RAPID DETERMINATION OF CUBE'S GRAVITY FIELD *

Gravity modeling involves the evaluation of gravity field due to bodies of irregular shape. This is commonly accomplished by dividing the body into smaller units of regular shape whose field can be determined analytically.

Cubes are ideal building blocks for constructing bodies of irregular shape. However, the exact expression defining the gravity field of a cube‐shaped body is very long and requires tedious numerical work. Approximation formulas for rapid evaluation of the cube's gravity field are presented and discussed in detail. Their use for computing the field for small distances leads to large errors in the results; on the other hand, using the exact formula for large distances where approximation formulas yield practically identical results, is waste of time. After a detailed analysis about the nature of the cube's gravity field, certain criteria are established for suitably combining the two alternatives. This results in tremendous reduction in the task of computations without affecting the accuracy of data.