From this thread, someone (me) asked the question about the day night cycle on moons like Europa, and how bright Jupiter would be in the Europan (or other moons’) sky. I think this is actually a pretty interesting question- has anyone calculated how bright the Europan (or Callistoan, Titanian, etc) night is when their planet is shining? If not, how would this be calculated? What effects could this have on hypothetical life on a gas giant’s moon?
It seems like it could be done using things like reflectivity of the planet’s surface, haziness of the moon’s atmosphere, distance from the sun, etc… what do you think?
Yes, it should be possible to calculate this using those parameters and the distance between moon and planet. The term for this is planetshine. It’s sometimes possible to see the entire moon dimly when it is new due to this phenomena. Looking at Europa, Jupiter is about 5 times further from the sun than Earth. Also, Europa is about 50% further away from Jupiter. Double the distance to a lightsource and you receive a quarter of the light. Without doing the math, Europa would receive much less planetshine than the moon does.
Through a small telescope, Earthshine is bright enough to show up features across the disc of a new moon. I’ve seen maria and craters.
I missed an important point. Jupiter is much bigger than the Earth, so would reflect more sunlight towards Europa as a result. I’m not sure how all the factors would work out, but I’d still expect the planetshine to be dimmer.
But Jupiter is also 11.2 times the diameter of the Earth, which means its disc in the sky would be 125 times bigger than the Earth’s disc, at the same distance from each planet. It’s albedo is also roughly 50% higher than that of the Earth.
So, back of the envelope, comparing Jupitershine on Europa to Earthshine on the moon:
Distance from the sun gives a factor of 1/5[sup]2[/sup], or 1/25
Distance from planet to moon gives a factor of 1/1.5[sup]2[/sup], or 1/2.25
Size of planet’s disc gives a factor of 125/1
Albedo gives a factor of 2/1
1/25 x 1/2.25 x 125/1 x 2/1 = 4.4
Which suggests Europa would actually get more planetshine than the moon, by a factor of more than 4. Where am I going wrong?
That should have been “albedo gives a factor of 1.5/1”, so the factor would be 3.3, not 4.4. Still comfortably brighter than Earthshine on the moon, though.
Yes, I picked that up. I was surprised how high Jupiter’s albedo is, though: 0.52, compared with 0.367 for Earth. My factor of 1.5 is still a bit high as an approximation, it should be closer to 1.4.
Definitely. Europa only gets 1/25 as much light from the sun as Earth does (actually 1/27 as much, as it is 5.2 AU from the sun, to be more accurate), but it gets 3 times more planetshine than the Moon gets from the Earth.
Clearly the Moon gets much more Earthshine than the Earth gets Moonshine:
albedo of Moon = 1/3 of albedo of Earth
size of Moon’s disc = 1/13 of Earth’s disc
making Earthshine on the Moon about 40 times brighter than Moonshine on the Earth.
So “Jupitershine” on Europa should be more than 100 times brighter than full moonshine on Earth, given a “full Jupiter”, whereas full daylight will be 27 times dimmer than daylight on Earth.
If you look at Wikipedia’s page for Planetshine, you can see images of Earth’s ability to light up the moon compared to the sun’s.
In more absolute terms, The sun from Earth is an apparent magnitude of -26, and the full moon is -13, a difference of about 400,000x.
I’ve heard that the apparent magnitude of the Earth seen from the moon is -16, whereas the Sun would still be -26, about a 10,000x difference in brightness.
The sun from Jupiter is -23 apparent magnitude. Using our current calculations in this thread, the apparent magnitude of Jupiter from Europa would be about -14 (-16, our Earthshine number, +1 for Jupiter’s increased reflection, -3 for distance from sun). This is about a 4,000x difference in brightness.
I would still call that a pronounced night/day cycle, but human eyes might find daytime on Europa so dim that we’d just think of it as moving from one dim cycle to a dimmer one.
Human eyes are remarkably good at adapting to different brightnesses. I mean, with a full moon and a clear sky here on Earth it’s possible to read a book by moonlight, once your eyes have adjusted*. A factor of 4,000 is not that great - for example, a poorly lit room might be 1,000 times darker than the sunny great outdoors (100 lux versus 100,000 lux, cite), but our eyes can cope.
Bizarrely, this NASA page says you can’t, which is nonsense, because you can and I have.