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These assumptions, although unrealistic, greatly simplify calculations. The Roche limit for a rigid spherical satellite is the distance, , from the primary at which the gravitational force on a test mass at the surface of the object is exactly equal to the tidal force pulling the mass away from the object: [3] [4]
A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction. For example, 3 is a square root of 9, since 3 2 = 9, and −3 is also a square root of 9, since (−3) 2 = 9.
Earth radius (denoted as R 🜨 or R E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of nearly 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).
The square root appearing above can be eliminated for such applications as ordering locations by distance in a database query. On the other hand, some methods for computing nearest neighbors, such as the vantage-point tree, require that the distance metric obey the triangle inequality, in which case the square root must be retained.
Decimal fractions like 0.3 and 25.12 are a special type of rational numbers since their denominator is a power of 10. For instance, 0.3 is equal to , and 25.12 is equal to . [20] Every rational number corresponds to a finite or a repeating decimal. [21] [c]
This is because the distance between Earth and the Sun is not fixed (it varies between 0.983 289 8912 and 1.016 710 3335 au) and, when Earth is closer to the Sun , the Sun's gravitational field is stronger and Earth is moving faster along its orbital path. As the metre is defined in terms of the second and the speed of light is constant for all ...
The yottametre (SI symbol: Ym) is a unit of length in the metric system equal to 10 24 meters. [55] To help compare different orders of magnitude, this section lists distances starting at 1 Ym (10 24 m or 105.702 million light-years). 1.2 Ym – 127 million light-years – distance to the closest observed gamma ray burst GRB 980425
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.