An artificial satellite is moving in a circular orbit of radius 42250 km calculate its speed if it takes 24 hours to revolve around the earth

General
1

an artificial satellite is moving in a circular orbit of radius 42250 km calculate its speed if it takes 24 hours to revolve around the earth

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An artificial satellite is moving in a circular orbit of radius 42250 km calculate its speed if it takes 24 hours to revolve around the earth

Answer: To calculate the speed of an artificial satellite moving in a circular orbit, we need to determine the circumference of the orbit and then divide it by the time it takes to complete one revolution.

  1. Calculate the circumference of the orbit:
    The formula for the circumference (C) of a circle is:

    C = 2\pi r

    where (r) is the radius of the orbit.

    Given:

    r = 42250 \text{ km}

    So,

    C = 2\pi \times 42250 \text{ km}

    Calculating the circumference:

    C \approx 2 \times 3.14159 \times 42250 \text{ km}
    C \approx 265,165 \text{ km}

  2. Convert the time period from hours to seconds:
    Given that the satellite takes 24 hours to complete one revolution, we need to convert this time into seconds to use it in our speed calculation.

    1 \text{ hour} = 3600 \text{ seconds}
    24 \text{ hours} = 24 \times 3600 \text{ seconds}
    24 \text{ hours} = 86400 \text{ seconds}

  3. Calculate the speed of the satellite:
    Speed (v) is given by the formula:

    v = \frac{C}{T}

    where (C) is the circumference and (T) is the time period.

    Substituting the values:

    v = \frac{265,165 \text{ km}}{86400 \text{ s}}

    Calculating the speed:

    v \approx 3.07 \text{ km/s}

Therefore, the speed of the artificial satellite is approximately (3.07 \text{ km/s}).