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For objects likewise, the question of whether they can withstand the mechanical g-force without damage is the same for any type of g-force. For example, upward acceleration (e.g., increase of speed when going up or decrease of speed when going down) on Earth feels the same as being stationary on a celestial body with a higher surface gravity ...
For two pairwise interacting point particles, the gravitational potential energy is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): = = where is the displacement vector of the mass, is gravitational force acting on it and denotes scalar product.
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.
For free bodies, the specific force is the cause of, and a measure of, the body's proper acceleration. The acceleration of an object free falling towards the earth depends on the reference frame (it disappears in the free-fall frame, also called the inertial frame), but any g-force "acceleration" will be present in all frames.
Nevertheless, he had the opportunity to estimate the order of magnitude of the constant when he surmised that "the mean density of the earth might be five or six times as great as the density of water", which is equivalent to a gravitational constant of the order: [14] G ≈ (6.7 ± 0.6) × 10 −11 m 3 ⋅kg −1 ⋅s −2
It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r 12 and m instead of m 2 and define the gravitational field g(r) as:
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Peak ground acceleration can be expressed in fractions of g (the standard acceleration due to Earth's gravity, equivalent to g-force) as either a decimal or percentage; in m/s 2 (1 g = 9.81 m/s 2); [7] or in multiples of Gal, where 1 Gal is equal to 0.01 m/s 2 (1 g = 981 Gal).