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The torque-free precession rate of an object with an axis of symmetry, such as a disk, spinning about an axis not aligned with that axis of symmetry can be calculated as follows: [1] = where ω p is the precession rate, ω s is the spin rate about the axis of symmetry, I s is the moment of inertia about the axis of symmetry, I p is moment ...
Larmor precession is important in nuclear magnetic resonance, magnetic resonance imaging, electron paramagnetic resonance, muon spin resonance, and neutron spin echo. It is also important for the alignment of cosmic dust grains, which is a cause of the polarization of starlight.
Mass–energy equivalence states that all objects having mass, or massive objects, have a corresponding intrinsic energy, even when they are stationary.In the rest frame of an object, where by definition it is motionless and so has no momentum, the mass and energy are equal or they differ only by a constant factor, the speed of light squared (c 2).
The special and general theories of relativity give three types of corrections to the Newtonian precession, of a gyroscope near a large mass such as the earth. They are: They are: Thomas precession a special relativistic correction accounting for the observer being in a rotating non-inertial frame.
This third force causes the particle's elliptical orbit to precess (cyan orbit) in the direction of its rotation; this effect has been measured in Mercury, Venus and Earth. The yellow dot within the orbits represents the center of attraction, such as the Sun. The orbital precession rate may be derived using this radial effective potential V.
Frame-dragging is an effect on spacetime, predicted by Albert Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses causing that field may be non-static — rotating, for instance.
Precession causes the stars to change their longitude slightly each year, so the sidereal year is longer than the tropical year. Using observations of the equinoxes and solstices, Hipparchus found that the length of the tropical year was 365+1/4−1/300 days, or 365.24667 days (Evans 1998, p. 209).
Non-spherical mass effects are caused by the application of external potential(s): the centrifugal potential of spinning bodies causes flattening between the poles and the gravity of a nearby mass raises tidal bulges. Rotational and net tidal bulges create gravitational quadrupole fields ( 1 / r 3 ) that lead to orbital precession.