Inertial space
Encyclopedia
In physics, the expression inertial space refers to the background reference that is provided by the phenomenon of inertia
.
Inertia is opposition to change of velocity, that is: change of velocity with respect to the background, the background that all physical objects are embedded in. Accelerometers measure how hard an object is accelerating with respect to inertial space. More precisely, accelerometers measure the magnitude of the change of velocity with respect to inertial space.
The Inertial guidance systems that are used in navigation and in guidance of missiles work by detecting acceleration and rotation with respect to inertial space.
and acceleration
form a natural sequence. Position can be seen as the zeroth time derivative of position, velocity is the first time derivative of position, and acceleration is the second time derivative of position.
The scientific understanding of space and time is that there does not exist such a thing as measuring an object's position with respect to inertial space, and no such thing exists as measuring an object's velocity with respect to inertial space. It is the third in the sequence, acceleration with respect to the background, that is the first to be physically manifest.
, when suspended in such a way that no torque
acts on the gyroscope wheel, will remain pointing in the same direction with respect to inertial space. The spinning gyroscope is locked onto the direction of inertial space that the gyroscope happened to be directed in when it was spun up. Two gyroscopes that start out pointing in the same direction will remain aligned with respect to each other. Since both gyroscopes are locked onto the same inertial space, it is impossible for two spinning gyroscopes to drift with respect to each other.
pointed out an observation about double stars. The motion of two stars orbiting each other is planar, the two orbits of the stars of the system lie in a plane. In the case of sufficiently near double star systems, it can be seen from Earth whether the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the solar system. Schwarzschild pointed out that that was invariably seen: the direction of the angular momentum
of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar system. The logical inference is that just like gyroscopes, the angular momentum of all celestial bodies is angular momentum with respect to a universal inertial space.
For detecting rotation, gyroscopes and fiber optic ring interferometers are used. The operating principle of ring interferometers is called the Sagnac effect
A gyrocompass
, employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference. The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour.
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
.
Inertia is opposition to change of velocity, that is: change of velocity with respect to the background, the background that all physical objects are embedded in. Accelerometers measure how hard an object is accelerating with respect to inertial space. More precisely, accelerometers measure the magnitude of the change of velocity with respect to inertial space.
The Inertial guidance systems that are used in navigation and in guidance of missiles work by detecting acceleration and rotation with respect to inertial space.
Derivatives with respect to time
Position, velocityVelocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
and acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
form a natural sequence. Position can be seen as the zeroth time derivative of position, velocity is the first time derivative of position, and acceleration is the second time derivative of position.
The scientific understanding of space and time is that there does not exist such a thing as measuring an object's position with respect to inertial space, and no such thing exists as measuring an object's velocity with respect to inertial space. It is the third in the sequence, acceleration with respect to the background, that is the first to be physically manifest.
Gyroscopes
A spinning gyroscopeGyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...
, when suspended in such a way that no torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
acts on the gyroscope wheel, will remain pointing in the same direction with respect to inertial space. The spinning gyroscope is locked onto the direction of inertial space that the gyroscope happened to be directed in when it was spun up. Two gyroscopes that start out pointing in the same direction will remain aligned with respect to each other. Since both gyroscopes are locked onto the same inertial space, it is impossible for two spinning gyroscopes to drift with respect to each other.
Astronomy
In 1899 the astronomer Karl SchwarzschildKarl Schwarzschild
Karl Schwarzschild was a German physicist. He is also the father of astrophysicist Martin Schwarzschild.He is best known for providing the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he accomplished...
pointed out an observation about double stars. The motion of two stars orbiting each other is planar, the two orbits of the stars of the system lie in a plane. In the case of sufficiently near double star systems, it can be seen from Earth whether the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the solar system. Schwarzschild pointed out that that was invariably seen: the direction of the angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar system. The logical inference is that just like gyroscopes, the angular momentum of all celestial bodies is angular momentum with respect to a universal inertial space.
Applications in navigation
Inertial guidance systems detect acceleration with respect to inertial space, and with those data it is possible to calculate the current velocity and position with respect to the velocity and position at the moment the acceleratometers started registering data.For detecting rotation, gyroscopes and fiber optic ring interferometers are used. The operating principle of ring interferometers is called the Sagnac effect
Sagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
A gyrocompass
Gyrocompass
A gyrocompass is a type of non-magnetic compass which bases on a fast-spinning disc and rotation of our planet to automatically find geographical direction...
, employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference. The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour.