THIS is one of a series of books from Harvard Observatory, all of which are compiled by specialists in their own particular sphere. The present volume gives up-to-date information about the bodies in the solar system, and as it is written in language which is almost entirely free from technicalities, it will appeal to a wide circle of readers. The author devotes some space to a consideration of origins and evolution, especially to the origin of lunar craters and to the origin of the planetary system. He favours the volcanic theory of the formation of craters on the moon, but admits that meteors may be responsible for the more recent craters-those with ray systems and some of the whiter ones, and also for many of the craterlets and crater pits. In dealing with the origin and evolution of the planets in Chapter 14, he examines the arguments for and against the planetesimal hypothesis of Chamberlin and Moulton and the tidal theory, and gives his opinion in favour of a fairly rapid condensation as more probable than an accretion ; but he admits that the choice between the two processes is not conclusive as the problems are complex. Earth, Moon and Planets By Fred L. Whipple. (Harvard Books on Astronomy.) Pp. vii + 293. (London: J. and A. Churchill, Ltd., 1946.) 18s.

Earth, Moon and Planets

We discuss the existence, location, and stability of the collinear equilibrium points of a generalized Hill problem with radiation of the primary (the Sun) and oblateness of the secondary (the planet), and present some remarkable fractals created as basins of attraction of Newton’s method applied for their computation in several cases of the parameters.

Collinear equilibrium points of Hill’s problem with radiation and oblateness and their fractal basins of attraction

This paper investigates the triangular libration points in the photogravitational restricted three-body problem of variable mass, in which both the attracting bodies are radiating as well and the infinitesimal body vary its mass with time according to Jeans' law. Firstly, applying the space-time transformation of Meshcherskii in the special case when q=1/2, k=0, n=1, the differential equations of motion of the problem are given. Secondly, in analogy to corresponding problem with constant mass, the positions of analogous triangular libration points are obtained, and the fact that these triangular libration points cease to be classical ones when alpha not equal 0, but turn to classical L (4) and L (5) naturally when alpha=0 is pointed out. Lastly, introducing the space-time inverse transformation of Meshcherskii, the linear stability of triangular libration points is tested when alpha > 0. It is seen that the motion around the triangular libration points become unstable in general when the problem with constant mass evolves into the problem with decreasing mass.

https://www.tpbin.com/Uploads/Subjects/af4990e7-9af8-40e5-bd78-fa647ef77803.pdf

On the triangular libration points in photogravitational restricted three-body problem with variable mass

Parametric evolution of periodic orbits in the restricted four-body problem with radiation pressure

The restricted three-body problem when the primaries are triaxial rigid bodies is considered and its basic dynamical features are studied. In particular, the equilibrium points are identified as well as their stability is determined in the special case when the Euler angles of rotational motion are accordingly $\theta_{i} = \psi_{i} = \pi/2$
 and $\varphi_{i} = \pi/2$
 , $i = 1, 2$
 . It is found that three unstable collinear equilibrium points exist and two triangular such points which may be stable. Special attention has also been paid to the study of simple symmetric periodic orbits and 31 families consisting of such orbits have been determined. It has been found that only one of these families consists entirely of unstable members while the remaining families contain stable parts indicating that other families bifurcate from them. Finally, using the grid-search technique a global solution in the space of initial conditions is obtained which comprises simple and of higher multiplicities symmetric periodic orbits as well as escape and collision orbits.

The planar restricted three-body problem when both primaries are triaxial rigid bodies: Equilibrium points and periodic orbits

We discuss a modern state of the three-body problem when an infinitesimal mass is effected not only by gravitation but also by light pressure from one (or both) of the primaries. This problem, called the photogravitational one, attracted much attention during the last ten years. Many aspects of the libration point locations and their stability for all values of radiation pressure and mass ratios are shown and discussed. A retrospective chronological review of the results is given.

A. L. Kunitsyn

Papers

The restricted photogravitational three-body problem: A modern state