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For example, for an observer B with a height of h B =1.70 m standing on the ground, the horizon is D B =4.65 km away. For a tower with a height of h L =100 m, the horizon distance is D L =35.7 km. Thus an observer on a beach can see the top of the tower as long as it is not more than D BL =40.35 km away.
The height of the elevated point plus the Earth radius form its hypotenuse. If both the eyes and the object are raised above the reference plane, there are two right-angled triangles. If both the eyes and the object are raised above the reference plane, there are two right-angled triangles.
This reduces the shadow zone, but causes errors in distance and height measuring. In practice, to find , one must be using a value of 8.5·10 3 km for the effective Earth's radius (4/3 of it), instead of the real one. [2] So the equation becomes:
If the height h is given in feet, and the distance d in statute miles, d ≈ 1.23 ⋅ h {\displaystyle d\approx 1.23\cdot {\sqrt {h}}} R is the radius of the Earth, h is the height of the ground station, H is the height of the air station d is the line of sight distance
Range (r) = approximate height of object (h) × (1000 ÷ aperture in milliradians (a)) r = h(1000/a) → where r and h are identical units, and a is in milliradians. r = h/a → where r and h are identical units, and a is in radians. The above formula functions for any system of linear measure provided r and h are calculated with the same units.
The comoving distance from an observer to a distant object (e.g. galaxy) can be computed by the following formula (derived using the Friedmann–Lemaître–Robertson–Walker metric): = ′ (′) where a(t′) is the scale factor, t e is the time of emission of the photons detected by the observer, t is the present time, and c is the speed of ...
On the chart he marks the assumed position AP and draws a line in the direction of the azimuth Zn. He then measures the intercept distance along this azimuth line, towards the body if Ho>Hc and away from it if Ho<Hc. At this new point he draws a perpendicular to the azimuth line and that is the line of position LOP at the moment of the observation.
The equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides. [2] [3]: 14