Abstract
In Chap. 3 we assumed the source of gravity is stationary and only one object moves. Now we are ready to study what happens when both objects are free to move. As we will see, there is a deep connection between the one-body and two-body problems that provides a powerful opportunity to understand binary star systems and extrasolar planets.
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- 1.
With help from Mathematica [1].
- 2.
In Chap. 14 we study spectral lines created by atoms and molecules in the outer layers of stars.
- 3.
Strictly speaking, we measure angles on the spherical sky. If the angular extent of a system is small, we can project onto a plane tangent to the sphere to obtain Euclidean coordinates without making a significant error.
- 4.
Recall from Sect. 4.1.4 that we can determine e from the shape of the velocity curves.
- 5.
By convention, planets are named by appending letters starting with “b” to the name of the star. For example, HD 209458b is a planet orbiting the star HD 209458.
- 6.
We follow common practice and quote planet densities in CGS rather than MKS units because densities are of order unity in g cm−3. For example, water has a density of 1 g cm−3 at standard temperature and pressure on Earth, while rocks and metals have densities of several g cm−3. Earth’s average density is about 5.5 g cm−3.
- 7.
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Keeton, C. (2014). Gravitational Two-Body Problem. In: Principles of Astrophysics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9236-8_4
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