4.10 Artificial satellites  (Page 4/4)

Let us check out this requirement for the case of “Earth-satellite” system. The mechanical energy of Earth- satellite system is indeed negative :

$$E=-\frac{G\mathrm{Mm}}{2r}$$

where “M” and “m” are the mass of Earth and satellite. Hence, "Earth - satellite" system is a bounded system.

We can infer from the discussion of a bounded system that the "binding energy" is the amount of energy required to disintegrate (dismember) a bounded system. For example, we can consider a pebble lying on Earth’s surface. What is the energy required to take this pebble far off in the interstellar space, where Earth’s gravity ceases to exist? We have seen that infinity serves as a theoretical reference, where gravitational field ceases to exits. Further, if we recall, then potential energy is defined as the amount of work done by external agency to bring a particle slowly from infinity to a position in gravitational field. The work by external force is negative as its acts opposite to the displacement. Clearly, taking pebble to the infinity is reverse action. Work by external force is in the direction of displacement. As such, work done in this case is positive. Therefore, binding energy of the pebble is a positive quantity and is equal to the magnitude of potential energy for the pebble. If its mass is “m”, then binding energy of the "Earth-pebble" system is :

$$\Rightarrow E_B=-U=-\left(-\frac{G\mathrm{Mm}}{r}\right)=\frac{G\mathrm{Mm}}{r}$$

where “M” and “m” are the mass of Earth and pebble respectively and “R” is the radius of Earth.

This is, however, a specific description of dismembering process. In general, a member of the system will have kinetic energy due to its motion. Let us consider the case of “Earth-satellite” system. The satellite has certain kinetic energy. If we want to take this satellite to infinity, we would first require to bring the satellite to a dead stop and then take the same to infinity. Therefore, binding energy of the system is a positive quantity, which is equal to the magnitude of the mechanical energy of the system.

Binding energy

Binding energy is equal to the modulus of mechanical energy.

Going by the definition, the binding energy of the “Earth-satellite” system is :

$$\Rightarrow E_B=-E=-\left(-\frac{G\mathrm{Mm}}{2r}\right)=\frac{G\mathrm{Mm}}{2r}$$

where “r” is the linear distance between the center of Earth and satellite.

Satellite systems

The satellites are made to specific tasks. One of the most significant applications of artificial satellite is its use in telecast around the world. Earlier it was difficult to relay telecast signals due to spherical shape of Earth. In recent time, advancements in communication have brought about astounding change in the way we live. The backbone of this communication wonder is variety of satellite systems orbiting around Earth.

Satellite systems are classified for different aspects of satellite motion. From the point of physics, it is the orbital classification of satellite systems, which is more interesting. Few of the famous orbits are described here. Almost all orbits generally describe an elliptical orbit. We shall discuss elliptical orbits in the module dedicated to Kepler’s law. For the present, however, we can approximate them to be circular for analysis purpose.

1: Geocentric orbit : It is an orbit around Earth. This is the orbit of artificial satellite, which is launched to revolve around Earth. Geocentric orbit is further classified on the basis of distance from Earth’s surface (i) low Earth orbit up to 2000 km (ii) middle Earth orbit between 2000 and geo-synchronous orbit (36000 km) and (iii) high Earth orbit above geo-synchronous orbit (36000 km).

2: Heliocentric Orbit : It is an orbit around Sun. The orbits of planets and all other celestial bodies in the solar system describe heliocentric orbits.

3: Geosynchronous Orbit : The time period of this orbit is same as the time period of Earth.

4: Geostationary Orbit : The plane of rotation is equatorial plane. The satellite in this orbit has time period equal to that of Earth. Thus, motion of satellite is completely synchronized with the motion of Earth. The sense of rotation of the satellite is same as that of Earth. The satellite, therefore, is always above a given position on the surface. The orbit is at a distance of 36000 km from Earth’s surface and about 42400 (= 36000 + 6400) km from the center of Earth. The orbit is also known as Clarke’s orbit after the name of author, who suggested this orbit.

5: Molniya Orbit – It is an orbit having inclination of 63.4° with respect to equatorial plane and orbital period equal to half that of Earth.

6: Polar orbit : The orbit has an inclination of 90° with respect to the equatorial plane and as such, passes over Earth’s poles.

Another important classification of satellite runs along the uses of satellites. Few important satellite types under this classification are :

1: Communication satellites : They facilitate communication around the world. The geostationary satellite covers ground locations, which are close to equator. Geostationary satellites appears low from a positions away from equator. For locations at different latitudes away from equator, we need to have suitably designed orbits so that the area can be covered round the clock. Molniya orbit is one such orbit, which is designed to provide satellite coverage through a satellite system, consisting of more than one satellite.

2: Astronomical satellites : They are designed for studying celestial bodies.

3: Navigational satellites : They are used to specify location on Earth and develop services based on navigation.

4: Earth observation satellites : They are designed for studying Earth system, environment and disaster management.

5: Weather satellites : They facilitate to monitor weather and related services.

6: Space station : It is an artificial structure in space for human beings to stay and do assigned experiments/works

As a matter of fact, there is quite an elaborate classification system. We have only named few important satellite systems. In particular, there are varieties of satellite systems, including reconnaissance satellites, to meet military requirement.

Acknowledgment

Author wishes to thank Arunabha guha, Physics dept, Georgian court university, Lakewood, New jersey, USA for pointing out a mistake in the example contained in this module.