Gravitation

Gravitation

UNIVERSAL LAW OF GRAVITATION : NEWTON’S LAW
According to this law "Each particle attracts every other particle. The force of attraction between them is directly proportional to the product of their masses and inversely proportional to square of the distance between them".
     The direction of force is along the line joining the centers of two objects.
Derivation of Newton's law of universal gravitation

Let there are two objects of mass m₁ and m₂ and the distance between the objects is r, then according to law of universal attraction, the attraction between the objects
    F\( \alpha \,m_1 \,x\,\,m_2 \)  Eq-1
    \( F\alpha \frac{1} {{r^2 }} \)          Eq-2
    By combining Eq-1 and Eq-2 we get
    \( F\alpha \frac{{m_1 \,x\,\,m_2 }} {{r^2 }} \)
    \( F = G\frac{{m_1 \,x\,\,m_2 }} {{r^2 }} \)
Where G is constant which is called Universal Gravitational constant & the value is 6.67 × 10^-11.

Important Charecterstics Of Newton’s Law Of Gravitaion
(i)  Gravitational force between two bodies form an acting and reaction pair i.e. the forces are equal in magnitude but opposite in direction.
(ii) Gravitational force is a central force i.e., it acts along the line joining the centers of the two interacting bodies.
(iii) Gravitational force between two bodies is independent of the nature of the medium, in which they lie.
(iv) Gravitational force between two bodies does not depend upon the presence of other bodies.
(v)  Gravitational force is negligible in case of light bodies but becomes appreciable in case of massive bodies like stars and planets.
(vi) Gravitational force is long range-force i.e., gravitational force between two bodies is effective even if their separation is very large. For example, gravitationalforce between the sun and the earth is the order of 10²⁷ N although distance between them is 1.5 × 10⁷ km.

GRAVITATIONAL CONSTANT “G”
(i)  Gravitational constant is a scalar quantity.
(ii) UNIT : S I : G = 6.67 × 10^–11 N-m²/kg CGS 6.67 × 10^–8 dyne-cm²/g²    Dimensions [M^–1L³T^–2]
(iii) Its value is same throughout the universe, G does not depend on the nature and size of the bodies, it also does not depend upon nature of the medium between the bodies.
(iv) Its value was first find out by the scientist “Henry Cavendish” with the help of “Torsion Balance”experiment.    
(v) Value of G is small therefore gravitational force is weaker than electrostaticforcce.