3 3 Artificial Satellites – Class 11TH Physics

3.3 Artificial Satellites

Satellites are objects that orbit in nearly circular path around the Earth. They are put into orbit by rockets and are held in orbits by the gravitational pull of the Earth. The low flying Earth satellites have acceleration $g = 9.8\,\mathrm{m/s^{2}}$ towards the centre of the Earth. If there is no gravitational pull, they would fly off in a straight line along tangent to the orbit. When the satellite is moving in a circle, it has an acceleration $v^{2}/R$ . In a circular orbit around the Earth, the centripetal acceleration is supplied by gravity and we have:

g = \frac{v^{2}}{R} \quad \ldots (3.14)

where $v$ is the orbital velocity and $R$ is the radius of the Earth ( $6400\,\mathrm{km}$ ). From Eq. 3.14, we have:

v = \sqrt{gR}

= \sqrt{9.8\,\mathrm{m/s^{2}} \times 6.4 \times 10^{6}\,\mathrm{m}}

= 7.9 \times 10^{3}\,\mathrm{m/s} = 7.9\,\mathrm{km/s}

This is the minimum velocity necessary to put a satellite into the orbit, called the critical velocity. The period $T$ is given by:

T = \frac{2\pi R}{v} = \frac{(2 \times 3.14 \times 6400\,\mathrm{km})}{(7.9\,\mathrm{km/s})}

= 5060\,\mathrm{s} = 84\,\mathrm{min}\ \text{approx.}

If, however, a satellite in a circular orbit is at a distance $h$ much greater than $R$ above the Earth's surface, we must take into account the experimental fact that the gravitational acceleration decreases inversely as the square of the distance from the centre of the Earth (Fig. 3.11).

The higher the satellite, the slower will be the required speed and longer it will take to complete one revolution around the Earth.

3.3 Artificial Satellites

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