How Many Feet Is 10 Kilometers – The radius of the Earth (noted as R🜨 or R E } ) is the distance from the center of the Earth to a point on or near its surface. The Earth’s sphere is roughly the shape of the Earth, with a radius ranging from a maximum of nearly 6,378 km (3,963 miles) (equatorial radius, point a) to a minimum of nearly 6,357 km (3,950 miles) (polar radius , period). ).
The nominal radius of the Earth is sometimes used as a unit of measurement in astronomy and geophysics, recommended by the International Astronomical Union as the equatorial value.
How Many Feet Is 10 Kilometers
The global average is generally considered to be 6,371 kilometers (3,959 miles) with a variation of 0.3% (±10 km) for the following reasons. The International Union of Geodesy and Geophysics (IUGG) provides three reference values: mean radius (R)
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) of three radii measured at two equators and one pole; valid radius, which is the radius of a sphere with the same surface (R
); and the radius of the volume, which is the radius of the sphere with the same volume as the ellipse (R
Other ways to determine and measure the radius of the Earth involve the radius of curvature. Some definitions yield values that lie outside the range between the polar and equatorial radii because they include local or topographic terrain or because they depend on abstract geometric considerations.
A scale diagram of the oblaess of the IERS 2003 reference ellipsoid, with north on top. The clear sky area is a circle. The outer edge of the dark blue line is an ellipse with the same minor axis as the circle and the same eccentricity as the Earth. The red line represents the Karman line at 100 km (62 miles) above sea level, while the yellow area represents the height of the ISS in low Earth orbit.
Plane And Solid Geometry With Answers
The Earth’s rotation, changes in internal density and external tidal forces cause its shape to systematically deviate from a perfect sphere.
Local topography increases the variance, resulting in a surface of deep complexity. Our description of the Earth’s surface must be simpler than it actually is to be manipulated. So we create models to simulate the features of the Earth’s surface, based mainly on the simplest model that fits the need.
Each of the commonly used models involves some concept of geometric rays. Strictly speaking, a sphere is the only solid with a radius, but the wider use of the term radius is common in many fields, including those dealing with models of the Earth. This is a partial list of models of the Earth’s surface, ranked from most accurate to most approximate:
In the case of geoids and ellipsoids, the fixed distance from each point of the model to the specified cter is called “Radius of the Earth” or “Radius of the Earth at that point”.
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It is also common to call each mean radius of a spherical model the “radius of the earth”. On the other hand, when considering the current surface of the Earth, it is not common to refer to “radius”, since there is usually no practical need. Instead, altitude above or below sea level is useful.
Regardless of model, all radii are between a minimum of about 6,357 km and an equatorial maximum of about 6,378 km (3,950 to 3,963 miles). Therefore, the Earth deviates from a perfect sphere by only one third of one percent, which supports the spherical model in most contexts and justifies the term “Radius of the Earth”. While specific values vary, the concepts in this article generalize to any major planet.
The rotation of a planet makes it roughly resemble an ellipse/flat sphere with bulges at the equator and flattening at the North and South Poles, so that the equatorial radius a is about aq larger than the pole radius b. . The oblique constant q is given by
Where ω is the angular frequency, G is the gravitational constant, and M is the mass of the planet.
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For Earth 1 / q ≈ 289, close to the measured inverse flatness 1 / f ≈ 298,257. Also, the equatorial bulge shows slow variations. The bulge has decreased, but since 1998, the bulge has increased, possibly due to a redistribution of ocean mass through the folds.
Variations in the density and thickness of the crust cause gravity to change on the surface and over time, so the mean sea level is different from the ellipsoid. This difference is the height of the geoid, positive above or outside the ellipsoid, negative below or inside. Geoid elevation variation below 110 m (360 ft) on Earth. Geoid heights can change abruptly due to earthquakes (such as the Sumatra-Andaman earthquake) or ice mass reduction (such as Greenland).
Not all distortions originate from Earth. Gravity from the Moon or the Sun can cause the Earth’s surface at a given point to change by millimeters over a period of almost 12 hours (see Earth tides).
Al-Biruni’s method of calculating the radius of the Earth (973-1048) simplifies the measurement of the circumference compared to taking measurements from two distant places.
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With local and transitive effects on surface height, the values determined below are based on a “general object” model, displayed as globally as accurately as possible to 5 m (16 ft) of height of the reference ellipse and within 100. m (330 ft) of mean sea level (ignoring geoid elevation).
Alternatively, the radius can be estimated from the curvature of the Earth at a point. Like a torus, the curvature at a point will be larger (tighter) in one direction (north-south on Earth) and smaller (flatter) in a perpendicular direction (east-west). The corresponding bending radius depends on the position and direction of the measurement from that point. Consequently, the distance to the true horizon at the equator is slightly shorter in the north-south direction than in the east-west direction.
In few, local variations in the previous terrain define a single “correct” radius. One can only apply an idealized model. Since the estimation of Eratosthes, many models have been created. Historically, these models are based on regional topography, giving the best reference ellipsoid for the surveyed area. As satellite remote control and especially the Global Positioning System became important, true global models were developed which, although not accurate for regional work, are more approximate with the whole Earth.
It is an idealized surface, and the measurements of the Earth used to calculate that surface have an uncertainty of ± 2 m at the equator and at the poles.
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Additional differences caused by topographic changes in specific locations can be significant. When determining the position of an observable, the use of more precise values for the WGS-84 radius may not give a corresponding improvement in accuracy.
The value for the equatorial radius is specified to the nearest 0.1 m in WGS-84. The value for the pole radius in this section has been rounded to the nearest 0.1 m, which is expected to be adequate for most uses. Refer to the WGS-84 ellipsoid if a more precise value for its polar radius is needed.
The three different radii are a function of the Earth’s latitude. R is the geological radius; M is the radius of curvature along the meridian; and N is the vertical radius of curvature before.
The geographic radius is the distance from the center of the Earth to a point on the spherical surface at geodetic latitude φ:
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The polar radius on the ellipsoid coincides with the equatorial and polar radii. They are the vertices of the ellipse and coincide with the minimum and maximum curvature.
Where e is the electricity of the earth. This is the radius that Eratosthes measured in his arc measure.
If one point is due east of the other, one will find an approximate east-west bend.
The vertical elemental radius of curvature of the Earth, also known as the horizontal radius of curvature of the Earth, is defined perpendicularly (orthogonally) to M at the geodetic latitude φ.
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N can also be explained geometrically as the normal distance from the ellipsoidal surface to the polar axis.
The radius of a parallelogram is given by p = N cos ( φ ).
N = N| N| }} is the unit perpendicular to the surface at r , and since ∂ r ∂ φ }} and ∂ r ∂ λ }} are tangent to the surface,
The first and second rays of curvature correspond to the meridians and the first longitudinal rays of curvature of the Earth.
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Geometrically, the second basic form gives the distance from r + d r to the plane tangent to r .
The azimuthal radius of curvature of the Earth, along the normal cross-section of the Earth at azimuth (measured clockwise from north) α and at latitude φ, is derived from Euler’s curvature formula as following:
Where K is the Gaussian curvature, K = κ 1 κ 2 = det B det A , kappa _=}} .
The Earth can be modeled as a sphere in many ways. This section describes common modes. The different radii are obtained here using the notation and opacity noted above for the Earth as derived from the WGS-84 ellipsoid;
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A sphere is a rough approximation of the sphere itself, an approximation of the geoid, the units here are given in kilometers, not the appropriate millimeter resolution for
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