Newton's cannonball

Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his book A Treatise of the System of the World.^[1]

Thought experiment

In this experiment from his book (p. 5-8),^[1] Newton visualizes a cannon on top of a very high mountain. If there were no forces of gravitation or air resistance, the cannonball should follow a straight line away from Earth, in the direction that it was fired. If a gravitational force acts on the cannonball, it will follow a different path depending on its initial velocity. If the speed is low, it will simply fall back on Earth. (A and B) for example horizontal speed of 0 to 7,000 m/s for Earth.

Speed of cannonball at 0 m/s launched horizontally from newton's very tall mountain.

Speed of cannonball at 6,000 m/s launched horizontally from newton's very tall mountain.

If the speed is the orbital speed at that altitude, it will go on circling around the Earth along a fixed circular orbit, just like the Moon. (C) for example horizontal speed of at approximately 7,300 m/s for Earth.

Speed of cannonball at 7,300 m/s launched horizontally from newton's very tall mountain.

If the speed is higher than the orbital velocity, but not high enough to leave Earth altogether (lower than the escape velocity), it will continue revolving around Earth along an elliptical orbit. (D) for example horizontal speed of 7,300 to approximately 10,000 m/s for Earth.

Speed of cannonball at 8,000 m/s launched horizontally from newton's very tall mountain.

If the speed is very high, it will leave Earth in a parabolic (at exactly escape velocity) or hyperbolic trajectory. (E) for example horizontal speed of approximately greater than 10,000 m/s for Earth.

Speed of cannonball at 11,200 m/s launched horizontally from newton's very tall mountain.

Other appearances

An image of the page from the System of the World showing Newton's diagram of this experiment was included on the Voyager Golden Record^[2] (image #111).

This is a photograph of page 6 from Newton's Philosophiæ Naturalis Principia Mathematica Volume 3, De mundi systemate (On the system of the world). It is part of the image collection on the Voyager Golden Record that is being carried into deep space aboard the Voyager 1 and 2 spacecraft.

Notes

1 2 Newton, Sir Isaac (1728). A Treatise of the System of the World. London: F. Fayram. Retrieved 2 June 2014.
↑ Sagan, Carl et al. (1978) Murmurs of Earth: The Voyager Interstellar Record. New York: Random House. ISBN 0-394-41047-5 (hardcover), ISBN 0-345-28396-1 (paperback)

External links

Isaac Newton

Publications	De analysi per aequationes numero terminorum infinitas (1669, published 1711) Method of Fluxions (1671) De motu corporum in gyrum (1684) Philosophiæ Naturalis Principia Mathematica (1687) General Scholium (1713) Opticks (1704) The Queries (1704) Arithmetica Universalis (1707)

Other writings	Notes on the Jewish Temple Quaestiones quaedam philosophicae The Chronology of Ancient Kingdoms Amended (1728) An Historical Account of Two Notable Corruptions of Scripture (1754)

Newtonianism	Bucket argument Newton's inequalities Newton's law of cooling Newton's law of universal gravitation Post-Newtonian expansion Parameterized post-Newtonian formalism Newton–Cartan theory Schrödinger–Newton equation Gravitational constant Newton's laws of motion Newtonian dynamics Newton's method in optimization Gauss–Newton algorithm Truncated Newton method Newton's rings Newton's theorem about ovals Newton–Pepys problem Newtonian potential Newtonian fluid Classical mechanics Newtonian fluid Corpuscular theory of light Leibniz–Newton calculus controversy Rotating spheres Newton's cannonball Newton–Cotes formulas Newton's method Newton fractal Generalized Gauss–Newton method Newton's identities Newton polynomial Newton's theorem of revolving orbits Newton–Euler equations Newton number Kissing number problem Power number Solar mass Dynamics Absolute time and space Finite difference Table of Newtonian series Impact depth Structural coloration Inertia

Life	Cranbury Park Woolsthorpe Manor Early life of Isaac Newton Later life of Isaac Newton Religious views of Isaac Newton Isaac Newton's occult studies The Mysteryes of Nature and Art Scientific revolution Copernican Revolution

Friends and family	Catherine Barton John Conduitt William Clarke Benjamin Pulleyn William Stukeley William Jones Isaac Barrow Abraham de Moivre John Keill

Discoveries and inventions	Calculus Newton disc Newton polygon Newton–Okounkov body Newton's reflector Newtonian telescope Newton scale Newton's metal Newton's cradle Sextant

Phrases	"Hypotheses non fingo" "Standing on the shoulders of giants"

Theory expansions	Kepler's laws of planetary motion Problem of Apollonius

Related	Writing of Principia Mathematica Newton (Blake) List of things named after Isaac Newton Newton (unit) Isaac Newton in popular culture Elements of the Philosophy of Newton Isaac Newton S/O Philipose

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Newton's cannonball

Thought experiment

Other appearances

See also

Notes

External links