Final answer:
To find the height where the gravitational force is 10% of its surface value, we apply Newton's law of universal gravitation using the given Earth's radius and mass values. By setting the force at height h to be 10% of the surface force, we obtain an equation to solve for h.
Step-by-step explanation:
The question involves calculating at what height above the Earth's surface the gravitational force is reduced to 10% of its value at the Earth's surface. Given the Earth's radius of 6370 km, we want to find the distance at which the gravitational force is one-tenth its original amount. This is a physics problem that involves understanding and applying Newton's law of universal gravitation, which states that the force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
To solve this, we use the formula F = G (m1 * m2) / r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the two masses, and r is the distance between the centers of the two masses. At a certain height h above the Earth’s surface, the new distance from the center of the Earth will be r + h. We know the force of gravity at the surface, and we set the force at height h to be 10% of that, forming the equation 0.1 * F_surface = G (m1 * m2) / (r + h)^2.
We already know the force of gravity at Earth's surface (F_surface), and we have the values for G, m1 (the mass of the Earth), and r (the radius of the Earth). By substituting these known values into the equation, we can solve for h, which gives us the height above the Earth's surface where the gravitational force is 10% of its value at the surface. After rearranging the equation and solving for h, we can calculate the required height.