Abstract
There is much to say about galaxies, but with our current theme we focus on motion and mass. The stars in a galaxy are always moving, but the sheer number of them means the galaxy’s overall mass distribution hardly changes with time. To a good approximation we can take the mass distribution to be static, which makes the gravitational force static and effectively puts us back in the realm of the one-body problem. The difference now is that the mass distribution is spatially extended, which affects the gravitational force and therefore the motion.
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- 1.
See the book by Sparke and Gallagher [1] for a more thorough discussion of galaxies.
- 2.
Unless the galaxy is undergoing some dramatic event such as a collision. We will examine interactions between galaxies in Sect. 8.3.
- 3.
We can write this as an indefinite integral because Φ is only defined up to an arbitrary constant.
- 4.
Evidence for “missing mass” appeared as early as the 1930s, from an analysis of motions in the Coma cluster of galaxies by Fritz Zwicky [6] and an analysis of vertical motions of stars in the Milky Way by Jan Oort [7]. Those analyses were hindered, especially by poor knowledge of mass-to-light ratios, but notice that they too were based on the motion → mass principle.
- 5.
We will study gas in a gravitational potential in Sect. 12.2.
- 6.
“Cold” refers to the fact that the particles are slow compared with the speed of light. As we will see in Chap. 12, the temperature of a gas is related to the typical speed of its constituent particles.
- 7.
With one important modification: dark energy.
- 8.
This question is inspired in part by a problem in the book by Carroll and Ostlie [27].
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Keeton, C. (2014). Extended Mass Distributions: Spiral Galaxies. In: Principles of Astrophysics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9236-8_7
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