Laboratory frame of reference (wiki)
In physics, the laboratory frame of reference, or lab frame for short, is a frame of reference centered on the laboratory in which the experiment (either real or thought experiment) is done. This is the reference frame in which the laboratory is at rest. Also, this is usually the frame of reference in which measurements are made, since they are presumed (unless stated otherwise) to be made by laboratory instruments. An example of instruments in a lab frame, would be the particle detectors at the detection facility of a particle accelerator.
Center of momentum frame (wiki)
A center of momentum frame (or zero-momentum frame, or COM frame) of a system is any inertial frame in which the center of mass is at rest (has zero velocity). Note that the center of momentum of a system is not a location, but rather defines a particular inertial frame (a velocity and a direction). Thus "center of momentum" already means "center of momentum frame" and is a short form of this phrase. A special case of the center of momentum frame is the center of mass frame: an inertial frame in which the center of mass (which is a physical point) is at the origin at all times. In all COM frames, the center of mass is at rest, but it may not necessarily be at rest at the origin of the coordinate system.
In the centre of momentum frame, the total linear momentum of the system is zero. Also, the total energy of the system is the minimal energy as seen from all possible inertial reference frames. In relativity, COM frame exists for a massive system. In the COM frame the total energy of the system is the "rest energy", and this quantity (when divided by the factor c2) therefore gives the rest mass (positive invariant mass) of the system.
Systems which have energy but zero invariant mass (such as photons moving in a single direction, or equivalently, plane electromagnetic waves) do not have COM frames, because there is no frame which they have zero net momentum. Because of the invariance of the speed of light, such massless systems must travel at the speed of light in any frame, and therefore always possess a net momentum-magnitude which is equal to their energy divided by the speed of light: p = E/c.
Let us note that:
"A “frame of reference” is a standard relative to which motion and rest may be measured; any set of points or objects that are at rest relative to one another enables us, in principle, to describe the relative motions of bodies. A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces involved. A dynamical account of motion leads to the idea of an “inertial frame,” or a reference frame relative to which motions have distinguished dynamical properties. For that reason an inertial frame has to be understood as a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions. The laws of Newtonian dynamics provide a simple definition: an inertial frame is a reference-frame with a time-scale, relative to which the motion of a body not subject to forces is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions. It follows that, in an inertial frame, the center of mass of a system of bodies is always at rest or in uniform motion. It also follows that any other frame of reference moving uniformly relative to an inertial frame is also an inertial frame. For example, in Newtonian celestial mechanics, taking the “fixed stars” as a frame of reference, we can determine an (approximately) inertial frame whose center is the center of mass of the solar system; relative to this frame, every acceleration of every planet can be accounted for (approximately) as a gravitational interaction with some other planet in accord with Newton's laws of motion."
da http://plato.stanford.edu/entries/spacetime-iframes/
NOTA BENE: stiamo parlando di un riferimento inerziale, con un sistema di particelle in esso. Non ci devono essere azioni esterne altrimenti non siamo più in un sistema ienrziale.
In physics, the laboratory frame of reference, or lab frame for short, is a frame of reference centered on the laboratory in which the experiment (either real or thought experiment) is done. This is the reference frame in which the laboratory is at rest. Also, this is usually the frame of reference in which measurements are made, since they are presumed (unless stated otherwise) to be made by laboratory instruments. An example of instruments in a lab frame, would be the particle detectors at the detection facility of a particle accelerator.
Center of momentum frame (wiki)
A center of momentum frame (or zero-momentum frame, or COM frame) of a system is any inertial frame in which the center of mass is at rest (has zero velocity). Note that the center of momentum of a system is not a location, but rather defines a particular inertial frame (a velocity and a direction). Thus "center of momentum" already means "center of momentum frame" and is a short form of this phrase. A special case of the center of momentum frame is the center of mass frame: an inertial frame in which the center of mass (which is a physical point) is at the origin at all times. In all COM frames, the center of mass is at rest, but it may not necessarily be at rest at the origin of the coordinate system.
In the centre of momentum frame, the total linear momentum of the system is zero. Also, the total energy of the system is the minimal energy as seen from all possible inertial reference frames. In relativity, COM frame exists for a massive system. In the COM frame the total energy of the system is the "rest energy", and this quantity (when divided by the factor c2) therefore gives the rest mass (positive invariant mass) of the system.
Systems which have energy but zero invariant mass (such as photons moving in a single direction, or equivalently, plane electromagnetic waves) do not have COM frames, because there is no frame which they have zero net momentum. Because of the invariance of the speed of light, such massless systems must travel at the speed of light in any frame, and therefore always possess a net momentum-magnitude which is equal to their energy divided by the speed of light: p = E/c.
Let us note that:
"A “frame of reference” is a standard relative to which motion and rest may be measured; any set of points or objects that are at rest relative to one another enables us, in principle, to describe the relative motions of bodies. A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces involved. A dynamical account of motion leads to the idea of an “inertial frame,” or a reference frame relative to which motions have distinguished dynamical properties. For that reason an inertial frame has to be understood as a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions. The laws of Newtonian dynamics provide a simple definition: an inertial frame is a reference-frame with a time-scale, relative to which the motion of a body not subject to forces is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions. It follows that, in an inertial frame, the center of mass of a system of bodies is always at rest or in uniform motion. It also follows that any other frame of reference moving uniformly relative to an inertial frame is also an inertial frame. For example, in Newtonian celestial mechanics, taking the “fixed stars” as a frame of reference, we can determine an (approximately) inertial frame whose center is the center of mass of the solar system; relative to this frame, every acceleration of every planet can be accounted for (approximately) as a gravitational interaction with some other planet in accord with Newton's laws of motion."
da http://plato.stanford.edu/entries/spacetime-iframes/
NOTA BENE: stiamo parlando di un riferimento inerziale, con un sistema di particelle in esso. Non ci devono essere azioni esterne altrimenti non siamo più in un sistema ienrziale.
,
;
.
.
![r_{geos} =\sqrt[3] {\frac {G M T_{rot}^2} {4 \pi^2}} = 42.168 \, km](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uYMUJ5JOSdoL7tUd2x_krRR948M0GzgtW1bvQyG4VQZeNC4pI1IwjrMeC_JBZr1U0A-z11se7aAWcF3Kn7gzHlvKlg10lqPhNZ0pGSZSGzBcm2iprIymFr1UdbSpiyV8WCZ2JRqygGs_v5AZIEOA=s0-d)
