The diagram shows a communications satellite moving in a circular orbit around the Earth. Its orbital radius is 4.20 × 107 m, measured from the centre of th...
Question 1 Report
The diagram shows a communications satellite moving in a circular orbit around the Earth. Its orbital radius is 4.20 × 107 m, measured from the centre of the Earth. The satellite completes one orbit in 24.0 h so that it stays above the same region of the Earth. A student uses the orbit circumference to determine the satellite speed. Take the orbit as circular and use π = 3.14.
(a) State the force that provides the centripetal force for this satellite. [1]
(b) Calculate the distance travelled by the satellite in one orbit. [2]
(c) Calculate the speed of the satellite in m/s. [3]
(d) Explain why the direction of the satellite velocity changes continuously, even when its speed is constant. [2]
Answer Details
(a) The centripetal force is provided by gravitational force between the Earth and the satellite. [1]
(b) One orbit has circumference \(2\pi r\):
\[2\times3.14\times4.20\times10^7=2.64\times10^8\text{ m}\]
Distance travelled in one orbit = \(2.64\times10^8\text{ m}\). [2]
(c) First convert the period to seconds:
\[24.0\times3600=86400\text{ s}\]
Then use \(v=\frac{d}{t}\):
\[v=\frac{2.64\times10^8}{86400}=3.06\times10^3\text{ m/s}\]
The speed is \(3.06\times10^3\text{ m/s}\), or \(3060\text{ m/s}\). [3]
(d) Gravity acts continually towards the centre of the Earth. A force changes velocity, and velocity includes direction as well as speed, so this inward force continuously changes the satellite's direction of motion. [2]
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