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These figures should be compared with the temperature and density of Earth's atmosphere plotted at NRLMSISE-00, which shows the air density dropping from 1200 g/m 3 at sea level to 0.125 g/m 3 at 70 km, a factor of 9600, indicating an average scale height of 70 / ln(9600) = 7.64 km, consistent with the indicated average air temperature over ...
Geopotential height differs from geometric height (as given by a tape measure) because Earth's gravity is not constant, varying markedly with altitude and latitude; thus, a 1-m geopotential height difference implies a different vertical distance in physical space: "the unit-mass must be lifted higher at the equator than at the pole, if the same ...
For example, gravity is 0.1% stronger in the northern United States than in the southern, so a level surface that has an orthometric height of 1000 meters in one place will be 1001 meters high in other places. In fact, dynamic height is the most appropriate height measure when working with the level of water over a large geographic area. [4]
The transformation from a reference frame 1 to a reference frame 2 can be described with three translations Δx, Δy, Δz, three rotations Rx, Ry, Rz and a scale parameter μ. The Helmert transformation (named after Friedrich Robert Helmert , 1843–1917) is a geometric transformation method within a three-dimensional space .
In the latter the equator is a single standard parallel and the parallel scale increases from k=1 to compensate the decrease in the meridian scale. For the Gall the parallel scale is reduced at the equator (to k=0.707) whilst the meridian scale is increased (to k=1.414). This gives rise to the gross distortion of shape in the Gall-Peters ...
The vertical exaggeration is given by: = where VS is the vertical scale and HS is the horizontal scale, both given as representative fractions.. For example, if 1 centimetre (0.39 in) vertically represents 200 metres (660 ft) and 1 centimetre (0.39 in) horizontally represents 4,000 metres (13,000 ft), the vertical exaggeration, 20×, is given by:
Height above mean sea level is a measure of a location's vertical distance (height, elevation or altitude) in reference to a vertical datum based on a historic mean sea level. In geodesy, it is formalized as orthometric height. The zero level varies in different countries due to different reference points and historic measurement periods.
On Earth the effect on gravity of elevation is 0.3086 mGal m −1 decrease when going up, minus the gravity of the Bouguer plate, giving the Bouguer gradient of 0.1967 mGal m −1. More generally, for a mass distribution with the density depending on one Cartesian coordinate z only, gravity for any z is 2π G times the difference in mass per ...