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Chapter 14
Gravitation

Gravitation
In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down…
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…
Gravitation Between Spherically Symmetric Masses
The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies,…
Gravity between Spherical Bodies
Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the…
Reduced Mass Coordinates: Isolated Two-body Problem
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any…
Acceleration due to Gravity on Earth
According to Newton's law of gravitation, the gravitational force on a body is proportional to its mass. According to Newton's second law of…
Acceleration due to Gravity on Other Planets
The gravitational acceleration of an object near the Earth's surface is called the acceleration due to gravity. It can be measured by conducting…
Apparent Weight and the Earth's Rotation
Since all objects on the Earth's surface move through a circle every 24 hours, there must be a net centripetal force on each object, directed…
Variation in Acceleration due to Gravity near the Earth's Surface
An object's apparent weight is its weight measured by a spring balance at its location. It is different from its true weight, the force with…
Potential Energy due to Gravitation
Since gravitational force is a conservative force, the amount of work done to move an object between two points in the gravitational field in which…
The Principle of Superposition and the Gravitational Field
The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force…
Escape Velocity
The escape velocity of an object is defined as the minimum initial velocity that it requires to escape the surface of another object to which it is…
Circular Orbits and Critical Velocity for Satellites
The Moon orbits around the Earth. In turn, the Earth (and other planets) orbit the Sun. The space directly above our atmosphere is filled with…
Energy of a Satellite in a Circular Orbit
Thousands of artificial satellites orbit the Earth every day at various distances from the Earth. Satellites that orbit the Earth below an altitude…
Kepler's First Law of Planetary Motion
In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system.…
Kepler's Second Law of Planetary Motion
In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system.…
Kepler's Third Law of Planetary Motion
In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system.…
Tidal Forces
The origin of Earth's ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered…
Schwarzschild Radius and Event Horizon
No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of…
Detection of Black Holes
Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s. Their…
Principle of Equivalence
According to Albert Einstein (1897-1955), free-falling and feeling weightless are intrinsically linked. If a person were in free-fall under gravity,…
Space-Time Curvature and the General Theory of Relativity
In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater…

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