Tidal effects in a spacecraft

Abstract

Within a vehicle in free fall, such as a spacecraft orbiting the Earth, everything appears as if there was no force of gravity: objects float and remain stationary with respect to the walls, a situation commonly described as “weightlessness.” In relativity, such a vehicle is considered an inertial reference system. In fact, this is not exactly true because of the non-uniformity of the gravitational field. Tidal effects and forces appear, and complicated motions are generated. This article examines these effects, limiting the use of complicated mathematical formalism in favor of physical reasoning. Two particular cases are treated: a spacecraft that rotates about its center of mass in sync with its orbit, so it always faces the Earth the same way, and a spacecraft that maintains the same orientation with respect to the fixed stars throughout its orbit. The static problem is solved by finding the tidal forces acting on an object at different positions within the spacecraft. The trajectories of objects released from various positions within the spacecraft are then calculated. Some concluding conceptual observations are given.