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Does the orbit of the sun (and other stars within the Milky way) around the galaxy result directly from radial gravitational force toward the objects in the center of the galaxy, or is there additional forces at play?

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I would say the answer to your question is yes and no. Yes that the orbit of our Sun in the Milky Way is due solely to gravitational forces as you suggest, but no in that they are not all radial towards the center of the galaxy.

The motion of the Sun around the center of our galaxy can be broken into two motions. The first is an "azimuthal" orbital motion around the center of the galaxy due to radial gravitational forces from mass interior to our orbit (be it stars, gas/dust, dark matter, dragons, etc.). The other type of motion is an oscillation into and out of the plane of the milky way. This is also caused by gravitational forces, albeit not radial forces from the center of the milky way. As the sun moves "above" the plane of the Milky Way, there is more mass below than above and it gets pulled "down". When it is in the plane it has residual energy from "falling down" and continues to fall "below" the plane where it then gets pulled back "up". This type of oscillatory motion is constant and analogous to a mass on a spring.

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Stars in the Milky Way orbit the Milky Way because of all of the mass that comprises the Milky Way. That other stuff includes stars, other ordinary matter such as gas clouds, and perhaps dark matter. I used "perhaps" because dark matter has not yet been confirmed.

General relativity does not explain the orbits of stars about a galaxy with the assumption that the only form of mass is ordinary matter. This leads to two possibilities: Either general relativity (and by extension, Newtonian gravity) is somehow wrong at galactic scales, or mass comes in flavors other than ordinary matter. The former leads to alternative formulations of gravitation such as MOND. The latter leads to alternative forms of mass such as dark matter. Even though the existence of dark matter is yet to be confirmed, the vast majority of astrophysicists lean toward the latter assumption, that ordinary matter is not the only form of matter.

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  • $\begingroup$ I know some astrophysicists who would scoff at you for even mentioning MOND. $\endgroup$ – zephyr Mar 24 '16 at 19:39
  • $\begingroup$ The motion of stars etc. only demands that there is lots of dark, non-dissipative matter. Normal matter in the form of low-mass stars etc. would fit the bill (but has not been found). The non-baryonic nature of dark matter is derived from other considerations -e.g. the primordial abundances and dynamics of galaxy clusters. $\endgroup$ – Rob Jeffries Mar 24 '16 at 23:22
  • $\begingroup$ @RobJeffries Given that it is accepted now that dark matter strongly effects the orbit of the sun around the galactic center, is it still thought that it "bobs" up and down about four times each orbit due to the concentration of matter in the galactic plane? $\endgroup$ – Jack R. Woods Mar 25 '16 at 0:26
  • $\begingroup$ @JackR.Woods Actually it doesn't and it isn't. There isn't thought to be a huge amount of dark matter interior to the Sun's orbit and no concentration of dark matter in the plane. My recollection is it speeds up the Sun in its orbit by a few tens of km/s (out of 230 km/s). The Sun executes vertical oscillations with a 70 million year period. There are also thought to be radial oscillations of a similar size with a 150 million year cycle. $\endgroup$ – Rob Jeffries Mar 25 '16 at 0:40
  • $\begingroup$ @JackR.Woods - The dark matter halo (if it exists) should be close to a spherically symmetric distribution of mass. This most certainly does change the period, but it cannot make stars "bob up and down." That is the work of the spiral arms. $\endgroup$ – David Hammen Mar 25 '16 at 0:40

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