In the development of the standard atmospheric model, the variation of the acceleration of gravity with altitude is ignored; that is, the acceleration of gravity is approximated as constant with altitude. Using the Newtonian gravitational model, compute the acceleration of gravity at sea level, 50,000 ft, and 100,000 ft. Based on these computations, describe the accuracy of this approximation.

The accuracy percentage for 50000 ft is 0.47%.

The accuracy percentage for 100000 ft is 0.92%.

Explanation:

Given that,

Height = 50000 ft and 100000 ft

We need to calculate the new acceleration due to gravity

Using newtonian gravitational formula

Where, g = acceleration due to gravity

h = height

R = radius

Put the value into the formula

We need to find the accuracy percentage

Using formula for accuracy

Put the value into the formula

Now, For other height,

We need to calculate the new acceleration due to gravity

Using newtonian gravitational formula

Put the value into the formula

We need to find the accuracy percentage

Using formula for accuracy

Put the value into the formula

Hence, The accuracy percentage for 50000 ft is 0.47%.

The accuracy percentage for 100000 ft is 0.92%.

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