Newton’s Law of Gravitation

Everyone is familiar with the Earth pull or attractive force. It causes thing s to fall and is also responsible for a pretty hard work if we need to carry stones to build a house. The man who discovered that every mass attracts another one was Sir Isaac Newton. In 1687 he formulated his discovery into the equation (2.1) called the Newton’s Law of Gravitation:

where F denotes the gravitational force, γ is the universal gravitational constant (6.673 × 10−11 N(m/kg)2 ), m are weights of attracting bodies and r is the distance between them. This equation (2.1) enables us to calculate a gravitational force the Earth is pulling e.g. a rock on the Earth surface:

where ME is the weight of the Earth, mr is the weight of the rock and RE is the diameter of the Earth. We can see that it is inconvenient to use and measure the gravitational force, since it depends on weights (masses) of both bodies ME and mr. Dividing both sides of equation (2.2) by mr we get:

defining the acceleration caused by the Earth. The acceleration g is called the “acceleration due to gravity” or “acceleration of gravity”. The value of g on the Earth surface is 9.80665 m/s 2 which is often simplified to 10 m/s 2 . The unit of acceleration of gravity – 1 cm/s2 – is also referred to as galileo or Gal, in honour of Galileo Galilei, who was the first who measured its value. The modern gravimeters are capable of readings with the precision of 0.001 mGal (0.01 µm/s 2 ).