Physics equations/06-Uniform Circular Motion and Gravitation/A:history

Newton's law of universal gravitation

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Newton published this in 1687, his knowledge of the numerical value of the gravitational constant was a crude estimate. For our purposes, it can be conveniently state as follows [1]:

 
Click here if you are not sure what these terms mean

Solution:

  is the force applied on object 2 due to object 1
  is the gravitational constant
  and   are respectively the masses of objects 1 and 2
  is the distance between objects 1 and 2
  is the unit vector from object 1 to 2

(Note: the minus sign is a complexity that is often ignored in simple calculations. Don't fuss with minus signs unless you have to.)

Since the magnitude of the unit vector is "one"  , the unit vector vanishes when we take the magnitude of both sides of the equation to get:

 .

Weight and the acceleration of gravity

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The force of gravity is called weight,  , If one of two masses greatly exceeds the other, it is convenient to refer to the smaller mass, (e.g.stone held held by person) as the test mass,  . A vastly more massive body (e.g. Earth or Moon) can be referred to as the central body, with a mass equal to  . It is convenient to express the magnitude of the weight ( ) as,

 ,

where   is called the acceleration of gravity (or gravitational acceleration). Near Earth's surface,   is nearly uniform and equal to 9.8 m/s2. In general the gravitational acceleration is a vector field, meaning that it depends on location, g = g(r) or even location and time, g = g(r,t).

Gravity as a vector field

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under construction

  1. define the vector field for a single massive point object
  2. make analogy to magnetic field as that which causes a torque on a magnet
  3. mention temperature and wind velocity fields in meteorology
  4. perhaps mention the need for vector calculus on a spherical object (problem solved by Newton, I think)

How G was actually measured

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under construction: keep it brief and include an image and a reference to good wikipedia article

  1. https://en.wikibooks.org/w/index.php?title=Physics_with_Calculus/Mechanics/Newton%27s_Law_of_Gravitation_and_Weight&oldid=1571974