# 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.

<img align="center" src="./tree.png">

<BR CLEAR="all">

**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:

$$
a(\text{tree}) = G\cfrac{M}{(R_E)^2} = \text{ pretty much close to } g.
$$