So, Why Don't Kepler's Laws Apply to Stellar Motion around Galactic Centers?

[Fiery Phoenix]

I've been wondering why Kepler's laws don't apply to stellar motion around galactic centers. I have come up with two layman theories:

1. Galactic centers aren't composed of a single massive body (or a few) as is the case with star systems.
2. The orbits of stars are different compared with planetary orbits. I'm guessing that stellar orbits are quite unstable due to the fact that each star orbits in the middle of billions of other stars that are relatively nearby.

I'd like to hear your comments. But please try to use simple terms so I can understand this better.

[NEOWatcher]

I've been wondering why Kepler's laws don't apply to stellar motion around galactic centers. I have come up with two layman theories:

1 and 2.
Kepler's laws consider the orbit around the whole of the mass, not just the center of the mass. The star is not outside the mass, it is within it, so you can't compute the orbit as if the mass were concentrated at the center.

[Fiery Phoenix]

1 and 2.
Kepler's laws consider the orbit around the whole of the mass, not just the center of the mass. The star is not outside the mass, it is within it, so you can't compute the orbit as if the mass were concentrated at the center.

Are you telling me my so-called theories are accurate? Good for me, I guess.

Thanks, dude. I get it now. Any more comments are most welcome.

[Argos]

You might like to take a look at the role of Dark Matter in the general motion of stars in galaxies.

Together with fellow staff-member Kent Ford, Rubin announced at a 1975 meeting of the American Astronomical Society the astonishing discovery that most stars in spiral galaxies orbit at roughly the same speed, which implied that their mass densities were uniform well beyond the locations with most of the stars (the galactic bulge). This result suggests that either Newtonian gravity does not apply universally or that, conservatively, upwards of 50% of the mass of galaxies was contained in the relatively dark galactic halo.

[Jeff Root]

Your "theories" 1 and 2 appear to be one and the same. But yes, they
are both accurate descriptions of what is going on.

-- Jeff, in Minneapolis

[Cougar]

I'm going to take an alternative view here.

I've been wondering why Kepler's laws don't apply to stellar motion around galactic centers....

It depends on what you mean by "around galactic centers." Orbits of stars at small radii from the center ARE keplerian, I believe. In such a high mass region, the dark matter plays a lesser role. As the radius increases, the dark matter apparently becomes the more dominant gravitational source as the density of stars and gas falls off exponentially, and the orbits no longer appear keplerian.

I have come up with two layman theories:
1. Galactic centers aren't composed of a single massive body (or a few) as is the case with star systems.

Well, the mass ratios might not be the same, but most galactic centers ARE found to house a supermassive black hole. Still, its mass is typically a very small percentage of all the stars and gas and dust in the galaxy.

2. The orbits of stars are different compared with planetary orbits. I'm guessing that stellar orbits are quite unstable due to the fact that each star orbits in the middle of billions of other stars that are relatively nearby.

So you're talking about in close to the central black hole, at small radii... Yes, it's going to be more crowded, but I wouldn't necessarily conclude that therefore the orbits are going to be "quite unstable." Yes, probably less stable than at our radius, but then we are also orbiting among billions of stars, and they're obviously in fairly stable orbits, at least for the past 5 billion years.

[Jeff Root]

Cougar,

I think that when the original poster said "each star orbits in the middle
of billions of other stars that are relatively nearby" he was referring to
the entire galaxy, exactly as you do at the start of your final sentence.

The stars of any galaxy are *not* in stable orbits. They are chaotic
orbits. A stable orbit follows a highly predictable path. Stars in galaxies
do not follow highly predictable paths. The stars interact with each
other gravitationally, causing slight changes at each interaction, and
these changes add together.

It just occurred to me that you might think a non-stable orbit means
the star is going to dive into the center of the galaxy. Nope. It just
means that the orbit changes. In the case of stars in the galaxy, the
orbits are chaotic-- the orbits change in unpredictable ways.

While dark matter is an important factor in determining how stars orbit,
it is not primarily responsible for the orbits not being Keplerian. That is
due simply to the mass of the galaxy not being predominantly at the
center.

-- Jeff, in Minneapolis