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.

Question

State which of the following situations are possible and give an example for each of these:

an object with a constant acceleration but with zero velocity
an object moving with an acceleration but with uniform speed.
an object moving in a certain direction with an acceleration in the perpendicular direction.

Answer 1

Calculation of Speed of an Artificial Satellite

Given:

Radius of the orbit, \(r = 42,250 \, \text{km} = 4.225 \times 10^7 \, \text{m}\)
Time taken for one revolution, \( T = 24 \, \text{hours} = 24 \times 60 \times 60 = 86,400 \, \text{seconds}\)

Formula for Speed:

The speed of the satellite \( v \) is given by the formula for the orbital speed of a satellite: \[ v = \frac{2\pi r}{T} \] where: - \( v \) is the speed of the satellite, - \( r \) is the radius of the orbit, - \( T \) is the time period of revolution.

Substitute the Given Values:

\[ v = \frac{2 \pi \times 4.225 \times 10^7}{86,400} \]

Calculation:

\[ v = \frac{2 \pi \times 4.225 \times 10^7}{86,400} \approx \frac{2 \times 3.1416 \times 4.225 \times 10^7}{86,400} \approx \frac{2.653 \times 10^8}{86,400} \approx 3,067.3 \, \text{m/s} \]

Answer:

The speed of the artificial satellite is approximately \( 3,067.3 \, \text{m/s} \).