According to Newton's law of gravity, every object in the universe attracts every other object... with a gravitational force... F = m M G R 2 {\displaystyle F={\frac {mMG}{R^{2}}}}
... almost as famous as E = m c 2 {\displaystyle E=mc^{2}}
... On the left side is the force, F {\displaystyle F}
, between two masses... On the right side, the bigger mass is M {\displaystyle M}
and the smaller mass is m {\displaystyle m}
. ...The last symbol... G {\displaystyle G}
, is a numerical constant called Newton's constant. ...Ironically, Newton never knew the value of his own constant. ... G {\displaystyle G}
was too small to measure until the end of the eighteenth century. ...Cavendish found that the force between a pair of one-kilogram masses separated by one meter is approximately 6.6 x 10-11 newtons. (The Newton is... about one-fifth of a pound.) ...Newton had one lucky break... the special mathematical properties of the inverse square law. ...[B]y the miracle of mathematics, you can pretend that the entire mass is located at a single point. This... allowed Newton to calculate the escape velocity... E s c a p e v e l o c i t y = 2 M G / R {\displaystyle Escape\;velocity={\sqrt {2MG/R}}}
... the bigger the mass [ M {\displaystyle M}
] and the smaller the radius R {\displaystyle R}
, the larger the escape velocity.
The Origins of Modern Science (1949)Edit