Equation of motion of an interstellar Bussard ramjet with radiation and mass losses

TL;DR

This paper derives analytical equations describing the motion of an interstellar Bussard ramjet considering radiation and mass losses, analyzing its behavior at various speeds including near the limit speed.

Contribution

It extends previous models by providing analytical parametric equations for the ramjet's motion with mass loss, covering relativistic and non-relativistic regimes.

Findings

Limit speed is more strongly reduced with mass loss.

Analytical equations for position, time, and proper time are derived.

Motion near the limit speed is characterized and analyzed.

Abstract

An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. In recent papers, it was shown that the relativistic equation of motion of an ideal ramjet and of a ramjet with radiation loss are analytical. When a mass loss appears, the limit speed of the ramjet is more strongly reduced. But, the parametric equations, in terms of the ramjet's speed, for the position of the ramjet in the inertial frame of the interstellar medium, the time in this frame, and the proper time indicated by the clocks on board the spaceship, can still be obtained in an analytical form. The non-relativistic motion and the motion near the limit speed are studied.