Gauss’s Law for Gravity - pgccphy.net

gauss s Law for Simpson, of Physical Sciences and EngineeringPrince George s Community CollegeDecember 6, 2006 Newton s Law of GravityNewton s law of Gravity gives the forceFbetween two point massesMandm, separated by a distancer:FDGMmr2;(1)whereGis the universal gravitational constant,6:67428 10 11m3kg 1s 2. By Newton s second law,force is related to acceleration byFDma:(2)Equating equations (1) and (2), we can solve for the accelerationadue to the Gravity of a point charge:aDgDGMr2:(3)Newton was able to show that the gravitational field due to a uniform sphere of mass is the same as if thesphere were a point mass located at the sphere s center of mass. (Newton invented the calculus in the process!)So, for example, we can use Equation (3) to find the acceleration due to Gravity at the surface of the sphericalEarth:gDGMeR2e;(4)whereMeis the mass of the Earth, andReis the radius of the Earth.

Gauss’s Law for Gravity D.G. Simpson, Ph.D. Department of Physical Sciences and Engineering Prince George’s Community College December 6, 2006

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