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Calculate the speed of an artificial satellite if it takes 24 hours to revolve around the earth. It is given that an artificial satellite is moving in a circular orbit of radius 42250 km.

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Last updated date: 18th Jun 2024
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Answer
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Hint As the orbit is circular use the formula of circumference of circle to calculate the distance covered by the satellite in 24 hours. Then, calculate the speed by dividing the distance travelled from time taken.
Formula used: - The formula for circumference of circle is given by –
$ \Rightarrow $ Circumference $ = 2\pi r$
where, $r$ is the radius

Complete step by step solution
In the question, it is already given that an artificial satellite moves in a circular orbit of radius 42250 kilometers. As we know that, circumference of the circle is the total perimeter of the circle. So, we can use the formula of circumference of the circle to calculate the distance covered by the artificial satellite in 24 hours. Therefore, -
We know that, circumference of the circle is given by –
Circumference $ = 2\pi r$
where, $r$ is the radius of the circle
Let the distance covered by the artificial satellite be $S$.
$\therefore S = 2\pi r$
Putting the value of radius and we know that, $\pi = 3.14$ -
$
   \Rightarrow S = 2 \times 3.14 \times 42250 \\
   \Rightarrow S = 265464.58km \\
 $
Now, we have to calculate the speed of an artificial satellite to cover the distance of $265464.58km$ in 24 hours –
Now, we have to convert the 24 hours into its S.I unit which is seconds. Therefore, -
$
  t = 24 \times 60 \times 60 \\
   \Rightarrow t = 86400\sec \\
 $
 We know that distance is equal to the product of the speed and time taken. This can be represented as-
$
  S = v \times t \\
  \therefore v = \dfrac{S}{t} \\
 $
Putting the values of distance and time in the above formula of speed –
$
   \Rightarrow v = \dfrac{{265464.58}}{{86400}} \\
   \Rightarrow v = 3.07km/\sec \\
 $

Hence, the speed of an artificial satellite in 24 hours to revolve around the earth is $3.07km/\sec $.

Note During the calculation of distance of the circular object we can use the formula of circumference of the circle because this gives the perimeter of that circle. Generally, the perimeter is the curve length around any closed figure.