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.

tree

The Answer:

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

$R_E$ 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.