Gravitational Force (Astronomy)
Gravitational force in astronomy is the attractive force between any two masses, governed by Newton's Law of Universal Gravitation, which states that the force is proportional to the product of the masses and inversely proportional to the square of the distance between them. This force is responsible for holding planets in orbit around the Sun, governing the motion of moons, shaping the structure of galaxies, and dictating the trajectories of spacecraft. It is the dominant long-range force at astronomical scales and underlies phenomena from tidal locking to the formation of planetary systems.
Key Formula
F = G × (m₁ × m₂) / r²
LaTeX: F = G \frac{m_1 m_2}{r^2}
| Symbol | Meaning | Unit |
|---|---|---|
| F | Gravitational force between the two masses | Newtons (N) |
| G | Universal gravitational constant (6.674 × 10⁻¹¹) | N·m²·kg⁻² |
| m₁ | Mass of the first object | kilograms (kg) |
| m₂ | Mass of the second object | kilograms (kg) |
| r | Distance between the centres of the two masses | metres (m) |
Worked Example
Problem
Calculate the gravitational force between the Earth (mass = 5.972 × 10²⁴ kg) and the Moon (mass = 7.342 × 10²² kg), separated by a distance of 3.844 × 10⁸ m.
Solution
Step 1: Write the formula: F = G × m₁ × m₂ / r². Step 2: Substitute values: F = (6.674 × 10⁻¹¹) × (5.972 × 10²⁴) × (7.342 × 10²²) / (3.844 × 10⁸)². Step 3: Numerator = 6.674 × 10⁻¹¹ × 4.384 × 10⁴⁷ = 2.924 × 10³⁷. Step 4: Denominator = (3.844 × 10⁸)² = 1.478 × 10¹⁷. Step 5: F = 2.924 × 10³⁷ / 1.478 × 10¹⁷ = 1.978 × 10²⁰ N.
Answer
F ≈ 1.98 × 10²⁰ N (approximately 198 quintillion Newtons).
Surface gravitational acceleration on Solar System bodies
| Body | Mass (kg) | Radius (km) | Surface Gravity (m/s²) | Relative to Earth |
|---|---|---|---|---|
| Sun | 1.989 × 10³⁰ | 695,700 | 274.0 | 27.9× |
| Earth | 5.972 × 10²⁴ | 6,371 | 9.81 | 1.0× |
| Moon | 7.342 × 10²² | 1,737 | 1.62 | 0.165× |
| Mars | 6.39 × 10²³ | 3,390 | 3.72 | 0.379× |
| Jupiter | 1.898 × 10²⁷ | 69,911 | 24.79 | 2.53× |
Interactive Tools
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Related Terms
Kepler's Third Law
Kepler's Third Law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit around the Sun. This relationship, discovered by Johannes Kepler in 1619, applies to all objects orbiting the same central body and allows astronomers to calculate orbital periods or distances when one is known. It was later explained theoretically by Newton's law of universal gravitation and remains a foundational tool for planetary science and space mission planning.
Tidal Force
A tidal force is the differential gravitational force exerted on one body by another, arising because gravitational pull varies across the extended body — the side closer to the source experiences stronger gravity than the side farther away. This stretching effect causes Earth's ocean tides (due to the Moon and Sun), drives tidal heating on moons like Io and Europa, and can eventually lead to tidal locking, where a body's rotation period equals its orbital period. In extreme cases near compact objects, tidal forces become strong enough to disrupt and shred orbiting material, a process called spaghettification.
Orbital Mechanics
Orbital mechanics (also called astrodynamics) is the branch of aerospace engineering and applied physics that studies the motion of spacecraft, satellites, and celestial bodies under the influence of gravitational forces. It is governed by Newton's law of universal gravitation and Kepler's three laws of planetary motion, and it underpins the planning of satellite launches, orbital transfers, interplanetary trajectories, and re-entry profiles. Mastery of orbital mechanics is essential for mission design, ground-track prediction, and spacecraft manoeuvring.
From Latin gravitas meaning "weight" or "heaviness," from gravis ("heavy"). The concept was formally quantified by Isaac Newton in his 1687 work Philosophiae Naturalis Principia Mathematica.