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During the first 0.05 s the ball drops one unit of distance (about 12 mm), by 0.10 s it has dropped at total of 4 units, by 0.15 s 9 units, and so on. Near the surface of the Earth, the acceleration due to gravity g = 9.807 m/s 2 ( metres per second squared , which might be thought of as "metres per second, per second"; or 32.18 ft/s 2 as "feet ...
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 equation for universal gravitation thus takes the form: =, where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.
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
Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula [2] [3] = = where: G is the universal gravitational constant (G ≈ 6.67 × 10 −11 m 3 ⋅kg −1 ⋅s −2 [4])
Since 2012, the AU is defined as 1.495 978 707 × 10 11 m exactly, and the equation can no longer be taken as holding precisely. The quantity GM —the product of the gravitational constant and the mass of a given astronomical body such as the Sun or Earth—is known as the standard gravitational parameter (also denoted μ).
A gravitational field is used to explain gravitational phenomena, such as the gravitational force field exerted on another massive body. It has dimension of acceleration (L/T 2 ) and it is measured in units of newtons per kilogram (N/kg) or, equivalently, in meters per second squared (m/s 2 ).
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.}