Abstract
In this chapter some aspects of Newtonian gravitational theory are recalled. This theory initially postulates the gravitational force between two mass points as an action-at-a-distance. Subsequently, the gravitational force is extended to the case in which matter is continuously distributed in a bounded region of space. This theory, which still satisfies the Galilean principle of relativity, has been widely developed and its forecasts experimentally confirmed.
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- 1.
The mass contained in a sphere \(C_r\) of radius r is
$$ \int _{C_{r}}\varrho \, dv= \int _{0}^{2\pi }\, d\varphi \int _{0}^{\theta } d\theta \int _0^r\xi ^2\varrho , d\xi . $$when spherical coordinates \((r,\theta ,\varphi )\) are adopted.
- 2.
For a historical account of the equilibrium configuration of a rotating fluid, see [79].
- 3.
An interesting overview of the above problems can be found in [106].
- 4.
All the calculations of this section can be found in the notebook Geometry.nb.
- 5.
See the notebook Geometry.nb.
- 6.
See, for instance, [143].
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Romano, A., Mango Furnari, M. (2019). Newtonian Gravitation. In: The Physical and Mathematical Foundations of the Theory of Relativity. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-27237-1_6
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DOI: https://doi.org/10.1007/978-3-030-27237-1_6
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-27236-4
Online ISBN: 978-3-030-27237-1
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