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Gravitational Fields

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Formula for calculating the gravitational field created by a massive object.

Andrew Zimmerman Jones

Gravity Index

Newton's law can be restated into the format of a gravitational field, which can prove to be a useful means of looking at the situation. Instead of calculating the forces between two objects every time, we instead say that an object with mass creates a gravitational field around it. The gravitational field is defined as the force of gravity at a given point divided by the mass of an object at that point, as depicted to the right.

You'll notice that here both g and Fg have arrows above them, denoting their vector nature. The source mass M is now capitalized. The r at the end of the rightmost two formulas has a carat (^) above it, which means that it is a unit vector in the direction from the source point of the mass M. Since the vector points away from the source while the force (and field) are directed toward the source, a negative is introduced to make the vectors point in the correct direction.

This equation depicts a vector field around M which is always directed toward it, with a value equal to an object's gravitational acceleration within the field. The units of the gravitational field are m/s2.

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