How to derive the formula for Gravitational Potential Energy?

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The formula for gravitational potential energy, -GMm/r, is derived using integral calculus to calculate the work needed to move an object from an infinite distance to a point r. The gravitational force is expressed as F_grav = -GMm/r², and the potential energy is found by integrating this force from infinity to r. Newton's law of gravitation is empirical and cannot be derived from other fundamental laws. The derivation highlights the relationship between gravitational force and potential energy. Understanding this derivation is essential for grasping the principles of gravitational interactions.
Tommy1995
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How did scientists derive the formula -GMm/r=Ep in order to calculate the amount of work required to move an object from an infinitely large point (or an extremely large distance as my textbook says) ?
 
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How did scientists derive the formula -GMm/r=Ep in order to calculate the amount of work required to move an object from an infinitely large point (or an extremely large distance as my textbook says) ?

Experimental observation and number fudging to find the constant of proportionality G.
 
Tommy1995 said:
How did scientists derive the formula -GMm/r=Ep

not "G"...
 
Tommy1995 said:
How did scientists derive the formula -GMm/r=Ep

They used integral calculus.

$$PE_{grav} = - \int^r_\infty {F_{grav} dr^\prime}
= - \int^r_\infty {\left( -\frac{GmM}{{r^\prime}^2} \right) dr^\prime}
= - \frac{GmM}{r}$$
 
Newton's law of graviation is emperical - it can't be derived from some other fundamental law or set of equations. This is the case with all the basic laws of physics - nature is the way it is.

If you want to read more about the history try here and related pages:

http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation
 
Thanks ya'll!
 

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