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The energy required to remove a satellite from its orbit around the earth to infinity is called Binding energy of a satellite.
We know that the satellite revolves around the earth in an orbit near the surface of earth. The satellite gets the necessary centripetal force from the gravitational force of earth. Assume a satellite, revolving around the earth of mass ‘Me’ and radius ‘Re’. It is height ‘h’ above the surface of earth. If ‘v’ is the orbital velocity of the satellite and ‘m’ is the mass of satellite then
Where ‘g’ is acceleration due to gravity
The numerical value of orbital velocity for a satellite launched near the surface of earth is 7.2 km/s. A satellite revolving around the earth has potential energy as well as kinetic energy. It has potential energy due to its position above the earth’s surface & it remains within the gravitational field of the earth. It has kinetic energy because it is moving around the earth. The total mechanical energy of a satellite is the sum of its potential energy (U) and kinetic energy (K).
Expression for total energy
If a satellite is revolving around the earth in a circular orbit close to the surface of earth, the radius of its orbit can be taken as Re. Let ‘m’ be the mass of satellite and ‘v’ be its orbital velocity then its gravitational potential energy is given by:
Where Me is mass of earth and ‘G’ is universal gravitational constant. The Kinetic energy of a satellite is given by
As, satellite gets necessary centripetal force from the earth’s gravitational force, therefore
Putting eq. (3) in eq. (2), we get
Therefore total energy of a satellite is
Thus, the total energy of a satellite is negative. At infinity (that is, Re = ∞), both potential energy and Kinetic energy becomes zero. Hence at infinity, the total energy becomes zero. The Kinetic energy can never be negative. Thus a negative total energy means, in order to send a satellite to infinity, we have to give energy to the satellite. Unless a revolving satellite gets extra energy, it would not leave its orbit.
Expression for Binding Energy
The energy required for a satellite to leave its orbit around the earth and escape to infinity is called the ‘binding energy‘ for that satellite. The total energy of a satellite revolving close to earth is
Therefore in order to escape, the satellite would require an amount of energy
So that the total energy ‘E’ becomes zero. Thus Binding Energy of satellite is
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