Does dark matter have an influence on the earth orbit ?

Submitted by CrDe t3_z2brw2 in askscience

My title is a bit of a click bait but my question is more technical. Let's assume that the dark matter theory is the correct one. It affects how stars are orbiting around their respective galactic center. Since dark matter is really additional mass and not some anti-gravity matter, it should be everywhere in a galaxy and its vicinity (and I assume the amount is more or less equally spread). So dark matter should also give our solar system additional mass that have an impact on the object orbiting around our sun for instance no ?

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Aseyhe t1_ixgzkwx wrote

Ordinary matter loses its kinetic energy through inelastic collisions, which allows it to gravitationally condense into star systems. Our best understanding of dark matter is that it is not able to cool in this way. Consequently, star systems are extremely overdense in ordinary matter but much less overdense in dark matter.

In particular, the local density of dark matter is expected to be about 0.4 GeV/cm^(3), i.e. less than a proton mass per cubic centimeter. The mass of dark matter that is relevant to the earth's orbit is then about 10^-17 times as massive as the sun. So dark matter affects the earth's orbit at the 10^-17 level, which is unfortunately not measurable.

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mfb- t1_ixhfrdd wrote

Replying to [deleted] (#630,725)

> Does that make sense?

No.

Dark matter doesn't behave like clumps of dense metals in any way, otherwise it wouldn't be dark. For all we know it's not "far away", we are inside the dark matter halo and we expect its particles to cross Earth all the time (unless it's mainly primordial black holes).

> Go 100km up and 11-12 kilometers a second sideways, and you're in an orbit around that same point.

No, you reached escape velocity.

> The lumpy, heterogeneous density of the crust and mantle do affect the surface gravity and orbits over the Earth

Sure, but this has nothing to do with OP's question.

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PlaidBastard t1_ixhxlal wrote

Replying to mfb- (#631,727)

Woops, you were right about that velocity, but I don't think you not understanding my analogy for Newtonian gravitation really has anything to do with OP's question, either. You're absolutely right that dark matter isn't in clumps, but to detect it at all ever, it has to be less homogeneous than, say, the cosmic microwave background. I made the analogy to show how little distant, diffuse masses affect orbits.

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Aseyhe t1_ixih6fa wrote

Replying to PlaidBastard (#633,686)

> to detect it at all ever, it has to be less homogeneous than, say, the cosmic microwave background

That's not accurate: a uniform distribution exerts a nontrivial gravitational effect (and indeed this is something Newton got wrong, although with careful treatment, Newtonian gravity correctly predicts it).

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PlaidBastard t1_iximnuc wrote

Replying to Aseyhe (#635,641)

Pardon the barely detectable difference in gravitational acceleration out of me. What is your problem?

Are you familiar with the hydraulic analogy in E&M? And how it's not perfect for all behavior in actual electrical circuits?

My analogy isn't perfect for the effect of many randomly dispersed tiny point masses (certainly <kg, we have to agree?) on the orbits of planets (10^20-25 kg?) around stars, but I get the intense impression that you're actively refusing to see how it might be useful in someone trying to understand undergrad-level astrophysics in spite of it not being a perfect analogous model for the nature and distribution of dark matter in and around our galaxy.

Yeesh.

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