What is Gravitational Force?Gravity or gravitational forces are forces of

attraction. We're not talking about finding someone really cute and adorable. It's like the Earth pulling on you and keeping you on the ground. That pull is gravity at work. 

Every object in the universe that has mass exerts a gravitational pull, orforce, on every other mass. The size of the pull depends on the masses of the objects. You exert a gravitational force on the people around you, but that force isn't very strong, since people aren't very massive. When you look at really large masses, like the Earth and Moon, the gravitational pull becomes very impressive. The gravitational force between the Earth and the molecules of gas in the atmosphere is strong enough to hold the atmosphere close to our surface. Smaller planets, that have less mass, may not be able to hold an atmosphere. 

Newton's Law of GravitationIdea: Newton's Universal Law of Gravitation states that any two objects exert a gravitational force of attraction on each other. The direction of the force is along the line joing the objects (See Fig.(7.3)). The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them. For the two objects in Figure 7.3: 

  Figure 7.3: Gravitational Force

Between Two Masses

m1 exerts a force   on m2 .

m2 exerts a force   on m1 . By Newton's third law:

 = -  . The magnitude of the gravitational force is:

F12 = G .(22)

G is Newton's constant:

G = 6.67 x 10- 11 N m 2 /kg 2. (23)

Note:

The inertial mass of an object determines the amount of force needed to produce a given acceleration of that object. The gravitational massdetermines the force of gravitational attraction between two bodies. In Newtonian mechanics, these two masses have no obvious connection with each other. Nonetheless, it was observed empirically that they are numerically equal. This remarkable fact was known for centuries, but remained unexplained until Einstein's General Theory of relativity.

Newton's gravitational constant is extremely small when expressed in terms of laboratory sized objects: the gravitational force between two 1  kgobjects separated by 1  m is only 6.67 x 10- 11 Newtons.

For an object of mass m near the Earth's surface:

Fgrav = - G m = - mg

(24)

where ME = 5.98 x 1024 kg is the mass of the Earth and RE = 6.38 x 106 m is the radius of the earth and

g   G  = 9.8 m/s 2

(25)

in agreement with the expression in Chapter 3.

Definition: Gravitional Potential Energy

Due to the gravitational force of attraction, any two objects with masses m1 and m2 located a distance r apart have the ability to do work. Hence they have potential energy. The gravitational potential energy of such objects is:

PE grav = - G .(26)

Note:

Recall that only differences in potential energy are physically relevant. In the above, the zero of gravitational potential energy has been arbitrarily chosen to be zero at r =   . i.e. when the objects are infinitely far apart.

The negative sign is a consequence of the attractive nature of the gravitational force. When the objects are far apart, the gravitational force naturally moves them closer, decreasing their potential energy (i.e. making it more negative).

Gravitational potential energy near Earth's surface: For an object of mass m a distance h above the earth's surface:

PE grav = - G .If h < < RE we can approximate:

   so that: 

PEgrav

- G

  

  =

- G  + m h

  

  = constant + mgh.