Final answer:
The acceleration due to gravity is independent of a falling object's mass but changes with the object's distance from Earth, as does the gravitational field strength. Options b), f), and g) from the list provided are correct interpretations of the gravity equation.
Step-by-step explanation:
The correct interpretation of the expression for the acceleration due to gravity, a = g = GME, where the universal gravity constant, G, the mass of Earth, mE, and the distance from the center of the planet to the object experiencing the force of gravity, r, are involved, is that the free-fall acceleration is independent of the falling object's mass and that free-fall acceleration changes with an object's distance from Earth. Furthermore, gravitational field strength changes with an object's distance from Earth. This means that options b), f), and g) are correct. The reason behind this interpretation is Newton's law of universal gravitation which states that every point mass attracts every other point mass by a force acting along the line intersecting both points. This force is proportional to the product of the two masses and inversely proportional to the square of the distance between them. Hence, the mass of the falling object cancels out in the equation, showing independence from the falling object's mass. However, the acceleration due to gravity g does depend on the distance from the object to the center of Earth, as indicated by the variable r in the denominator.