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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.
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.
Potential is expressed as gravity times distance, m 2 ·s −2. Travelling one metre in the direction of a gravity vector of strength 1 m·s −2 will increase your potential by 1 m 2 ·s −2 . Again employing G as a multiplier, the units can be changed to joules per kilogram of attracted mass.
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.
His answer came in his law of universal gravitation, which states that the force between a mass M and another mass m is given by the formula =, where r is the distance between the masses and G is the gravitational constant. Given this force law and his equations of motion, Newton was able to show that two point masses attracting each other ...
A naive application of Newtonian gravity can yield exactly half this value, where the light ray is assumed as a massed particle and scattered by the gravitational potential well. This approximation is good when 4 G M / c 2 b {\displaystyle 4GM/c^{2}b} is small.
The metric tensor is a central object in general relativity that describes the local geometry of spacetime (as a result of solving the Einstein field equations). Using the weak-field approximation , the metric tensor can also be thought of as representing the 'gravitational potential'.
In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of Earth's gravity, on or near its surface, by means of a mathematical model. The most common theoretical model is a rotating Earth ellipsoid of revolution (i.e., a spheroid ).
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