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Let's say we have a planetary system that has somehow attracted an unusually high amount of dark matter and dark energy. We can hand-wave the physics and any impossibilities behind the method of that attraction and assume that this amount, while significant, remains essentially constant. There's just a planet with a lot of dark matter and energy around it.

As for just how much there is of this "unusually high amount", let's just say there's enough to have observable effects, however much that may be.

What are those noticeable effects? What could we see in local celestial mechanics? Would the planet rotate faster? Would surface gravity be greater? That sort of thing.

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    $\begingroup$ I guess you'll somehow mess up gravity on that planet (probably depends on the shape & center of the dark matter) - science doesn't really know how that stuff works so it's mostly pure speculation $\endgroup$ – Nicolai Jun 14 '17 at 2:48
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    $\begingroup$ @Nicolai not exactly… we don’t know how it is related to normal matter, but we do know a lot about it. In fact, how it affects the orbits of bodies in a cloud of the stuff is exactly what we do know! $\endgroup$ – JDługosz Jun 14 '17 at 3:09
  • $\begingroup$ @JDługosz I think it's arguable whether what we know is 'a lot' or not ^^. I also mostly wanted to say that any effects apart from gravity (which I adressed first) are going to more speculation than anything else - which fits your more detailed answer. $\endgroup$ – Nicolai Jun 14 '17 at 4:16
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First, you need to understand that Dark Matter and Dark Energy are very different things. You should start by reading the Wikipedia article linked to get some general idea of what you’re asking about!

The final component, dark energy, is an intrinsic property of space, and so has a constant energy density regardless of the volume under consideration

So, Dark Energy will not be “more concentrated” near a planet. That's just a non sequitur.

Dark Matter will clump on the scale of galaxies, not a small region within a solar system. Now cutting edge research indicates that there are different kinds of Dark Matter: some is completely non-interacting, and some may interact (and thus condense) a little. So, it may be conceivable that you could get a cloud of DM that’s a “small” clump within a galaxy.

A planet in a system embedded in this cloud would notice nothing. The density is still very low, and it's all around so the gravity cancels out.

Suppose you were to handwave a cloud of DM that’s only millions of miles across, and condensed onto a planet. As far as the rest of the solar system in concerned, that planet would be more massive. You notice the difference when looking at it and seeing that the normal matter seems to be some smaller amount.

This would be very subtle and not immediately apparent in terms of other planet’s interactions. But the moons of that planet — that you would notice. The distant moons would orbit fast, and possibly more distant than the apparently small planet would permit. It would point to a strange excess of mass. Closer moons, those within the DM cloud, would not obey Kepler’s third law! Looking at each moon, you would deduce different values for the mass of the planet! This would certainly confuse the explorers!

The planet would not rotate faster because of it. The surface gravity would be close to normal! You are inside most of the cloud, so only the DM that’s actually inside the planet will add to the surface gravity. You won’t notice this because the effect is small and you can just suppose the rock is of a slightly heavier type, deep inside the world.

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    $\begingroup$ I think dark energy is far not enough well known for us to have such categoric statements. It looks as antigravitating, dispersed matter, but this antigraviting behavior is visible only on very long distances. $\endgroup$ – Gray Sheep Jun 14 '17 at 3:40
  • $\begingroup$ This was just what I was looking for. Very insightful and some really cool stuff to consider. Thank you very much! $\endgroup$ – bmacklin Jun 15 '17 at 0:24
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From the dark energy is actually nothing more known except that it seems an antigravitating thing filling out the Universe. It is even possible that it isn't even matter, or it is not from particles.

The dark matter is... dark. Not in the sense of "black", it is dark in the sense of "invisible". It doesn't take part in the electromagnetic interaction, thus it doesn't interact with photons. Thus, we can't see it in telescopes.

Likely it doesn't take part in the strong nuclear force, too. It has more complex reasoning.

But it may take part in the weak nuclear force. If yes, then it may catalyze beta decays in the planet, in its whole volume. Thus, it would make the planet radioactive.

It takes also part in the gravitational interaction, thus its mass would add to the planets mass.

The result would be an ordinary planet, with unusually high gravitation and natural radioactivity.

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