Lesson 5.1 • Competency 5.1Complete Lesson

Universal Gravitation and Field Intensity

Newton’s Law of Universal Gravitation, Cavendish experiment, gravitational field intensity g, variations with altitude h, depth d, and Earth rotation, and neutral points between masses.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

State and apply Newton’s Universal Law of Gravitation (F = G m₁m₂ / r²) to point masses and spherical celestial bodies.
Define gravitational field strength g = F/m and deduce its variations above the surface (g_h), beneath the surface (g_d), and across latitudes.
Determine the location of neutral points between two celestial bodies (such as Earth and Moon) where net gravitational field strength vanishes.

Core Theory & Concepts

Gravitation is the universal attractive force acting between all matter in the universe. Isaac Newton formulated that every mass attracts every other mass with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Newton’s Universal Law of Gravitation

The mutual attractive force F between two point masses m₁ and m₂ separated by center-to-center distance r is F = G (m₁ m₂) / r², where G = 6.674 × 10⁻¹¹ N m² kg⁻².

F = G \frac{m_1 m_2}{r^2}

Gravitational Field Strength (Intensity)

The force experienced per unit mass placed at a point in the field: g = F/m = GM/r² (radially inward towards center of mass).

g = \frac{GM}{r^2}

Variation with Altitude and Depth

Above surface: g_h = g₀ [R / (R + h)]². Inside uniform sphere at depth d: g_d = g₀ (1 - d/R). At Earth’s center, g = 0.

g_h = g_0 \left(\frac{R}{R+h}\right)^2, \quad g_d = g_0 \left(1 - \frac{d}{R}\right)

Common Misconceptions

Misconception

Gravitational acceleration g is a fundamental constant that never changes anywhere on Earth.

Physical Clarification:g varies with altitude (decreases with height), depth (decreases linearly towards zero at the center), latitude (greater at poles than equator due to rotation and oblate shape), and local geology.

Syllabus Topic Outline

Competency 5.1

1Newton’s Law of Universal Gravitation and the inverse-square law
2Measurement of G and Newton’s Shell Theorem for spherical masses
3Gravitational field strength g = GM/r² and surface value g₀ ≈ 9.8 m s⁻²
4Variation of g with altitude: g_h = g₀ [R / (R + h)]²
5Variation of g with depth: g_d = g₀ (1 - d/R)
6Effects of Earth’s oblate shape and diurnal rotation on effective g
7Neutral point calculation between two masses