To find the linear speed of the satellite, we can use the following relationship:

$v = \frac{2 \pi r}{T}$

Where:

• $v$ is the linear speed,
• $r$ is the radius of the satellite's orbit (which is the sum of Earth's radius and the altitude of the satellite),
• $T$ is the orbital period (the time it takes to complete one revolution).

Step 1: Calculate the radius of the orbit

The satellite's altitude is 1650 km, and the Earth's radius is 6400 km. Therefore, the total radius of the satellite's orbit is:

$r = 6400 \, \text{km} + 1650 \, \text{km} = 8050 \, \text{km}$

Step 2: Convert the orbital period to seconds

The orbital period $T$ is given as 180 minutes. We need to convert this to seconds:

$T = 180 \, \text{minutes} \times 60 \, \text{seconds/minute} = 10800 \, \text{seconds}$

Step 3: Calculate the linear speed

Now, we can substitute the values into the formula for linear speed:

$v = \frac{2 \pi \times 8050}{10800}$

$v = \frac{50538.1}{10800} \approx 4.68 \, \text{km/s}$

Final Answer:

The satellite's linear speed is approximately 4.68 km/s.

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Would you like further details on the calculation, or do you have any questions?

Here are some related questions to explore further:

1. How would the satellite's speed change if its altitude were increased to 2000 km?
2. What would happen to the orbital period if the satellite were closer to Earth?
3. How do we calculate the gravitational force acting on the satellite in orbit?
4. What is the relationship between the satellite's linear speed and the gravitational force?
5. How can we determine the escape velocity from this orbit?

Tip: The orbital speed is directly related to the radius of the orbit and the time it takes for a satellite to complete one revolution. Understanding these relationships can help you solve problems related to satellite motion.