Gravity
Gravity is the fundamental attractive force that acts between any two objects with mass, pulling them toward each other. On the surface of the Earth, gravity gives all objects a downward acceleration of approximately 9.8 m/s², which determines their weight and governs projectile motion. Gravity keeps planets in orbit around the Sun, holds the atmosphere in place, and causes tides through the Moon's gravitational pull on Earth's oceans.
Key Formula
F_g = G × (m1 × m2) / r²
LaTeX: F_g = G\frac{m_1 m_2}{r^2}
| Symbol | Meaning | Unit |
|---|---|---|
| F_g | Gravitational force between two objects | Newton (N) |
| G | Universal gravitational constant (6.674 × 10⁻¹¹) | N·m²/kg² |
| m1 | Mass of the first object | kilogram (kg) |
| m2 | Mass of the second object | kilogram (kg) |
| r | Distance between the centres of the two objects | metre (m) |
Worked Example
Problem
Calculate the gravitational force between Earth (mass = 5.97 × 10²⁴ kg) and a 1 kg ball on its surface (radius of Earth = 6.37 × 10⁶ m). Use G = 6.674 × 10⁻¹¹ N·m²/kg².
Solution
F_g = G × (m1 × m2) / r² = (6.674 × 10⁻¹¹) × (5.97 × 10²⁴ × 1) / (6.37 × 10⁶)² = (6.674 × 10⁻¹¹ × 5.97 × 10²⁴) / (4.058 × 10¹³) = 3.983 × 10¹⁴ / 4.058 × 10¹³ ≈ 9.81 N.
Answer
The gravitational force on the 1 kg ball is approximately 9.81 N, confirming g ≈ 9.8 m/s² on Earth's surface.
Gravitational Acceleration on Different Planets
| Planet / Body | g (m/s²) | Relative to Earth | Example: Fall time from 10 m (s) |
|---|---|---|---|
| Earth | 9.8 | 1.00 | 1.43 |
| Moon | 1.62 | 0.17 | 3.51 |
| Mars | 3.72 | 0.38 | 2.32 |
| Venus | 8.87 | 0.90 | 1.50 |
| Jupiter | 24.8 | 2.53 | 0.90 |
| Sun (surface) | 274 | 28.0 | 0.27 |
Interactive Tools
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Related Terms
Weight
Weight is the gravitational force exerted on an object due to a gravitational field, typically Earth's. It is a vector quantity directed toward the centre of the gravitational body and varies depending on the local gravitational acceleration. A person who weighs 686 N on Earth would weigh only about 114 N on the Moon, because the Moon's gravitational acceleration is approximately one-sixth that of Earth.
Newton's Second Law
Newton's Second Law of Motion states that the net force acting on an object equals the product of its mass and acceleration. It is the most quantitative of the three laws and provides the mathematical relationship between force, mass, and motion. This law is used in virtually every engineering and physics calculation involving dynamics, from designing car brakes to launching spacecraft.
Normal Force
The normal force is the contact force exerted by a surface on an object, acting perpendicular (normal) to the surface at the point of contact. It is a reaction force that prevents objects from passing through solid surfaces and adjusts in magnitude to balance components of other forces. On a flat horizontal surface, the normal force on a stationary object equals its weight; on an inclined surface, it equals the component of weight perpendicular to the slope.
From Latin 'gravitas' meaning heaviness, weight, seriousness — derived from 'gravis' (heavy). Newton formulated the Law of Universal Gravitation in 1687. Einstein later extended the concept with General Relativity in 1915, describing gravity as curvature of spacetime rather than a force.