Influence of Earth's Gravitation on the Requirements of the Vertical Trajectory Rocket with Special Reference to Escape

Abstract

The problem of reaching extreme altitudes is basically one of overcoming the earth's gravitation. Therefore, when the earth's gravitation is analyzed with respect to its influence on a rocketpropelled vehicle in a vertical trajectory, a theoretical analysis of the problem of reaching extreme altitudes is readily obtained. Since such an analysis is not new, the first portion of the paper is a review of the fundamental dynamic considerations of the problem. The review includes showing how the effect of earth's gravity on the requirement of the long-range rockets can be evaluated by the concept of a gravitational velocity, or a minimum velocity that must be attained by the rocket to achieve its objective. An ideal rocket for minimum expenditure of energy would leave the earth with a speed equal to the gravitational velocity and coast to its objective. The paper considers the principal differences between the ideal and actual long-range rockets, inasmuch as it accounts for the additional energy required of the actual rocket due to the time for acceleration of such a rocket to a gravitational velocity of escape. It also accounts for the variation of earth's gravitational attraction upon the rocket overpowered as well as coasting flight. As a result of these considerations a table of correction factors is given which can be used with the ideal rocket equations to give approximate actual rocket results.