Physics > Gravitation > 6.0 Satellites
Gravitation
1.0 Newton's law of gravitation
1.1 Characteristics of gravitational force
1.2 Universal gravitational constant
1.3 Principle of superposition of gravitation
1.4 Gravity
1.5 Acceleration due to gravity
1.6 Relation between $g$ and $G$
2.0 Variation of acceleration due to gravity
2.1 Variation of acceleration due to gravity $(g)$ due to shape of the earth
2.2 Variation of acceleration due to gravity $(g)$ due to altitude
2.3 Variation of acceleration due to gravity $(g)$ due to depth
2.4 Variation of acceleration due to gravity $(g)$ due to rotation of earth
3.0 Gravitational field
3.1 Gravitational field due to a point mass
3.2 Gravitational field due to a uniform solid sphere
3.3 Gravitational field due to a uniform spherical shell
3.4 Gravitatioal field due to a uniform circular ring at a point on its axis
4.0 Gravitational potential
4.1 Gravitational potential due to a point mass
4.2 Gravitational potential due to a uniform solid sphere
4.3 Gravitational potential due to a uniform thin spherical shell
4.4 Gravitational potential due to a uniform ring at a point on its centre
4.5 Relation between gravitational field and gravitational potential
5.0 Gravitational potential energy
5.1 Gravitational potential energy for a system of particles
5.2 Gravitational potential energy of a body on earth's surface
6.0 Satellites
6.1 Orbital speed of satellite
6.2 Time period of a satellite
6.3 Angular momentum of a satellite
6.4 Energy of a satellite
6.5 Types of satellite
6.6 Binding energy
6.7 Escape velocity
6.8 Weightlessness
7.0 Kepler's law of planetary motion
8.0 Problem solving technique
6.6 Binding energy
1.2 Universal gravitational constant
1.3 Principle of superposition of gravitation
1.4 Gravity
1.5 Acceleration due to gravity
1.6 Relation between $g$ and $G$
2.2 Variation of acceleration due to gravity $(g)$ due to altitude
2.3 Variation of acceleration due to gravity $(g)$ due to depth
2.4 Variation of acceleration due to gravity $(g)$ due to rotation of earth
3.2 Gravitational field due to a uniform solid sphere
3.3 Gravitational field due to a uniform spherical shell
3.4 Gravitatioal field due to a uniform circular ring at a point on its axis
4.2 Gravitational potential due to a uniform solid sphere
4.3 Gravitational potential due to a uniform thin spherical shell
4.4 Gravitational potential due to a uniform ring at a point on its centre
4.5 Relation between gravitational field and gravitational potential
5.2 Gravitational potential energy of a body on earth's surface
6.2 Time period of a satellite
6.3 Angular momentum of a satellite
6.4 Energy of a satellite
6.5 Types of satellite
6.6 Binding energy
6.7 Escape velocity
6.8 Weightlessness
As we know the total mechanical energy (potential $+$ kinetic) of a closed system is negative. The modulus of this total mechanical energy is known as binding energy of the system.
Consider a mass $m$ is placed on the surface of the earth. The radius of the earth is $R$ and its mass is $M$.
Kinetic energy of te system, $$K=0$$
Potential energy of the system, $$U = - \frac{{GMm}}{R}$$
The total mechanical energy of the system is, $$T = K + U$$$$T = 0 + \left( { - \frac{{GMm}}{R}} \right)$$$$T = - \frac{{GMm}}{R}$$
So, mathematically binding energy can be written as, $${\text{Binding energy}} = \left| T \right|$$ or $$B.\,E. = \frac{{GMm}}{R}$$
Due to the binding energy, the particle is attached with the earth.
If minimum this much energy $(B.E.)$ is supplied to the particle, the particle no longer remains bound to the earth. It goes out of the gravitational field of the earth.
Note: When the total energy of the system becomes zero, the system is no longer bound to each other.
