14.2
Newton's Law of Gravitation
Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downw…
Newton's law of gravitation states that "Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them."
Here, the proportionality constant G is known as the universal gravitational constant. Its value is 6.67 × 10−11 newton meter squared per kilogram squared.
Gravitational forces always act along the line joining the centers of two particles and form an action-reaction pair having equal magnitude.
For example, the force that the Earth exerts on the apple has the same magnitude as the force that the apple exerts on the Earth.
The Earth's mass is much greater than that of the apple. Therefore, its motion towards the apple is negligible compared to the apple's motion towards the Earth.
Gravitational force acts at very long distances without any direct contact between the bodies. It is this force that is responsible for holding the entire expanding universe together.
View the full transcript and gain access to JoVE Core videos
Q1: What does Newton's law of gravitation state?
Newton's law of gravitation states that every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Gravitational forces always act along the line joining the centers of two particles and form action-reaction pairs with equal magnitude.
Q2: What is the universal gravitational constant and why is it important?
The universal gravitational constant G is the proportionality constant in Newton's law of gravitation, with a value of 6.67 × 10−11 newton meter squared per kilogram squared. This incredibly small number demonstrates that gravity is the weakest of the four fundamental forces, yet it binds us to Earth, causes planets to orbit the Sun, and holds galaxies into clusters.
Q3: Why does an apple fall to Earth while Earth barely moves toward the apple?
Although gravitational forces form equal and opposite action-reaction pairs, Earth's mass is vastly greater than an apple's mass. This enormous mass difference means Earth's acceleration toward the apple is negligible compared to the apple's acceleration toward Earth, making the apple's fall visibly apparent while Earth's motion is imperceptible.
Q4: How did Isaac Newton connect the Moon's orbit to falling objects?
Isaac Newton reasoned that the same force of attraction causing the Moon to follow its path around Earth also causes an apple to fall from a tree. This insight linked celestial and terrestrial motion, revealing that gravitational attraction is a universal phenomenon governing both planetary orbits and everyday falling objects.
Q5: How does gravitational force act without direct contact between bodies?
Gravitational force acts at very long distances without any direct contact between bodies, operating through empty space. This action-at-a-distance property is fundamental to Newton's law and explains how the Sun's gravity holds planets in orbit and how Earth's gravity extends throughout space to affect distant objects.
Q6: What role did Henry Cavendish play in understanding universal gravitation?
A century after Newton published his law of universal gravitation, Henry Cavendish experimentally determined the proportionality constant G. This constant is universal in nature, applying to masses of any composition and remaining the same throughout the universe, making it fundamental to calculating gravitational forces.
Q7: How does the inverse square law affect gravitational force between objects?
Gravitational force is inversely proportional to the square of the distance between two particles. This means doubling the distance reduces the force to one-fourth its original value. Understanding this relationship is essential for analyzing how gravitational attraction changes with separation and applies to variation in acceleration due to gravity near the earth s surface.