Universal Gravitation

One of the most frequent and well known causes of  centripetal force is gravity. It keeps us in orbit around the sun, and affects  the paths of satellites. Sir Isaac Newton gave us our best early work on gravity and its implications. He was not only interested in  gravity’s effect on the Earth’s surface, but also with the force of gravity  between any two given objects. In his studies he concluded that:

OR: The force of gravity between any two given objects is proportional to the masses of the two objects. Through further research, Newton also concluded that:

OR: The force of gravity between any two given objects is inversely proportional to the distance between the objects squared. The inverse square relationship is an important relationship in many areas of physics. As an object doubles its distance from another object, the force between them becomes one fourth as strong. If the distance were tripled, the force would be one ninth as strong. We will see inverse square relationships a lot.

Newton combined these two relations, and came up with his Law of Universal Gravitation:

OR: Every object in the universe attracts all other objects in the universe with a force that is proportional to the product of the objects’ masses, inversely proportional to the distance between the objects squared, and occurs on a straight line between the objects. This doesn't apply just to stars and planets. ANY two objects with mass have a gravitational force of attraction between them. Most of the time, however, this force is way too small to be noticable.

The quantity G was defined as the Universal Gravitation Constant. Newton knew that it existed and how to use it, but he could not figure its value. The value of G remained undetermined until Henry Cavendish, a British scientist, performed an experiment in 1798 which later allowed it to be calculated. Cavendish’s experiment to determine the Universal Gravitation Constant used a torsion line with two masses attached at the ends, two larger masses to draw the smaller ones, and a mirror attached to the line which a light was reflected off of. He moved the larger masses around the smaller ones and calculated G by measuring the change in the position of light as it reflected off the mirror as the line moved with the smaller masses. With this experiment, Cavendish determined:

G = 6.673 x10-11 Nm2/kg2

This was incredibly arduous work, but little improvement has been made on Cavendish's work. One major outcome of this was that this equation could be used to give the first reasonably accurate mass of the Earth.

Try these additional resources:

Cavendish’s Experiment on the Universal Gravitational Constant:

http://physnet2.pa.msu.edu/home/modules/pdf_modules/m100.pdf

Law of Universal Gravitation:

http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

http://www.physicsclassroom.com/class/circles/u6l3a.cfm  Follow this to a page which will take you on more detailed looks at each element discussed above