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Let's say there's an OCEAN planet smaller than Earth but larger than the Moon. The Sun lights on the ocean planet reflecting the water textures onto Earth.

Would it be possible to see watery reflections on Earth during night?

If not... do you have any idea how to achieve similar result?

I'm talking about this kind of reflections. enter image description here

enter image description here

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  • $\begingroup$ 'The transient effects of light on water' This sounds pretty, and even if it weren't physically possible you should implement it anyway. $\endgroup$ – punkerplunk Jul 11 '15 at 23:07
  • $\begingroup$ Are you talking about one planet casting these reflections onto another? How close do you want those planets to be? $\endgroup$ – Philipp Jul 11 '15 at 23:27
  • $\begingroup$ Yes. I haven't thought about that. Hmm... as close as possible?. It could even be extremely close if necessary. $\endgroup$ – Reinkkwer Jul 12 '15 at 3:54
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    $\begingroup$ A thought: the Earth is already more than halfway an "ocean planet," but it does not project such a pattern on the Moon. $\endgroup$ – sumelic Jul 12 '15 at 17:45
  • $\begingroup$ @sumelic Just noticed your comment... looks like we had the same idea! $\endgroup$ – 2012rcampion Jul 13 '15 at 3:56
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NO

Let's reverse the scenario for a second, and talk about reflections from the Earth onto the Moon. The Earth is not 100% water, and is partially covered by clouds, but since it's a lot bigger than your watery planet the visible water area is similar on average. Plus, the Moon makes a much better "canvas" for any possible reflections since its surface is far more uniform than the Earth's.

Can we see any reflections on the Moon?

enter image description here

Well, maybe the moon is just too far away and the earthshine too dim. What if we get really close to the oceans... like 400 km close?

enter image description here

Note that, in this picture, we're looking at the nadir (Earth-facing side) of the ISS (you can tell from the Leonardo module sticking out the bottom) and that the sunlight is coming from the top of the screen (see the shadow of the Orbiter's wing on the starboard solar array). This means that the scene is partially lit by earthshine; in particular the underside of the radiators is completely lit by reflected sunlight. No patterns are visible.

Why?

The pattern of light you're looking for is a type of caustic. Caustics are caused when reflection or refraction off of a curved surface causes light to be concentrated at some points and diffused at others.

You can think of each wave in the surface of the water as a poor approximation to a lens, focusing the light that it refracts or reflects. The kicker is that the approximate focus point is relatively close to the surface. Take a look at this computer rendering:

enter image description here

As you get further and further from the surface, the refracted light becomes defocused and the patterns start to blur together. The distance at which the caustics totally disappear is one or two orders of magnitude larger than the wave dimensions. So even under ideal circumstances, a planet with 10 m waves couldn't have caustics visible at 1 km or more, much less the hundred thousand or million kilometers to another heavenly body.

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It's almost completely impossible

Those textures occur because of the waves on a surface. Each reflect light in a slightly different direction. Where many patches of water reflect, the effect is bright. Where few patches reflect, it is dim.

However, this effect fades over distance. Near the water, you get most of your light from water nearby. The r^2 losses from distance make the lighting effects from further away patches dimmer. This means the lightness or darkness is based on the variation in angle of a very small region of water. At greater distances, the difference in brightness from near patches and far patches is much less. Thus your effects are averaged out over a larger patch of water.

At planetary distances, you would get a completely blurred light source. The planet may shimmer like a star, but you will be hard pressed to have visibly different effects in Moscow vs. Tokyo. The angles are just too close and the effect is too blurred.

To get this effect you would have to get the planet to actively cast a light pattern directly at the earth, rather than relying on accidental effects. You would need the ocean planet to take on holographic properties, ensuring all light that hits the ocean is columned properly to generate the desired effects. You could do it with complete planetary control... but at some point it would be easier to achieve the effect with a large array of holographic gratings.

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