Final answer:
The magnitude of the gravitational force on a mass m at a distance r from Earth's center for r>re is given by the formula F = (G × M × m)/r^2, using the universal gravitational constant G.
Step-by-step explanation:
The expression for the magnitude of the gravitational force on a mass m at a distance r from the earth's center for r>re, where re is the radius of Earth, is derived using Newton's law of universal gravitation. The formula is F = (G × M × m)/r^2, where F is the magnitude of the gravitational force, G is the gravitational constant (6.674 × 10^-11 N·m^2/kg^2), M is the mass of Earth, and m is the mass of the object experiencing the force.
For distances beyond the Earth's surface (r>re), this formula applies directly since the mass m of the object does not affect the expression for g, the gravitational field strength, as it cancels out in the derivation. It's important to note that this equation assumes that the Earth's mass distribution is sufficiently uniform and that the force acts as if all of Earth's mass were concentrated at its center.