# Question #f66fb

##### 1 Answer

A gravitational quadrupole is a mathematical concept to explain the gravitational effect of a mass which is not just a point but which has an extension in the space

#### Explanation:

The most easy way to show its effects is considering 4 equal masses (m each of them) placed in every corner of a square of side

By using the Newton's gravitational law

the same for the distance from mass M to every corner of square

the total gravitational force in the system is

Taken in account the approximation formula

In this expression, we have 2 elements. The first one

concentrated in a single point, just in the center of the square. The

second one

quadropole for this example. See that this element is negative and decrease faster with distances.

This concept can be generalised to any geometrical configuration with 4 masses and also to larger number of masses (octopole, hexapole, etc.). When we have a extensive mass, its gravitational effects can be approximated in this way (point mass plus gravitational dipole plus gravitational quadrupole plus ...).