"Gauss's theorem can be established as follows. consider an attracting particle of mass m at the point P, and let a cone of small solid angle ω be generated by radii through P. This cone cuts the surface at the points Q(adsbygoogle = window.adsbygoogle || []).push({}); _{1}, Q_{2}, ... taken in order from P; the parts of the surface cut off by the cone at these points are S_{1}, S_{2}, ... and the outward-drawn normals are denoted n_{1}, n_{2}, ...

Now if P lies outside Σ (region of masses, each at points Q_{1}, Q_{2}, ...), the cone will cut S an even number of times, and the signs will be plus and minus alternately, so that the total normal force across S_{1}, S_{2}, ... will be zero. On the other hand, if P lies inside Σ, the cone will cut S an odd number of times, the sign being minus and plus alternately, so that the total normal forces across S_{1}, S_{2}, ... will be -mω."

Source: Spherical harmonic T.M.Macrobert

Help with this text! I don't understand the second paragraph as to why the cone will cut S an odd number of times, the sign being minus and plus alternately when P lies inside Σ vs when P lies outside Σ. I know the cone is just a mathematical object but I can't follow the author thought process here. How did he use the cone to cut the surface at Q_{1}, Q_{2}, ... ? Why will the normal force across S due to particle at P be zero when P is outside the mass but not inside the mass?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Gauss' law for gravity

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**