The Cosmologies of Galileo and Newton

Example 5: in a plane

The Question:

$g$ (the on-earth value) does it feel that far from the center of the earth? tree

tree

The Answer:

a(\text{plane}) = G\cfrac{M}{(R_E + 5\text{ miles})^2}.

$R_E$ $5\times 5280 = 26,400$ feet. So we have:

\begin{align*} a(\text{plane}) &= G\cfrac{M}{(17,000,000 + 26,400\text{ feet})^2} \\ a(\text{plane}) &= G\cfrac{M}{(17,026,400\text{ feet})^2} \end{align*}

g=G\frac{M}{R_E^2} = 32; a(plane)

’ $a(plane)$ $g$ :

\begin{align*} \frac{a(\text{plane})}{g} &= \frac{ G\frac{M}{17,026,400^2} }{ G\frac{M}{17,000,000^2} } \\ &= \frac{17,000,000^2}{17,026,400^2} \\ \frac{a(\text{plane})}{g} &= 0.9984 \end{align*}