I was thinking that the sun must orbit something within our spiral arm in the Milky Way, or be affected by other astronomical bodies - surely not just the supermassive black hole centre.
I have looked at some information and they say that the sun has a sine wave-like movement as it orbits the galactic centre. But what is causing this movement? And what sort of size or density would an object need to be to tug on our solar system uniformly? As I imagine the galaxy is like a soup, with everything churning around itself - still with a common centre (Galactic Centre.)
I'm looking at it in this way: There are black holes between us and the one at the centre which I would assume have enough gravitational energy to affect our star - if not have our star orbit one of them. Is that correct?
Answer
The Sun orbits in the gravitational potential of the entire Galaxy, not just the black hole at the centre (which is negligble actually - it has a mass of $4\times 10^{6}M_{\odot}$ compared to the rest of the mass inside the solar orbit, which is of order $10^{11}M_{\odot}$) or the few stars that are closest to us.
There are sufficient separate stars, gas, dust etc. to ensure that the "granularity" in the potential is reasonably small and so the approximation that the Sun moves in a smooth gravitational field is a very good one, unless it comes very close to another body (in which case the $r^{-2}$ influence of gravity comes to the fore).
The reason that the Sun executes a sinusoidal path up and down through the galactic disk, is because the galaxy has... a disc. i.e. The gravitational potential is not spherically symmetric and to a first approximation, the Sun executes a pseudo-simple harmonic motion, with a restoring force set by the gradient of the potential due to a planar disc.
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