# Are there reliable sources regarding the motion of the Solar System through the Milky Way?

So, I've been working on a Newtonian mechanics Solar System simulator. I want to explore what happens when the additional forces due to the other components of the Milky Way are included. My understanding is the the velocity of the Solar System with respect to the Galactic centre is said to be quite substantial ($\sim 800 {\rm km}\,{\rm hr}^{-1}$), so it isn't clear to me these effects can be totally ignored while still getting accurate results. However, this seems to be one of those topics where search engines choke on all the low-quality sources out there.

Can anyone help me out on:

1. How to best search for scholarly sources (i.e. cite primary references, etc.) on astronomical topics in general? For medical topics there is this great resource called pubmed; is there anything equivalent for astronomy/physics?

2. Any good sources on this specific topic (approximating the effect of the Milky Way in a Solar System simulation)?

PS: I don't expect to be able to compute the actual forces between $10^5$ stars or anything like that, rather just get some approximation like place a sphere with mass $M$ at distance $({\rm d}x,{\rm d}y,{\rm d}z)$ from the Solar System barycenter.

Edit:

First, regarding the main topic of this question (how to best find good resources on astronomy topics) I should mention that was suggested in the comments, ADS is a useful tool.

The other theme of the comments was that concerns about inaccuracies due to ignoring the effect of the Milky Way were unjustified. Along those lines, it looks like such effects are detectable but are not currently included in the most common models:

Analysis of VLBI observations relative to ICRF2 indicates a secular drift in aberration consistent with the solar system orbiting about the center of the galaxy [12]. This effect is not modeled in ICRF2 or in the ephemerides DE430 and DE431. It may need to be taken into account in future ephemerides as measurement accuracies improve.

The Planetary and Lunar Ephemerides DE430 and DE431. William M. Folkner, James G. Williams, Dale H. Boggs, Ryan S. Park, and Petr Kuchynka. IPN Progress Report 42-196. February 15, 2014. PDF link.

Another interesting thing is that there is apparently an unexpected vertical component of this motion:

The solar acceleration obtained by VLBI observations. M.H. Xu, G.L. Wang, and M. Zhao. A&A 544, A135 (2012). DOI: 10.1051/0004-6361/201219593

• Why are you bothered by the fact that other objects in the rest of the universe are moving fast relative to yourself? Are there any velocity dependent terms in Newton's equations? Unless you are simulating Oort cloud objects and the passage of other stars within a couple of light years and your numerical integrators are among the best ever devised you don't have to worry about influences from outside the solar system. – CuriousOne Aug 5 '16 at 20:45
• @CuriousOne Actually I am just having fun with it right now, and doing nearly exactly what you describe (Placing Nibiru-type objects into orbits that enter the system and watching the results). However, eventually I want to get a simulation good enough to estimate the probability a comet/asteroid will impact the earth based on known coordinates/velocities. Can you attach some numbers (with references or calculations) to the sources of error you mention? – Livid Aug 5 '16 at 20:57
• 800 kph is only ~222 m/s and we are ~70,000 ly (~$6.6 \times 10^{20}$ m) from the galactic center, thus $\omega$ ~ $3.4 \times 10^{-19}$ rad/s. So sure, 800 kph sounds fast to you since you rarely move that fast relative to other objects on Earth but in the universe it's quite slow compared to many things (e.g., the Earth's transverse velocity relative to the sun is ~29 km/s). – honeste_vivere Aug 5 '16 at 21:03
• What "force" is "causing that motion"? Gravity is not a force. – CuriousOne Aug 5 '16 at 22:48
• ADS is the indexing service to use -- it has every paper ever published in English in astronomy or astrophysics, and a great deal beside that. Note though that its search is only exact word matching to author names, titles, and the abstract. No one will ever have a search engine as flexible as google (that's what a billion dollars and thousands of people can accomplish), so you shouldn't expect it. You can always try google scholar, but it's not curated and will return all sorts of irrelevant results too. – user10851 Aug 9 '16 at 22:32

You're likely having trouble searching because you've got the wrong keywords. 'Milky Way rotation curve' is likely to serve you much better.

I'd like to clear up an error in the question (that is repeated several times in the comments). The orbital speed of the Sun around the Galaxy is about $220\,{\rm km}\,{\rm s}^{-1}$. Kilometers per second.

As was pointed out in the comments, the large-scale galaxy has little effect on the Solar System:

• You could model the galaxy mass distribution as a crude halo + disk + bulge, or similar. Your Solar System would then orbit around in this potential, but internally very little would change; the tidal acceleration from the coarse-grained distribution is insignificant when compared to accelerations internal to the Solar System.
• You could try to model the solar neighbourhood in more detail, but putting together initial conditions that are (1) based in reality and (2) even close to dynamically stable will be a lot of work. Like a career's worth of work.
• You could try to model a small region of the interstellar medium around the Solar System. This is more feasible, and the velocity of the Sun (relative to the medium, which will also be orbiting in the Galaxy) is pretty important since what you'd be looking at in this case is features like the heliopause. This is no longer a Newtonian dynamics simulation, however. This becomes full blown hydrodynamics, including a solid model for the solar wind and the physics of the interstellar medium.

There's a reason that serious research on Solar System dynamics mostly models the Solar System as an isolated system... well, there are two actually. (1) It's very difficult to include external effects and (2) they aren't very important anyway.

• The Sun is also moving inwards and upwards at around 10 km/s. – Rob Jeffries Aug 10 '16 at 7:20
• Thanks, the question should read 800,000 km/hr as it does in the source. Also, after comparing my results to DE431 (which I assume can be used as a gold standard?), I suspect extra-solar system effects are the least of my problems. – Livid Aug 11 '16 at 15:28
• @Livid indeed. Numerical integration is easy, high-precision numerical integration of complicated systems is... not ;) – Kyle Oman Aug 11 '16 at 18:31