What is the acceleration due to gravity at a distance of one Earth radius above the Earth's surface
To calculate the acceleration due to gravity at a distance of one Earth radius above the Earth's surface, we can use Newton's Law of Universal Gravitation. This law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The formula for the acceleration due to gravity (g) at a certain distance (r) from the center of the Earth is given by:
g = G * (M / r^2)
Where:
- G is the universal gravitational constant (6.67430 × 10^(-11) m^3 kg^(-1) s^(-2))
- M is the mass of the Earth (5.972 × 10^24 kg)
- r is the distance from the center of the Earth to the object's position (in this case, one Earth radius)
Since we know the value of G, M, and r, we can plug them into the formula to calculate the acceleration due to gravity.
Plugging in the values:
g = (6.67430 × 10^(-11) m^3 kg^(-1) s^(-2)) * (5.972 × 10^24 kg) / ((6371 km)^2)
Note that the radius of the Earth is approximately 6,371 kilometers.
Converting kilometers to meters to match the units of G:
g = (6.67430 × 10^(-11) m^3 kg^(-1) s^(-2)) * (5.972 × 10^24 kg) / ((6371 km * 1000)^2)
Calculating:
g ≈ 9.819 m/s^2
Therefore, at a distance of one Earth radius above the Earth's surface, the acceleration due to gravity is approximately 9.819 m/s^2.