The work of Tycho Brahe, the Danish astronomer, in making the most precise positioning of the planets of the day, the late sixteenth century, provided the foundation upon which the German astronomer Johannes Kepler developed his three laws of planetary motion.

Subsequently, the English mathematician, Sir Isaac Newton, showed that these laws were perfectly compatible with each planet possessing an acceleration towards the sun which was inversely proportional to the square of the distance from it. He was able to generalise this as being of the same nature as that experienced by objects in free fall close to the Earth's surface. As a result of this and other related observations, Newton deduced his three general laws of motion which were published in 1687 in his great work Philosophiae Naturalis Principia Mathematica.

The laws of motion of both Newton and Kepler are perfectly applicable today for whatever mechanical purpose may be pursued, including the space flight projects that have so far been undertaken. It is only in astronomical and cosmological aspects, in which motion at velocities approaching that of light, and/or over very long periods of time, that relativistic effects become significant and which may therefore affect their veracity.

This paper examines the applicability of both Newton's and Kepler's laws under these latter conditions. Because Kepler's laws are to do solely with motion due to gravity, the applicability of them will only be considered within the Gravitational Domain D₁. Newton's laws however, are to do with artificially induced motion as well as that due to gravitation, (free fall within the gravitational field), and therefore, his laws will be examined in both D₀, Pseudo-Euclidean Space-Time, and D₁, as appropriate. Because the three laws of Newton are the more general, they are considered first.

For a full understanding of the relativistic theory as presented in this paper, it is important to read the applicable sections of [2], [3], [6] and [7] first. Finally, to avoid multiple cross referencing, all equations referred to in the references will be repeated herein and their parameters re-defined.