Estimating Planetary Perihelion Precession
Estimating Planetary Perihelion Precession
Making the simplified approximation that planets move in an isotropic central potential and applying conservation of angular momentum, the planetary equations of motion reduce to one-dimensional and become exactly soluble. In this simple picture, the rate of perihelion precession can be calculated to arbitrary precision. Applying methods introduced in [1], we obtain a "big equation" for the precession rate of an orbit's perihelion. Using data from [2] and the pseudopotential formulation of [3, 4], we determine values for all unknowns (see Details).
Substituting all determined coefficients for all planets into the big equation, we finally obtain precession predictions, which closely match those of [3, 4]. From the convergence graphs we see that, except with Mercury, a zero-order or first-order approximation is usually accurate enough. After calculating classical precession, it becomes possible to calculate the tiny additional anomalous precession by applying the same formulas on a gravitational central potential derived from general relativity [5].
Planet symbols: Mercury , Venus , Earth , Mars , Jupiter , Saturn , Uranus , Neptune .
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