Chapter 5: Q46. (page 134)

Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 4800 km.

Short Answer

Expert verified

The speed of a satellite is $5.97 \times 10^{3} m / s$ .

Step by step solution

Step 1. Given Data

The height is $h = 4800 km$ .

Step 2. Understanding the speed of the satellite

In this problem, utilize the relation of the orbital speed in terms of mass of the certain body and its distance from the satellite to the centre for calculating the speed of a satellite.

Step 3. Estimating the speed of the satellite

The relation of orbital speedis given by,

$v = \sqrt{\frac{G m_{E}}{r_{E} + h}}$

Here, G is the gravitational constant, $r_{E}$ is the radius of the Earth and $m_{E}$ is the mass of the Earth.

On plugging the values in the above relation.

$\begin{array}{l} v = \sqrt{[\frac{(6.67 \times 10^{- 11} N \cdot m^{2} / {kg}^{2}) (5.98 \times 10^{24} kg)}{(6.38 \times 10^{6} m) + (4800 km \times \frac{1000 m}{1 km})}]} \\ v = 5.97 \times 10^{3} m / s \end{array}$

Thus, $v = 5.97 \times 10^{3} m / s$ is the required speed.

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Table 5-3 Principal Moons of Jupiter
Moon	Mass(kg)	Period (Earth days)	Mean distance from Jupiter (km)
Io	\({\bf{8}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{22}}}}\)	1.77	\({\bf{422 \times 1}}{{\bf{0}}^{\bf{3}}}\)
Europe	\({\bf{4}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{22}}}}\)	3.55	\({\bf{671 \times 1}}{{\bf{0}}^{\bf{3}}}\)
Ganymede	\({\bf{15 \times 1}}{{\bf{0}}^{{\bf{22}}}}\)	7.16	\({\bf{1070 \times 1}}{{\bf{0}}^{\bf{3}}}\)
Callisto	\({\bf{11 \times 1}}{{\bf{0}}^{{\bf{22}}}}\)	16.7	\({\bf{1883 \times 1}}{{\bf{0}}^{\bf{3}}}\)

Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 4800 km.

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Understanding the speed of the satellite

Step 3. Estimating the speed of the satellite

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