Transcription of Gauss’s Law for Gravity - pgccphy.net
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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. Substituting the known values ofGMeandRe, we findgD3:986005 1014m3s :378140 106m/2D9:80m s 2;(5)which is the familiar Gaussian Formulation of Newtonian GravityAn alternative formulation of Newtonian Gravity is gauss s Law for Gravity .
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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