Final answer:
The calculated value of g is obtained using the formula g = G * (M / r^2), where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the object to the center of the Earth. The proportional error in g refers to the percentage error in the calculated value of g, which can arise from uncertainties in the measurements of the gravitational constant, Earth's mass, or the distance.
Step-by-step explanation:
The calculated value of g, the acceleration due to gravity, can be determined by using the formula g = G * (M / r^2), where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the object and the center of the Earth. By plugging in the known values for G, M, and r, we can calculate the value of g.
The proportional error in g refers to the percentage error in the calculated value of g. This error can arise from uncertainties in the measurements of the gravitational constant, Earth's mass, or the distance. To calculate the proportional error, we would need to know the uncertainties associated with these measurements.