Introducing \( x=r\cos{(\theta)} \), \( y=r\sin{(\theta)} \) and $$ r = \sqrt{x^2+y^2}, $$ we can rewrite $$ F_{x}=-\frac{GM_{\odot}M_E}{r^2}\cos{(\theta)}=-\frac{GM_{\odot}M_E}{r^3}x, $$ and $$ F_{y}=-\frac{GM_{\odot}M_E}{r^2}\sin{(\theta)}=-\frac{GM_{\odot}M_E}{r^3}y, $$ for the \( y \) direction.