Final answer:
The acceleration of gravity at a height of 6400 km above Earth's surface is 2.45 m/s², calculated using the formula for gravitational acceleration derived from the universal law of gravitation.
Step-by-step explanation:
To determine the acceleration of gravity at a height of 6400 km (or one Earth radius) above Earth's surface, we use the formula for gravitational acceleration g modified from the universal law of gravitation. The formula that relates the gravitational force F is F = G(m1*m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers of the two masses. Since weight w equals the mass m times the gravitational acceleration g, and w = mg = F, we can solve for g giving us g = GM/r^2, where M is the mass of Earth and r is now the distance from the center of Earth, which at the surface is one Earth radius and at 6400 km above would be two Earth radii.
Since the acceleration of gravity at the Earth's surface is 9.8 m/s², we can calculate the acceleration at 6400 km above as follows: g' = 9.8 m/s² * (R/(R + H))^2 = 9.8 m/s² * (6400 km/(6400 km + 6400 km))^2 = 9.8 m/s² * (1/2)^2 = 9.8 m/s² * 1/4 = 2.45 m/s². Therefore, the acceleration due to gravity at 6400 km above Earth's surface is 2.45 m/s².