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Earth is rounded into an ellipsoid with a circumference of about 40,000 km. It is the densest planet in the Solar System. Of the four rocky planets, it is the largest and most massive. Earth is about eight light-minutes away from the Sun and orbits it, taking a year (about 365.25 days) to complete one revolution.
g h is the gravitational acceleration at height h above sea level. R e is the Earth's mean radius. g 0 is the standard gravitational acceleration. The formula treats the Earth as a perfect sphere with a radially symmetric distribution of mass; a more accurate mathematical treatment is discussed below.
R E is central body's equatorial radius (6 378 137 m for Earth), ω E is the central body's rotation rate ( 7.292 115 × 10 −5 rad/s for Earth), GM E is the product of the universal constant of gravitation and the central body's mass ( 3.986 004 418 × 10 14 m 3 /s 2 for Earth).
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [2] [3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2), [4] depending on altitude, latitude, and longitude.
For astronomical bodies other than Earth, and for short distances of fall at other than "ground" level, g in the above equations may be replaced by (+) where G is the gravitational constant, M is the mass of the astronomical body, m is the mass of the falling body, and r is the radius from the falling object to the center of the astronomical body.
Among them is the Balcony Station, the highest weather station on the planet, located at about 8,430 meters (27,657 feet) above sea level. Set up by climate scientists Tom Matthews and Baker Perry in 2019, this station is positioned just below the summit of Everest, which is the highest point on Earth.
The standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be expressed as G ( m 1 + m 2 ) , or as GM when one body is much larger than the other: μ = G ( M + m ) ≈ G M . {\displaystyle \mu =G(M+m)\approx GM.}
The geoid undulation (also known as geoid height or geoid anomaly), N, is the height of the geoid relative to a given ellipsoid of reference. N = h − H {\displaystyle N=h-H} The undulation is not standardized, as different countries use different mean sea levels as reference, but most commonly refers to the EGM96 geoid.