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

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Newton's law of universal gravitation[edit]

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[edit]

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[edit]

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[edit]

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