Sample Lesson
Gerber’s Gravity
In 1859 the French astronomer LeVerrier announced, based on many years of careful observations and calculations, that the perihelion of the planet Mercury evidently precesses at a slightly faster rate than can be accounted for by Newtonian mechanics given the known distribution of material in the solar system. This discovery led to two different avenues of research. Some people began to search for unknown material in the solar system (possibly even a new planet) that would account for the anomaly in Mercury’s orbit within the context of Newton’s laws. Others considered possible ways of modifying or re-interpreting Newton’s law of gravitation so that it would give Mercury’s precession for the currently accepted distribution of matter.
At about this same time, theoretical physicists such as Gauss and Weber were investigating modifications of the Coulomb inverse-square law by introducing a velocity-dependent potential to represent the electromagnetic field, consistent with the finite propagation speed of changes in the field (i.e., the speed of electromagnetic waves). It was found that this same type of law, when applied to gravitation, predicted perihelion advance for the two-body problem on the same order of magnitude as actually observed for Mercury. It became a fairly popular activity in the 1890s for physicists to propose various gravitational potentials based on finite propagation speed in order to account for some or all of Mercury’s orbital precession. Oppenheim published a review of these proposals in 1895. The typical result of such proposals is a predicted non-Newtonian advance of orbital perihelia per revolution of kπm/(Lc2) where c is the posited speed of propagation, m is the Sun’s mass, L is the semi-latus rectum of the orbit, and k is a constant depending on the precise form of the assumed potential. Of course, by Kepler’s law, we can express the mass m of the Sun in terms of the semi-major axis “a” and the angular speed ω of an orbiting planet as m = a3ω2. The angular speed can be expressed in terms of the orbital period T (revolutions per second) as ω = 2π/T. In addition, we know from elementary geometry that the semi-latus rectum of an ellipse is L = a(1 – ε2) where ε is the eccentricity. Making these substitutions, the angular precession per orbit can be written in the form
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