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# What Is Inertial Space?

Jerry Morrison
Jerry Morrison

Inertial space is a frame of reference against which acceleration, or change in motion, is measured. Within an inertial frame of reference, objects experience constant relative motion and appear to be at rest in reference to each other; this defines the inertia of the space and serves as the background against which an object's change in motion is measured. Results of measurements made in one inertial frame can be converted to another by a straightforward mathematical calculation.

One property of an inertial frame is that the behavior of its objects is not subject to forces from outside that frame of reference. In Newtonian physics, the fixed stars were considered an inertial reference frame; it is now known that the stars are not fixed but have their own relative motions in galaxies, as do galaxies in larger group structures. Using the stars as if their relative motion defines an inertial space introduces little error.

A spinning gyroscope free from rotational acceleration will retain its orientation to inertial space; if it spins at a constant speed, it will continue to point in the same direction relative to the fixed stars. Changes in motion relative to the gyroscope's orientation can be measured and the data used to calculate velocity and position. This is the basis for an inertial navigation system (INS), which determines a vehicle's speed and location solely from reference to a position in inertial space.

An INS typically consists of motion sensors, such as gyroscopes and accelerometers, and a computer. The system is given its initial speed and location, then calculates future position and velocity in real time from sensor data. Changes in linear and angular acceleration are measured in reference to the gyroscope's alignment to inertial space. Beyond its initial conditions, an INS is completely self-contained and is not subject to jamming or other interference.

Accumulated error from measurement and calculation tend to make an INS less accurate over an extended time frame. This deficiency has been offset somewhat by more sophisticated devices such as the fiber optic gyroscope, which relies on the Sagnac effect. In this type of device, counter-rotating lasers produce an interference pattern from which changes in angular velocity relative to a position in inertial space can be calculated.

On ships, a gyrocompass is used to point to the geographic North Pole. The device uses the properties of a gyroscope to maintain a fixed orientation to inertial space and a pendulum to align it with Earth's rotational axis. As long as the gyroscope's rotor is parallel to Earth's axis, there is no torque, or angular resistance, from the Earth's rotation. Misalignment is self-correcting from forces due to planetary rotation.