Pergunta

A satellite in circular orbit 1200 kilometers above Earth makes one complete revolution every 100 minutes Assuming that Earth is a sphere of radius 6378 kilometers, what is the linear speed (in kilometers per minute) of the satellite?(Round your answer to one decimal place.) square times km/min
Solução

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PabloProfissional · Tutor por 6 anos
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The linear speed of the satellite is approximately 477.4 km/min.
Explicação
## Step 1<br />The problem involves calculating the linear speed of a satellite in a circular orbit. The formula for linear speed is given by:<br />### \(v = \frac{2\pi r}{T}\)<br />where \(v\) is the linear speed, \(r\) is the radius of the circular path, and \(T\) is the time taken for one complete revolution.<br /><br />## Step 2<br />The radius of the satellite's orbit is the sum of the Earth's radius and the altitude of the satellite. Given that the Earth's radius is 6378 kilometers and the satellite's altitude is 1200 kilometers, the total radius \(r\) is:<br />### \(r = 6378 \, \text{km} + 1200 \, \text{km} = 7578 \, \text{km}\)<br /><br />## Step 3<br />The time taken for one complete revolution \(T\) is given as 100 minutes.<br /><br />## Step 4<br />Substitute the values of \(r\) and \(T\) into the formula for linear speed:<br />### \(v = \frac{2\pi \times 7578 \, \text{km}}{100 \, \text{min}}\)<br /><br />## Step 5<br />Calculate the value of \(v\).
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