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A year has about 365.24 solar days but 366.24 sidereal days. Therefore, there is one fewer solar day per year than there are sidereal days, similar to an observation of the coin rotation paradox. [5] This makes a sidereal day approximately 365.24 / 366.24 times the length of the 24-hour solar day.
Thus, the sidereal day is shorter than the stellar day by about 8.4 ms. [37] Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes 56 seconds. This is a result of the Earth turning 1 additional rotation, relative to the celestial reference frame, as it orbits the Sun (so 366.24 rotations/y).
The daily arc path of an object on the celestial sphere, including the possible part below the horizon, has a length proportional to the cosine of the declination.Thus, the speed of the diurnal motion of a celestial object equals this cosine times 15° per hour, 15 arcminutes per minute, or 15 arcseconds per second.
A geostationary orbit can be achieved only at an altitude very close to 35,786 kilometres (22,236 miles) and directly above the equator. This equates to an orbital speed of 3.07 kilometres per second (1.91 miles per second) and an orbital period of 1,436 minutes, one sidereal day.
A sidereal day or stellar day is the span of time it takes for the Earth to make one entire rotation [5] with respect to the celestial background or a distant star (assumed to be fixed). [6] Measuring a day as such is used in astronomy. [6] A sidereal day is about 4 minutes less than a solar day of 24 hours (23 hours 56 minutes and 4.09 seconds ...
Angles in the hours ( h), minutes ( m), and seconds ( s) of time measure must be converted to decimal degrees or radians before calculations are performed. 1 h = 15°; 1 m = 15′; 1 s = 15″ Angles greater than 360° (2 π ) or less than 0° may need to be reduced to the range 0°−360° (0–2 π ) depending upon the particular calculating ...
The paradox is related to sidereal time: a sidereal day is the time Earth takes to rotate for a distant star to return to the same position in the sky, whereas a solar day is the time for the sun to return to the same position. A year has around 365.25 solar days, but 366.25 sidereal days to account for one revolution around the sun. [6]
Geosynchronous orbit (GSO): An orbit around the Earth with a period equal to one sidereal day, which is Earth's average rotational period of 23 hours, 56 minutes, 4.091 seconds. For a nearly circular orbit, this implies an altitude of approximately 35,786 kilometers (22,236 mi). The orbit's inclination and eccentricity may not necessarily be zero.