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The gravity field of a particle

1959/01/01 by Charles Galton Darwin · 431 citations
Mathematics · Physics and Astronomy · #Astronomy #Astrophysics #Circular orbit #Cosmology and Gravitation Theories #Elliptic orbit #Experimental and Theoretical Physics Studies #Gravitational field #Mathematical analysis #Mathematics #Orbit (dynamics) #Physics #RADIUS #Relativity and Gravitational Theory #Spiral (railway)

paper · doi:10.1098/rspa.1959.0015

published in Proceedings of the Royal Society of London A Mathematical and Physical Sciences 249(1257), 180-194 (Royal Society)

openalex publication_date 1959/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

Abstract Einstein’s equations for the orbits round an attracting point mass, here called the sun, are examined so as to see whether there are orbits which end in the sun, as there are in the corresponding case of electrical attraction when relativity is allowed for. With the measure of the radius as usually taken, it is shown that no hyperbolic orbit can have perihelion inside r = 3m, and an elliptic orbit cannot have perihelion inside r = 4m. Particles going inside these distances will be captured. Circular orbits are possible for any greater radius. If 3m < r < 4m the orbit is unstable; with one disturbance it falls into the sun, with the opposite it escapes in a spiral to infinity. If 4m < r < 6m, it is also unstable, either falling into the sun, or moving out to some aphelion at a greater radius before returning to its circle. Only if r > 6m is the orbit stable. A study is made of the travel of light rays. No light ray from infinity can escape capture unless its initial asymptotic distance is greater than 3√3 m. A field of stars surrounds the sun, and is viewed in a telescope pointed at the sun from a distance. If the field as seen is mapped as though in a plane through the sun, each star, in addition to its direct image, will show a series of faint ‘ghosts’ on both sides of the sun. The ghosts all lie just outside the distance 3√3 m. A few technical details are given about the orbits of the captured particles.

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