Answer:
8.957 m/s^2
Step-by-step explanation:
First, let's calculate the mass of the Earth using the formula:
M = (4/3) * π * R^3 * ρ
where:
- π is approximately 3.14159
- R is the radius of the Earth in meters, which is approximately 6,371,000 m
- ρ is the density of the Earth in kg/m^3, which is given as 5540.0 kg/m^3
M = (4/3) * 3.14159 * (6,371,000)^3 * 5540.0
M ≈ 5.972 × 10^24 kg
Now, we can use the formula for gravitational acceleration:
g = (G * M) / r^2
where:
- G is the gravitational constant, which is approximately 6.67430 × 10^-11 m^3/(kg * s^2)
- M is the mass of the Earth, which we calculated as 5.972 × 10^24 kg
- r is the distance from the Earth's center in meters, which is 900,000 m
Plugging in the values, we get:
g = (6.67430 × 10^-11 * 5.972 × 10^24) / (900,000)^2
g ≈ 8.957 m/s^2
Therefore, at a distance of 900.0 km from the Earth's center, the value of gravitational acceleration is approximately 8.957 m/s^2.