Gas giant moons: nights brighter than days?

[Vertigo]

Strange one this but I was thinking last night about the night time sky on a moon orbiting a gas giant (lets call them David and Goliath). In particular the night time sky when David is directly between the star and the Goliath. At this point Goliath will be fully illuminated (as in a full moon seen from Earth) and shining down on David during it's night.

Now for simplicity lets assume the Goliath is comparable in size to Jupiter. Consider how bright it can be here on Earth in the middle of a clear night when our moon is full. According to my calculations the 'face' of Jupiter (that is the area of its visible disk) is approximately 1500 times that of the face of our moon, and since Goliath is the same size its face too will be 1500 times larger. However the orbit of David about Goliath is likely to be considerably larger than that of our moon, so lets half that figure to 750 times.

So this means that when Goliath is 'full' David's nighttime sky will contain the equivalent of 750 of our moons. I haven't done the figures (not sure I know how exactly!) but that is going to be pretty darn bright and, I would argue, possibly brighter than the daytime illumination David receives from its sun.

One thing I thought of was that Goliath is, of course, convex so most of the light would be reflected away from David. But then so is our moon and the proportion that is 'full on' towards us should be the same. So it still seems like the total illumination should be around 750 times brighter than our full moon. In other words 750 times the brightness of our brightest full moon night sky!

Now this seems counter intuitive to me so I'm wondering what the flaw is in my logic (there's usually one knocking around somewhere). I have completely failed to google this as I keep getting pages on our nighttime sky.

 

[Abernovo]

Obviously, the albedo of Goliath would be a factor, but I can see your logic. Perhaps (and I'm not sure of the exact terminology here) it involves a factor of distance. The sun would be brighter than Goliath, but the sheer size of the close planet reflecting the sunlight onto David would have a huge impact, similar to using mirrors behind a candle to add more light to the centre of a room. The sun would appear small in comparison, although possibly brighter than any one spot on Goliath (I'm guessing).

Would this make the night's brighter than the days? I don't know. I could imagine it would, especially with the right albedo, make for easy navigation at all times. It would also affect the plant life, either native or greenhoused. This never occurred to me before. Something to think about. Cheers, Vertigo.

 

[Vertigo]

Okay, I think I may have answered my own question and the answer seems to be NO.

I managed to turn up this table (assuming I can get it to format right!):


Illuminance Surfaces illuminated by:
10−4 lux Total starlight, overcast sky
0.002 lux Moonless clear night sky with airglow
0.01 lux Quarter moon
0.27 lux Full moon on a clear night
1 lux Full moon overhead at tropical latitudes
3.4 lux Dark limit of civil twilight under a clear sky
50 lux Family living room lights (Australia, 1998)
80 lux Office building lights in hallway/toilet
100 lux Very dark overcast day
320–500 lux Office lighting
400 lux Sunrise or sunset on a clear day.
1,000 lux Overcast day
10,000–25,000 lux Full daylight (not direct sun)
32,000–130,000 lux Direct sunlight

From that it would appear that sunlight is some 10-130 thousand times brighter than the full moon. So the gas giant would be bright but nowhere near as bright as full sunlight. Another factor I didn't bother with is the difference in albedo and here the moon has an albedo of 0.27 and Jupiter is almost double that at 0.52 (I was quite surprised by that but apparently it's clouds are highly reflective). However that is still nowhere near enough to compensate for that huge difference in illumination. It's remarkable how much our brain can compensate for different light levels!

Edit: Abernovo posted whilst I was typing this. And you're right I hadn't initially considered the albedo but it seems it would take a truly huge albedo level to get the effect of brighter nights. An interesting one that I too had never considered before.

 

[Metryq]

Some building architects never consider the folly of their designs. There is a Vegas hotel with a curved, glass face that was basically a solar furnace.

In the movie 2010 we see Jupiter collapsing from the influx of added mass. Now imagine that dimple doing the same thing with the sunlight as the Vegas hotel. "Quick, everyone under a rock!"

 

[Vertigo]

Hehe that is pretty wild. In fairness they do say the architects anticipated the problem and had the glass coated in some high tech film that was meant to prevent or alleviate the problem. I guess they just didn't put enough on!

 

[Metryq]

Yep, every bad design needs a little dark matter to make it work better. And if that doesn't work, add some more!

 

[Vertigo]

It just seems to me that someone should have figured out that having a huge concave wall of glass facing South really wasn't the best idea going.

 

[Galacticdefender]

I wrote a short story once about a war on a gas giant's moon (with an atmosphere). It just didn't have a day and night cycle. It was usually in constant twilight, with some time being in direct sunlight. Light from the gas giant or other moons was always reflecting at least some light onto the surface, or blocking out some of the sunlight.

 

[Vertigo]

Hmm, not sure that would be quite right Galactic Defender. Assuming your moon is not tide-locked to the gas giant then it should still have a normal day/night cycle. However Once an orbit you will get total darkness as the gas giant eclipses the star. At this time there will be no light from either the star or the gas giant, just star light. At the other extreme of the moon's orbit you will have a very bright night, lit up by the reflected light from the gas giant. In between those extremese you will have variations as the gas giant's rising time gradually shifts through the day (just as our moon rise at different times of the day - for example at new moon it rises and sets pretty much at the same time as the sun), so part of the night lit by the gas giant and part dark.

 

[Galacticdefender]

There is indeed a "regular" day and night cycle, but there are so many other sources of light, and periods where the sun is eclipsed by other moons, that it often doesn't seem that way. It's pretty much how you just described it, although a significant amount of light is reflected by other moons as well, not just the gas giant.