We present here a calculation of the precession of the perihelion of Mercury due to the perturbations from the outer planets. The time-average effect of each planet is calculated by replacing that planet with a ring of linear mass density equal to the mass of the planet divided by the circumference of its orbit. The calculation is easier than examples found in many undergraduate theoretical mechanics books and yields results which are in excellent agreement with more advanced treatments. The perihelion precession is seen to result from the fact that the outer planets slightly change the radial period of oscillation from the simple harmonic period usually calculated for small displacements from equilibrium. This new radial period therefore no longer matches the orbital period and the orbit consequently does not exactly retrace itself. The general question of whether a given perturbation will cause the perihelion to advance or regress is shown to have the following answer: if a perturbing force is central and repulsive and also becomes stronger as the distance from the force center increases, the perihelion will advance. If the central perturbing force is attractive and also becomes stronger as the distance from the force center increases, the perihelion will regress.
Photometric and spectrophotometric observations have been made of the reflection nebulae NGC1435, NGC2068, NGC7023, and IC1287 in an attempt to detect continuous fluorescence by dust grains. Several effects of importance for observations of such faint objects are discussed, including instrumental light scattering, a photographic effect, and a time delay effect which can occur if the illuminating star is a spectrum variable. It is found that continuous fluorescence by interstellar grains is not likely to exist and that it cannot account for more than 10 percent of the total surface brightness of these reflection nebulae. No evidence of diffuse interstellar features is found in the spectra of these nebulae.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.