Gauss’s law for gravity stands as a cornerstone of physics, offering profound insights into the gravitational interactions between masses. Named after the eminent mathematician and physicist Carl Friedrich Gauss, this law serves as a complementary counterpart to Newton’s law of universal gravitation, enriching our understanding of gravitational phenomena.

Basic tenets:

Connection to Newton’s Law: Gauss’s law for gravity establishes a pivotal relationship with Newton’s law of universal gravitation, offering a complementary perspective on gravitational interactions.

Mathematical Equivalence: The law can be mathematically derived from Newton’s law of universal gravitation, which delineates the gravitational field due to a point mass. Mathematically, this connection is articulated through ∇g = – 4πGρ, where ∇ ⋅ signifies divergence, G denotes the universal gravitational constant, and ρ represents the mass density at each point.

Analogy to Electrostatics: Analogous to Gauss’s law for electrostatics in Maxwell’s equations, Gauss’s law for gravity furnishes a convenient framework for analyzing gravitational interactions. Its mathematical resemblance to Gauss’s law for electrostatics and Coulomb’s law underscores the universality of inverse-square interactions in a three-dimensional space. Practically, Gauss’s law for gravity facilitates the calculation of gravitational flux, entailing the integration of the gravitational field over a closed surface. This concept parallels the notion of magnetic flux in electromagnetism, offering a means to quantify the gravitational influence exerted by enclosed masses.


Gauss’s law for gravity occupies a pivotal role in our comprehension of gravitational phenomena. By providing a mathematical tool to analyze gravitational fields and their ramifications on surrounding matter, this law stands as a testament to the elegance and utility of fundamental physical principles.


This Law, like Newton’s were based on the idea that gravity was connected to spherical mass and calculated the “Force” as a vector.