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The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them: [11] Diagram of two masses attracting one another = where F is the force between the masses; G is the Newtonian constant of gravitation (6.674 × 10 −11 m 3 ⋅kg −1 ⋅s −2);
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
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.
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n -body problem for details).
The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass. The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at 1 m·s −2 ...
One g is the force per unit mass due to gravity at the Earth's surface and is the standard gravity (symbol: g n), defined as 9.806 65 metres per second squared, [5] or equivalently 9.806 65 newtons of force per kilogram of mass. The unit definition does not vary with location—the g-force when standing on the Moon is almost exactly 1 ⁄ 6 that
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.
Gravity on the Earth's surface varies by around 0.7%, from 9.7639 m/s 2 on the Nevado Huascarán mountain in Peru to 9.8337 m/s 2 at the surface of the Arctic Ocean. [6] In large cities, it ranges from 9.7806 m/s 2 [ 7 ] in Kuala Lumpur , Mexico City , and Singapore to 9.825 m/s 2 in Oslo and Helsinki .