__Newton’s Law of Gravitation :__

__Newton’s Law of Gravitation :__**Every particle in this universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.**

**The gravitational force acting between two particles**

**on combining**

**where m _{1} and m_{2} are the masses of the particles, r is the distance of separation between them and G is the Universal Gravitational Constant. The value of G was first-experimentally measured by Cavendish in 1798 by using a torsion balance.**

**Magnitude of G = 6.67 × 10 ^{-11} N m^{2}/kg^{2}**

**.**__Characteristics of the Gravitational force:__

__Characteristics of the Gravitational force:__**(a) Attractive Force : Gravitational force between two particles is always attractive and directed along the line joining the particles.**

**(b) Independent of Medium: It is independent of the nature of the medium surrounding the particles.**

**(c) Universal : It holds good for long distances like inter-planetary distances and also for short distances like inter-atomic distances.**

**(d) Action – reaction: Both the particles experience forces of equal magnitude in opposite directions. If F _{1}^{→} , F_{2}^{→} are the forces exerted on particle 1 by particle 2 and on particle 2 by particle 1 respectively,**

**then F**_{1}^{→}= – F_{2}^{→}Since the forces F_{1}^{→}and F_{2}^{→}are exerted on different bodies, they are known as action-reaction pair.**(e) Gravitation is conservative: The work done by the gravitational force acting on a particle is independent of the path described by the particle. It depends upon the initial and final positions of the particle. Work done by gravity on a particle moving in a closed path is zero**

**(f) Superposition principle: If a particle is attracted by n particles, the net force exerted on it must be equal to the vector sum of the forces due to all the n particles.**

**Illustration : Three identical particles, each of mass m, are placed at the vertices of an equilateral triangle of side a. Find the force exerted by this system on a particle P of mass m placed at the**

**(a) the mid point of a side**

**(b) centre of the triangle.**

**Solution: Using the superposition principle, the net gravitational force on P is**

**F ^{→} = F_{A}^{→} + F_{B}^{→} + F_{C}^{→}**

**(a) As shown in the figure, when P is at the mid-point of a side, F _{A}^{→} and F_{B}^{->} will be equal in magnitude but opposite in direction. Hence they will cancel each other. So the net force on the particle P will be the force due to the particle placed at C only.**

** ; along PC**

**(b) At the centre of the triangle O, the forces F _{A}^{→} , F_{B}^{→} and F_{C}^{→} will be equal in magnitude and will be at 120° with each other.**

**Hence the resultant force on P at O is F**^{→}= F_{A}^{→}+ F_{B}^{→}+ F_{C}^{→}= O__Gravitational Field__

__Gravitational Field__**The space around a material body, where it exerts a gravitational force on other bodies, is known as the gravitational field.**

**The gravitational force field is a vector field because a particle placed at any point P within the field experiences a force which depends on the coordinates of the point P.**

__Gravitational Field Strength (Intensity ) :__

__Gravitational Field Strength (Intensity ) :__**The intensity of the gravitational field at a point P is the gravitational force per unit mass exerted on a test particle placed at point P.**

**The strength of the gravitational field**

**, where F _{g}^{→} is the net force acting on a test particle of mass m kept at the point P.**

**Its SI unit is N/kg and dimensions are M ^{0}LT^{-2}**

**For earth, the gravitational field**

**The above expression is equal to the acceleration due to gravity g ^{→}**

**⇒ Gravitational field strength at a point on the earth is equal to the acceleration due to gravity at that point.**

**To find g, due to a point mass M kept at a point O (the origin), we place a point test mass m at P, the observation point, and measure the force exerted by M on the test mass m**

** ; and it is directed towards the mass M.**