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Alternative derivation of the relativistic contribution to perihelic precession
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10.1119/1.3159611
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Am. J. Phys. 77, 890 (2009)
/content/aapt/journal/ajp/77/10/10.1119/1.3159611
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## Figures

Fig. 1.

Relativistic orbit in a Keplerian limit (solid line), as described by Eq. (24), compared to a corresponding Keplerian orbit (dashed line) [Eq. (13)]. The precession of the perihelion is one characteristic due to general relativity and is illustrated here for . The eccentricity is chosen to be for both the relativistic and Keplerian orbits. This characteristic is exaggerated by the choice of relativistic correction parameter for purposes of illustration. Precession is present for smaller (nonzero) reasonably chosen values of as well.

Fig. 2.

The effective potential in Eq. (32) derived from the Schwarzschild geometry (solid line) compared to that derived from Newtonian mechanics (dashed line). The vertical dotted lines identify the radii of the circular orbits, and , as calculated using the Schwarzschild geometry and Newtonian mechanics, respectively. The Schwarzschild geometry predicts a smaller radius for the circular orbit than that predicted by Newtonian mechanics [Eq. (33)]. The value is chosen for purposes of illustration.

/content/aapt/journal/ajp/77/10/10.1119/1.3159611
2009-10-01
2014-04-23

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