Engineering topics

Cox, L. P.

Publications and source records attributed to Cox, L. P..

4 records

NASA NTRS1985

The range of validity of the two-body approximation in models of terrestrial planet accumulation. II - Gravitational cross sections and runaway accretion

The validity of the two-body approximation in calculating encounters between planetesimals has been evaluated as a function of the ratio of unperturbed planetesimal velocity (with respect to a circular orbit) to mutual escape velocity when their surfaces are in contact (V/V-sub-e). Impact rates as a function of this ratio are calculated to within about 20 percent by numerical integration of the equations of motion. It is found that when the ratio is greater than 0.4 the two-body approximation is a good one. Consequences of reducing the ratio to less than 0.02 are examined. Factors leading to an optimal size for growth of planetesimals from a swarm of given eccentricity and placing a limit on the extent of runaway accretion are derived.

Wetherill, G. W.↗

NASA NTRS1984

A numerical investigation of planetesimal collision trajectories with a Moon accumulating in Earth orbit

In the scenario of lunar origin in which the Moon is assumed to have accreted most of its mass while in orbit about the Earth, ismals on the accrea knowledge of the relative impact rates of heliocentric planetting Earth and Moon is essential for any attempt to establish dynamical constraints on lunar origin. Numerical integrations of the regularized equations of motion for four bodies (Sun, Earth, Moon, planetismal) were done. A planetismal impact trajectory was calculated by assuming that the planetismal has hit the surface of the Moon at an assumed location, traveling in an assumed direction, and with an assumed impact speed. Next, the equations of motion were numerically integrated backward in time in order to determine from where the planetismal has come. In this way those volumes in heliocentric orbital element space which contribute trajectories that directly impact the Moon.

Cox, L. P.↗

NASA NTRS1980

Numerical simulation of the final stages of terrestrial planet formation

Three representative numerical simulations of the growth of the terrestrial planets by accretion of large protoplanets are considered. The mass and relative-velocity distributions of the bodies are free to evolve simultaneously in response to close gravitational encounters and occasional collisions between bodies. The collisions between bodies arise therefore in a natural way and the assumption of expressions for the relative-velocity distribution and the gravitational collision cross section is unnecessary. These simulations indicate that the growth of bodies with final masses approaching those of Venus and earth is possible, at least for the case of a two-dimensional system

Cox, L. P.↗

NASA NTRS1978

A model for close encounters in the planetary problem

A model is proposed for single close encounters between two small masses, m1 and m2, which orbit a much larger mass, M. The main new feature of the model is the assumption of conic motion of the center of mass of m1 and m2 in the gravitational field of M. Comparisons of the model with the three-body equations of motion indicate that the model is a useful approximation for m1, m2 not exceeding 0.00001 M. The model is therefore applicable for encounters between bodies of the order of an earth mass or smaller in the presence of the sun. Comparisons are also made of outcomes obtained by the model with outcomes of numerical integration for a large variety of close encounters. The above comparisons reveal that for many purposes the model is an adequate approximation for encounters with an eccentricity of the hyperbolic orbit of m1 about m2 not less than 4.

Cox, L. P.↗