Dark Matter in the Solar System

[50bmg]

If I understand correctly, the search for dark matter is due to the fact that the observable mass (normal matter) in a galaxy is not sufficient to account for its form or the motions of the stars. If normal matter was all that was there, then the stars around the edge of the galaxy should be rotating around the center of the galaxy much more slowly than the stars closer to the center, much the same way that neptune rotates around the sun more slowly than the earth rotates around the sun. So, there must be more matter out there contributing to the gravitational interactions than we are currently able to observe - Dark Matter. Do I understand this correctly?

Then - If there is dark matter within (or around) our solar system, wouldn't it likely have the same effect on the motions of the planets in our solar system, analagous to the effects on stars in the galaxy? But it doesn't, so there is either a different interaction on the larger scale and mass distrubition of a galaxy, or there is no dark matter in the solar system. I understand that dark matter may not be, or likely is not evenly distrubited throughout space, or in a galaxy, etc., so maybe that is the answer - there isn't any (or very little) dark matter in the solar system. But if that is the case, then our search for it locally (i.e. experiments in mines, etc.) will certainly be extremely difficult, if not simply futile.

Could someone expound on this for me, or explain where I am wrong in my thinking?
Thanks!

[Chris Peterson]

If I understand correctly, the search for dark matter is due to the fact that the observable mass (normal matter) in a galaxy is not sufficient to account for its form or the motions of the stars. If normal matter was all that was there, then the stars around the edge of the galaxy should be rotating around the center of the galaxy much more slowly than the stars closer to the center, much the same way that neptune rotates around the sun more slowly than the earth rotates around the sun. So, there must be more matter out there contributing to the gravitational interactions than we are currently able to observe - Dark Matter. Do I understand this correctly?

Yes, except that this isn't the reason for thinking that dark matter exists, it is only a reason. The unexpected rotation curves of galaxies was one of the first observations that argued for dark matter, but now there are many independent observations that do so as well.

Then - If there is dark matter within (or around) our solar system, wouldn't it likely have the same effect on the motions of the planets in our solar system, analagous to the effects on stars in the galaxy? But it doesn't, so there is either a different interaction on the larger scale and mass distrubition of a galaxy, or there is no dark matter in the solar system. I understand that dark matter may not be, or likely is not evenly distrubited throughout space, or in a galaxy, etc., so maybe that is the answer - there isn't any (or very little) dark matter in the solar system. But if that is the case, then our search for it locally (i.e. experiments in mines, etc.) will certainly be extremely difficult, if not simply futile.

I think it as you suggest, that the local density of dark matter (or of distributed dark matter) is simply too low to have a measurable gravitational effect. That doesn't necessarily mean that finding dark matter is any harder. The density even around the galaxy may be low as well- there's just a vast volume of it. The search for dark matter is on two fronts- its creation in the lab, or its observation in nature. In either case, it is individual particles being sought, so large concentrations are not necessarily helpful.

[neufer]

If there is dark matter within (or around) our solar system, wouldn't it likely have the same effect on the motions of the planets in our solar system, analogous to the effects on stars in the galaxy? But it doesn't, so there is either a different interaction on the larger scale and mass distrubition of a galaxy, or there is no dark matter in the solar system.

Dark matter in the form of Weakly Interacting Massive Particles (WIMPs) is assumed to collect in the center of the sun and planets and therefore it would be gravitationally indistinguishable from the mass of the sun and planets themselves.

[50bmg]

Thanks for your help.

What are some of the other examples of physical observations that imply there is dark matter?

Why doesn't dark matter have the same effect on planets in a solar/star system as it does on stars in a galaxy? (In other words, why doesn't it make Jupiter orbit at the same speed as earth?)

[neufer]

Thanks for your help.

What are some of the other examples of physical observations that imply there is dark matter?

Why doesn't dark matter have the same effect on planets in a solar/star system as it does on stars in a galaxy? (In other words, why doesn't it make Jupiter orbit at the same speed as earth?)

The period of an orbiting body is inversely proportional to the square root of the average density of matter inside its orbit.

There is no reason to believe that the average density of dark matter is anywhere high enough to significantly effect the period of orbiting bodies with orbital periods of less than a million years.

[50bmg]

But the average density of dark matter would be the same regardless of orbital size/period, even though the total amount of dark matter would differ with a larger orbit - right? Or, more likely, I'm misunderstanding something.
Is the average density of dark matter smaller in a star system than it is in instellar space inside a galaxy?

[Chris Peterson]

Is the average density of dark matter smaller in a star system than it is in instellar space inside a galaxy?

At the very least, the distribution of dark matter is different in a star system than it is in a galactic dark matter halo. It is either not present in star systems, or has ended up inside the stars and planets, not distributed in a cloud or halo around them. So the dynamics of the two situations will be completely different.

[neufer]

But the average density of dark matter would be the same regardless of orbital size/period, even though the total amount of dark matter would differ with a larger orbit - right? Or, more likely, I'm misunderstanding something.
Is the average density of dark matter smaller in a star system than it is in interstellar space inside a galaxy?

Right, the average density of dark matter would be the same regardless of orbital size/period.
You have the words right but you are missing the basic concept.

That average density of dark matter results in a dark matter orbital period contribution of ~ 100,000,000 years regardless of whether you are talking about a galaxy or the moon going around the earth.

However, this ~ 100,000,000 year dark matter contribution is negligible (frequency wise) if your natural orbit is only on the order of ~ 100 years or less.

It is only large galactic orbits with natural orbital periods of ~ 100,000,000 years themselves that come under the noticeable influence of the ~ 100,000,000 year dark matter orbital period.

[50bmg]

Maybe I'm starting to understand, but not quite there.

Chris Peterson's response about the distrubition being different is what I was originally guessing. But that seems like a different reason than Art Neuendorffer's reason.

If I understand correctly - It was stated that "The period of an orbiting body is inversely proportional to the square root of the average density of matter inside its orbit."
The average density of matter includes both dark matter and "normal" matter. So - you take the total mass inside the orbit (including dark and "normal" matter), divide it by the total volume enclosed by the orbit, and then take the square root of the result. This number would then be inversely proportional to the time it takes to complete one orbit. But this number would be the same if the distrubition of dark matter was uniform - increasing the total amount of dark matter while at the same time increasing the volume would not change the density (or average density), and would therefore not change the square root of the average density.

Is the dark matter making a larger contribution to the average density of mass inside the orbit of a star around the center of a galaxy than it is to the orbit of a planet around a star? If so, according to the equation, there must be a higher average density of dark matter in interstellar space in a galaxy than there is in inter-planetary space inside a star system.

Am I getting closer?

Thanks for your patience with me. I sure appreciate the time and help from your responses! This is really a great forum!

[neufer]

Am I getting closer?

Yes, but not there yet... Let's do some numbers:

The average density inside earth's orbit is /(1.612 AU)³ mostly due to the Sun.

Mercury has an orbital period of 0.241 years so the average density inside Mercury's orbit is /(0.624 AU)³ mostly due to the Sun.

Pluto has an orbital period of 248 years so the average density inside Pluto's orbit is /(63.63 AU)³ also mostly due to the Sun.

Now the Sun orbits the center of the Milky Way with an orbital period of 240,000,000 years
so the average density inside the Sun's orbit is / (623,000 AU)³
about half of which is dark matter and half of which is ordinary matter.

Hence, the average density of dark matter is ~ 0.5 x /(623,000 AU)³

Presumably, that is also the about the same density of dark matter as in the solar system but it is negligible
compared to the density of ordinary matter in the solar system which ranges from /(0.624 AU)³ to /(63.63 AU)³

The density of ordinary matter in the solar system ranges over a factor of 10⁶
such that planetary orbital period ranges over a factor of 10³ (by that square root factor)
but it still always greatly exceeds the density of dark matter.

The density of ordinary matter in galaxies, however, is low enough
that the density of dark matter can no longer be ignored.

[Chris Peterson]

Yes, but not there yet... Let's do some numbers:...

An excellent and clear analysis.

[neufer]

Yes, but not there yet... Let's do some numbers:...

An excellent and clear analysis.

Thanks, Chris.

[50bmg]

That was excellent. Thanks so much for the time you put into that.
I have a much clearer picture now.
Thanks again!

Ben

[Guest]

Another way to look at is that the distance to the nearest star is 4 light years. If we assume that normal matter for the solar system is about 2 * mass of the sun, and its all concentrated inside the Keiper belt - so it has a significant effect on the orbits of the planets. The Dark matter for the solar system, also about 2 * mass of the sun, is evenly distributed inside a sphere of diameter 4 light years - so the amount inside the Keiper belt is insignificant. Ergo, the planets aren't affected by Dark matter.

Of course that then raises the question of what effect the Dark matter outside the 4 ly diameter sphere is having ...

[dougettinger]

Am I getting closer?

Yes, but not there yet... Let's do some numbers:

The average density inside earth's orbit is /(1.612 AU)³ mostly due to the Sun.

Mercury has an orbital period of 0.241 years so the average density inside Mercury's orbit is /(0.624 AU)³ mostly due to the Sun.

Pluto has an orbital period of 248 years so the average density inside Pluto's orbit is /(63.63 AU)³ also mostly due to the Sun.

Now the Sun orbits the center of the Milky Way with an orbital period of 240,000,000 years
so the average density inside the Sun's orbit is / (623,000 AU)³
about half of which is dark matter and half of which is ordinary matter.

I cannot derive 623,000. My number is more like (2.69 x 10⁹AU)³.

Hence, the average density of dark matter is ~ 0.5 x /(623,000 AU)³

Why is the average density of dark matter only 1/2 when it represent 80 % of all matter ?

Presumably, that is also the about the same density of dark matter as in the solar system but it is negligible
compared to the density of ordinary matter in the solar system which ranges from /(0.624 AU)³ to /(63.63 AU)³

The density of ordinary matter in the solar system ranges over a factor of 10⁶
such that planetary orbital period ranges over a factor of 10³ (by that square root factor)
but it still always greatly exceeds the density of dark matter.

The density of ordinary matter in galaxies, however, is low enough
that the density of dark matter can no longer be ignored.

I still do not get some of these dazzling numbers ? And how is the basic equation derived ? Even Doug may begin to understand Dark Matter. Thanks guys.

[neufer]

The average density inside earth's orbit is /(1.612 AU)³ mostly due to the Sun.

Mercury has an orbital period of 0.241 years so the average density inside Mercury's orbit is /(0.624 AU)³ mostly due to the Sun.

Pluto has an orbital period of 248 years so the average density inside Pluto's orbit is /(63.63 AU)³ also mostly due to the Sun.

Now the Sun orbits the center of the Milky Way with an orbital period of 240,000,000 years
so the average density inside the Sun's orbit is / (623,000 AU)³
about half of which is dark matter and half of which is ordinary matter.

I cannot derive 623,000. My number is more like (2.69 x 10⁹AU)³.

Sun's orbital period of 240,000,000 years is ~ 10⁹ times Mercury orbital period of 0.241 years

Orbital period scales inversely with the square root of the density (i.e., ~ 1/√density).

Density inside the Mercury's orbit is ~ (10⁹)² = 10^(9x2) = 10^(6x3) = (10⁶)³ times that inside the Sun's orbit.

(0.624 x 10⁶ AU)³ ~ (623,000 AU)³ ~ (10 lyrs)³

Hence, the average density of dark matter is ~ 0.5 x /(623,000 AU)³

Why is the average density of dark matter only 1/2 when it represent 80 % of all matter ?

Most of the dark matter associated with the Milky Way lies outside the orbit of the Sun.

[dougettinger]

Where does the following equation come from ? The period of an orbiting body is inversely proportional to the square root of the average density of matter inside its orbit. P = ( (mass/volume )1/2 )-1

Where are those superscripts when you need them? This equation may come Newton's and Kepler's Laws, but I am not sure how volume or density comes into the picture.

[neufer]

Where does the following equation come from ? The period of an orbiting body is inversely proportional to the square root of the average density of matter inside its orbit. P = ( (mass/volume )1/2 )-1

Where are those superscripts when you need them? This equation may come Newton's and Kepler's Laws, but I am not sure how volume or density comes into the picture.

The equation comes from applying Newton's and Kepler's Laws to an equivalent circular orbit around a quasi-spherically symmetric mass distribution (e.g., the space shuttle orbiting the Earth). It is a handy rule of thumb I find.

Superscripts & subscripts (and other useful things) can be found in the tool bar above your Starship Asterisk* composition box.