Calculate the gravitational field of a object

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To calculate the gravitational field of an object, such as a black hole, the formula used is \vec{g} = \frac{GM_1}{r^2} \hat{r}, which incorporates the object's mass and distance from the center. For non-spherical mass distributions, it's necessary to integrate this equation by replacing mass with small elements (dm) and relating these to the object's geometry through density. The principle of superposition is crucial, as it allows for the summation of the gravitational fields generated by each dm. Clarification on the specific geometry or density function can lead to a more tailored calculation. Understanding these principles is essential for accurately determining gravitational fields in complex scenarios.
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how do you calculate the gravitational field of a object e.g black hole (does it refer to its density and mass?
 
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<br /> \vec{g} = \frac {GM_1} {r^2} \hat{r}<br /> <br /> <br /> <br />



if the source mass has a non spherical distribution and you know its density(or density function) you will have to integrate the above equation replacing m by little dm's. Since you must integrate on a geometry, you have to somehow relate the dms to the geometry of the problem (big hint use density) To justify this action, the principle of superposition applies, since it is the superposition of all the little fields generated by the dm's that are added up in the integral. Sorry this answer is so vague, if you can make your question more specific, I can give you a more specific answer.
 
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Gza, do you intend that \vec{r} is a unit vector of the r direction?
 
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