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Local reference frame

From Wikipedia, the free encyclopedia

In theoretical physics, a local reference frame (local frame) refers to a coordinate system or frame of reference that is only expected to function over a small region or a restricted region of space or spacetime.

The term is most often used in the context of the application of local inertial frames to small regions of a gravitational field. Although gravitational tidal forces will cause the background geometry to become noticeably non-Euclidean over larger regions, if we restrict ourselves to a sufficiently small region containing a cluster of objects falling together in an effectively uniform gravitational field, their physics can be described as the physics of that cluster in a space free from explicit background gravitational effects.

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  • Astronomy with MicroStation Local Coordinate Frame
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  • Coordinate systems and frames of reference

Transcription

Here we are going to learn about one of the simplest coordinate frames in observational astronomy and as any observation process involves it has two components the observer which we can see here and the observed which will be presented to the observer on a screen and that screen is going to be a sphere at the center of which the observer stands so everything in the universe the stars, galaxies, planets, nebulae ... everything would be projected onto the screen so the observer can see them this is called as a celestial sphere and we'll be presenting it with this circle now at no point of time the observer can see the whole celestial sphere He or she can see only half of it and that is limited by the horizon in the best possible conditions everything above the horizon will be seen but nothing below the horizon will be observable then we are going to established a few points the first point is called zenith. It is right above the observer on the celestial sphere and then let's establish north maybe we know how to find north using pole star or maybe we have a GPS or a compass or we ask the next person and once we know north we can also put down where is south, west and east then we are going to look at a star but as you know we're not going to look at the start directly but we are going to look at the projection of that star on our screen so here is the protection of the star as it appears on the celestial sphere and on the sphere we are going to draw an arc which will start at the zenith pass through the star and we will continue that till it meets the horizon so this is the arc over here and this arc is going to subtend an angle so this angle will be measured from the horizon to the star so this angle called as altitude represents how far up the star is in the sky but that alone is not sufficient to know the position of the star because there are going to be many celestial objects which are at the same height for example everthing on this circle will have the same angle of altitude and therefore to nail it down we need something more so let us have another angle here which will be measured from the north in the eastward direction till we hit this plane this is called as the azimuthal angle let us label it and these two angles together will be able to specify pinpoint anything in the sky so this is the local coordinate frame and it uses two angles - azimuth an angle measured from north towards the east til we hit the plane of the star and then we go up through the angle of altitude and we see the image of the star Let's recap the whole thing but this time in color So we start with the observer who is surrounded by the celestial sphere which is divided into two halves by the horizon. Only the upper half is seen In the upper half we have we have the highest point called as the zenith Then the north point is established from which east, west and south can be figured out and we start observing a star To do that we draw an arc passing through the zenith the star till it meets the horizon and then we measure the angle of altitude which represents how far up the sky is the star and then we measure another angle to pin it down which is major from north in the easterly direction till we hit the plane of the angle of altitude this is called as the azimuthal angle So together azimuth and altitude can pinpoint any location in the sky This is the local coordinate frame.

Equivalence principle

When constructing his general theory of relativity, Einstein made the following observation: a freely falling object in a gravitational field will not be able to detect the existence of the field by making local measurements ("a falling man feels no gravity"). Einstein was then able to complete his general theory by arguing that the physics of curved spacetime must reduce over small regions to the physics of simple inertial mechanics (in this case special relativity) for small freefalling regions.

Einstein referred to this as "the happiest idea of my life".

Laboratory frame

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.

See also


This page was last edited on 19 September 2023, at 15:27
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