Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The perihelion of Mercury advance calculated in Newton's theory   Three radii are associated with a circle: the "geodesic radius" R_1 which is
the distance from circle's center to its perimeter, the "circumferential
radius" R_2 which is the length of the perimeter divided by 2 pi and the
"curvature radius" R_3 which is circle's curvature radius in the Frenet sense.
In the flat Euclidean geometry it is R_1 = R_2 = R_3, but in a curved space
these three radii are different. I show that although Newton's dynamics uses
Euclidean geometry, its equations that describe circular motion in spherical
gravity always unambiguously refer to one particular radius of the three ---
geodesic, circumferential, or curvature. For example, the gravitational force
is given by F = -GMm/(R_2)^2, and the centrifugal force by mv^2/R_3. Building
on this, I derive a Newtonian formula for the perihelion of Mercury advance.

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The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: math
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph