The Cosmologies of Galileo and Newton

Example 4: attraction of an apple (a day)

The Question:

Let’s calculate the acceleration due to the earth’s attraction for an apple in a tree 10 feet above the earth’s surface as shown in the figure below.

The Answer:

\[ a(\text{tree}) = G\cfrac{M}{(R_E + 10\text{ feet})^2}. \]

Ask Mr. Google and you’ll find that that \(R_E\) is more than 17 million feet and you can readily see that the little 10 foot addition is minuscule: $\( a(\text{tree}) = G\cfrac{M}{(17,000,000 + 10\text{ feet})^2}. \)$

Maybe you can see that this is so close to: $\( a(\text{tree}) = G\cfrac{M}{(R_E)^2} = \text{ pretty much close to } g. \)$