A satellite is in a circular orbit at a height of 300 km above the Earth's surfa

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Question: A satellite is in a circular orbit at a height of 300 km above the Earth\'s surface. What is the approximate speed of the satellite?

Options:

Correct Answer: 7.9 km/s

Solution:

The orbital speed can be calculated using the formula v = √(GM/r). For a height of 300 km, the speed is approximately 7.9 km/s.

A satellite is in a circular orbit at a height of 300 km above the Earth's surface. What is the approximate speed of the satellite?

A satellite is in a circular orbit at a height of 300 km above the Earth's surface. What is the approximate speed of the satellite?

Step 1: Understand that the satellite is in a circular orbit above the Earth.
Step 2: Know that the height of the satellite is 300 km above the Earth's surface.
Step 3: Convert the height into meters: 300 km = 300,000 meters.
Step 4: Find the radius of the Earth, which is approximately 6,371 km or 6,371,000 meters.
Step 5: Calculate the total distance from the center of the Earth to the satellite: radius of Earth + height of satellite = 6,371,000 m + 300,000 m = 6,671,000 m.
Step 6: Use the formula for orbital speed: v = √(GM/r), where G is the gravitational constant (approximately 6.674 × 10^-11 m^3 kg^-1 s^-2) and M is the mass of the Earth (approximately 5.972 × 10^24 kg).
Step 7: Plug in the values into the formula: v = √((6.674 × 10^-11) * (5.972 × 10^24) / (6,671,000)).
Step 8: Calculate the value inside the square root and then take the square root to find the speed.
Step 9: The calculated speed will be approximately 7.9 km/s.

Orbital Mechanics – Understanding the relationship between gravitational force, orbital radius, and speed of a satellite.
Gravitational Constant – Knowledge of the gravitational constant (G) and its application in calculating orbital speed.
Circular Motion – Application of circular motion principles to determine the speed of an object in a stable orbit.