What is the orbital speed of a satellite in a low Earth orbit (LEO) approximately 2000 km above the Earth's surface? (2000)

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Q: What is the orbital speed of a satellite in a low Earth orbit (LEO) approximately 2000 km above the Earth's surface? (2000)

Solution: The orbital speed of a satellite in low Earth orbit is approximately 7.9 km/s.

Steps: 6

Step 1: Understand that a satellite in low Earth orbit (LEO) is orbiting the Earth at a height of about 2000 km above the surface.
Step 2: Know that the Earth's radius is approximately 6371 km.
Step 3: Calculate the total distance from the center of the Earth to the satellite by adding the Earth's radius and the altitude of the satellite: 6371 km + 2000 km = 8371 km.
Step 4: Convert the total distance from kilometers to meters: 8371 km = 8,371,000 meters.
Step 5: Use the formula for orbital speed: v = √(G * M / r), where G is the gravitational constant (approximately 6.674 × 10^-11 m^3 kg^-1 s^-2), M is the mass of the Earth (approximately 5.972 × 10^24 kg), and r is the distance from the center of the Earth to the satellite (8,371,000 meters).
Step 6: Calculate the orbital speed using the values in the formula. This will give you approximately 7.9 km/s.