On the Motion of Free Material Test Particles in Arbitrary Spatial Flows

TL;DR

This paper presents a straightforward vector calculus method to analyze the motion of free particles in arbitrary flows, aiding understanding in gravitational and rotating systems for engineers and non-specialists.

Contribution

It introduces an accessible approach for analyzing particle motion in complex flows, applicable to gravitational and rotating frame problems, including the two-body gravitational problem.

Findings

Applicable to rotating and accelerating frames

Useful for gravitational problems with spherical symmetry

Helps determine flow directions in two-body systems

Abstract

We show how the motion of free material test particles in arbitrary spatial flows is easily determined within the context of ordinary vector calculus. This may be useful for everyone, including engineers and other non-specialists, when thinking about gravitational problems. It already has valid application to simple problems such as the problems of motion in rotating and accelerating frames and to the gravitational problem of the single spherically symmetric attractor. When applied to the two body gravitational problem, it may help us determine the actual direction of the flow.