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A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them (the gravitational constant). Newton would need an accurate measure of this constant to prove his inverse-square law.
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.
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.
In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor). The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately 6.6743 × 10 −11 m 3 kg −1 s −2 ...
Accelerometers on the surface of the Earth measure a constant 9.8 m/s^2 even when they are not accelerating (that is, when they do not undergo coordinate acceleration). This is because accelerometers measure the proper acceleration produced by the g-force exerted by the ground (gravity acting alone never produces g-force or specific force).
For example, a stiff and compact object dropped from 1 m that impacts over a distance of 1 mm is subjected to a 1000 ɡ 0 deceleration. [citation needed] Jerk is the rate of change of acceleration. In SI units, jerk is expressed as m/s 3; it can also be expressed in standard gravity per second (ɡ 0 /s; 1 ɡ 0 /s ≈ 9.81 m/s 3). [citation needed]
Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, , between the bodies; thus: in = / for Newtonian gravity and in = / for electrostatic.