Question

If the distance between the sun and the earth is increased to three times then the attraction between the two will change by how much percentage?

Answer 1

$F=\frac{G{m}_1{m}_2}{r^2}\Rightarrow F\propto \frac{1}{r^2}$
$r(\uparrow )\Rightarrow F(\downarrow )$
$F=\frac{G{M}_s{M}_e}{r^2}$
$F^{\prime }=\frac{G{M}_s{M}_e}{(3r{)}^2}=\frac{G{M}_s{M}_e}{9r^2}$
$F^{\prime }=\frac{F}{9}$
$\%change\Rightarrow \left(\frac{F^{\prime }-F}{F}\right)\times 100$
$=\left(\frac{\frac{F}{9}-F}{F}\right)\times 100$
$=-\frac{8}{9}\times 100$
= -89%.
(Negative sign indicates that the force is decresed by 89%.)

So, the if the distance between sun and earth is increased by three times the attarction force is decreased by 89%.