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Surface Gravity

October 22, 2009 Leave a comment

Have you ever wondered what it is that keeps you glued to the Earth’s surface? If you have, then you are not alone. This question has been pondered since antiquity, with Aristotle launching one of the first documented theories up until Sir Isaac Newton defined mathematically and practically the force that is exerted on, around, or near the Earth’s surface, which is surface gravity.

Surface gravity is defined as the gravitational acceleration on the surface of an astronomical object such as a planet or a star. It is measured in units of acceleration, which is meters per second squared. Each astronomical body has a unique surface gravity which is determined by the product of the gravitational constant, G, and the mass of the object divided by radius of the object squared.

Aristotle, drawing from the theory of the geocentric model of the universe that was embraced by scientists and philosophers of the era, explained surface gravity by theorizing that all objects have the tendency to fall toward Earth, which was the center of the universe. His Greek contemporaries might ask, then, “Why don’t the planets fall toward Earth.” Aristotle explained this by asserting that the planets were embedded in crystal spheres which rotate with them while holding them in place within the firmament, which was the outermost celestial sphere that contains the stars. This theory was supported and refined further by Ptolemy and others until the introduction and adoption of the heliocentric model of the universe by Copernicus, which totally invalidated not only Aristotle’s theory of universal organization but also his theorems on surface gravity. Sir Isaac Newton revolutionized astronomy and the study of gravity in his book The Principia. Within his book, Newton defined the universal law of gravitation, and, within that law, Newton explained mathematically the formula to calculate the surface gravity of individual astronomical bodies as well as the gravitational relationship between different celestial bodies within the bounds of Kepler’s laws for planetary motion. Newton’s equations for gravitational calculation are still used today except in cases where extreme accuracy is necessary. In these cases, Albert Einstein’s theory of general relativity is applied to obtain the most accurate results.

The relative surface gravity of the Earth is 9.81 m/s². This means, that the gravitational pull of Earth exerts enough force to pull every object that is caught in its gravitational field toward itself at a speed of 9.81 m/s². Further, two objects that are accelerating toward the Earth’s surface will do so at this speed barring any outside interference. This outside interference is measured by multiplying the gravitational constant or G. For example, an F-16 fighter can withstand up to nine Gs. Within the equation, the number nine becomes the coefficient to measure the final modified surface gravity when taking into account the outside interference.

From Aristotle to Newton and finally to Einstein, the study of gravity has evolved from an improvable hypothesis to an exact scientific measurement that not only defines the surface gravity of the Earth and other measurable heavenly bodies, but how these celestial bodies relate to one another in relation to their gravitational properties. Surface gravity affects everything that we do by exerting constant downward acceleration on everything on the surface of the Earth, and without that constant downward acceleration, we would simply float into the void of space.

References

http://www.absoluteastronomy.com/topics/Surface_gravity

http://farside.ph.utexas.edu/teaching/301/lectures/node152.html

http://www.af.mil/information/factsheets/factsheet.asp?fsID=103

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