Gary Kolling, a 44 year old male from the Internet asks on July 24, 1999,What Satellite Galaxy is moving fastest toward the Galactic center? What Satellite Galaxy is moving fastest away from the Galactic center? What "arm" of the Galaxy is closest to the Galactic center? Would it be Perseus?
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The criteria for "satellite" galaxy of the Milky Way are somewhat arbitrary. Certainly the large and small Magellanic clouds are considered to fit into this category, but there are numerous tiny dwarf spheroidal galaxies in the Local Cluster at various distances, and some of these could be considered as satellite galaxies as well. To really map their motion requires that we know both their velocity towards or away from us (the so-called radial velocity), but also their sideways or "proper" motion in the sky. This last cannot as yet be measured because of the positional shift of the galaxy (or any galaxy as yet) in the sky over time is much too small to be measured with existing techniques. Eventually, techniques linking radio telescopes together over substantial distances in the solar system will give us this key, and then we can start mapping the full three-dimensional motion over time in this and other galactic clusters.
Your question about distances of spiral arms to the center of the Milky Way, is also difficult to answer. We obviously know a great deal about the structure of several spiral arms in our section of the galaxy, but when we trace these structures back towards the nucleus, they become obscured in visible light because of dust. They are best mapped in radio wavelengths, but the resolution is really not such as to permit an unambiguous answer to your question. You must remember that only a few years ago, it became the generally accepted viewpoint that our galaxy is actually a barred spiral and not a regular spiral -- this shows the uncertainty of mapping through lots of obscuration.
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