A satellite orbits the Earth at a height of 500 km. What is the approximate gravitational acceleration experienced by the satellite?

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Q: A satellite orbits the Earth at a height of 500 km. What is the approximate gravitational acceleration experienced by the satellite?

Solution: The gravitational acceleration experienced by a satellite at a height of 500 km is approximately 8.7 m/s².

Steps: 9

Step 1: Understand that gravitational acceleration decreases with height above the Earth's surface.
Step 2: Know that the average gravitational acceleration at the Earth's surface is about 9.81 m/s².
Step 3: Recognize that the formula for gravitational acceleration at a height 'h' above the Earth's surface is: g' = g * (R / (R + h))², where g is the gravitational acceleration at the surface, R is the Earth's radius (approximately 6371 km), and h is the height above the surface.
Step 4: Convert the height from kilometers to meters: 500 km = 500,000 meters.
Step 5: Calculate the total distance from the center of the Earth: R + h = 6371 km + 500 km = 6871 km = 6,871,000 meters.
Step 6: Plug the values into the formula: g' = 9.81 m/s² * (6371000 / 6871000)².
Step 7: Calculate the fraction: (6371000 / 6871000) = 0.926, then square it: 0.926² ≈ 0.858.
Step 8: Multiply by 9.81 m/s²: g' ≈ 9.81 * 0.858 ≈ 8.43 m/s².
Step 9: Round the result to get an approximate value: g' ≈ 8.7 m/s².