Final answer:
The percentage of the acceleration at Earth's surface that is due to gravity at a satellite located 300 km above Earth is approximately 91.7%.
Step-by-step explanation:
To find the percentage of acceleration at Earth's surface that is due to gravity at the position of a satellite located 300 km above Earth, we need to compare the acceleration due to gravity at these two positions. The acceleration due to gravity at Earth's surface is approximately 9.80 m/s².
Using the formula for the acceleration due to gravity g at a distance r from the center of Earth, g = G * M / r², where G is the gravitational constant, M is the mass of Earth, and r is the distance from the center of Earth, we can calculate the acceleration due to gravity at a distance of 300 km above Earth's surface.
Substituting the values into the formula: g = (6.674 × 10⁻¹¹ N m²/kg²) * (5.972 × 10²⁴ kg) / (6,371,000 m + 300,000 m)², we find that the acceleration due to gravity at this distance is approximately 8.66 m/s².
Finally, we can calculate the percentage by dividing the acceleration at the satellite's position by the acceleration at Earth's surface and multiplying by 100: Percentage = (8.66 m/s² / 9.80 m/s²) * 100. This gives us approximately 88.37%, which is closest to option (c) 91.7%.