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The gravity g′ at depth d is given by g′ = g(1 − d/R) where g is acceleration due to gravity on the surface of the Earth, d is depth and R is the radius of the Earth. If the density decreased linearly with increasing radius from a density ρ 0 at the center to ρ 1 at the surface, then ρ ( r ) = ρ 0 − ( ρ 0 − ρ 1 ) r / R , and the ...
[3] [4] Although the symbol ɡ is sometimes used for standard gravity, ɡ (without a suffix) can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth (see Earth's gravity). The symbol ɡ should not be confused with G, the gravitational constant, or g, the symbol ...
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: = (+). For several objects in the Solar System, the value of μ is known to greater accuracy than either G or M. The SI unit of the standard gravitational parameter is m 3 ⋅s −2.
[3] [5] Use of the gal was deprecated by the standard ISO 80000-3:2006, now superseded. The gal is a derived unit, defined in terms of the centimeter–gram–second (CGS) base unit of length, the centimeter, and the second, which is the base unit of time in both the CGS and the modern SI system. In SI base units, 1 Gal is equal to 0.01 m/s 2.
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.
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.
The eotvos is a unit of acceleration divided by distance that was used in conjunction with the older centimetre–gram–second system of units (cgs). The eotvos is defined as 10 −9 galileos per centimetre. The symbol of the eotvos unit is E. [1] [2] In SI units or in cgs units, 1 eotvos = 10 −9 second −2. [3]
The exact numerical values for the coefficients deviate (somewhat) between different Earth models but for the lowest coefficients they all agree almost exactly. For the JGM-3 model the values are: μ = 398600.440 km 3 ⋅s −2 J 2 = 1.75553 × 10 10 km 5 ⋅s −2 J 3 = −2.61913 × 10 11 km 6 ⋅s −2