Irodov Problem 1.221

Problem Statement

Find the gravitational field intensity g at a distance r from a point mass M.

Given

M (point mass), r = distance, G = gravitational constant.

Concepts & Formulas

Gravitational field: g = GM/r² directed toward M.

Step-by-Step Solution

Step 1: Gravitational force on test mass m: F = GMm/r².
Step 2: Field g = F/m = GM/r².
Step 3: Direction: radially inward (attractive).

Worked Calculation

g = GM/r².

Boxed Answer

g = GM/r² (directed inward)

Physical Interpretation

The field drops as 1/r², doubling the distance reduces the field by four — the same inverse-square law that governs light intensity from a point source.