / distance ) to get the temperature it would apply to a spherical blackbody subject to no other heat sources. For example, take the sun (temperature 5778K, radius 696,342 km, distance 149,600,000 km) and we get a blackbody temperature of 279K for the Earth. For an object at the roche limit, the result is 45% of the temperature (and 4% of the heat per unit area). This is significantly affected by which face of the giant is visible, and for low orbits whether or not the moon slips through the shadow of the giant.

[Flyndaran]

Does all that mean that double planets would be warmer than initially assumed because they reflect light and heat onto each other?