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At what altitude above earth’s surface would the gravitational acceleration be 4.9 m/s2

User GPP
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Final answer:

The altitude above Earth's surface where the gravitational acceleration is 4.9 m/s^2 is approximately 1,456,190 meters.

Step-by-step explanation:

The acceleration due to gravity at a given altitude above Earth's surface can be calculated using the formula:

g = G * M / r2

Where:

  • g is the acceleration due to gravity
  • G is the gravitational constant (approximately 6.67430 × 10-11 m3 kg-1 s-2)
  • M is the mass of Earth (approximately 5.9726 × 1024 kg)
  • r is the distance from the centre of Earth

Given that the gravitational acceleration is 4.9 m/s2, we can rearrange the formula to solve for r:

r = sqrt(G * M / g)

Substituting the values, we get:

r = sqrt(6.67430 × 10-11 * 5.9726 × 1024 / 4.9)

Calculating this expression gives us:

r ≈ 1,456,190 meters

Therefore, the altitude above Earth's surface where the gravitational acceleration is 4.9 m/s2 is approximately 1,456,190 meters.

User Alex Koukoulas
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