In the Feynman Lectures on Physics chapter 28, Feynman explains the radiation equation $$\vec{E}=\frac{-q}{4\pi\epsilon_0 c^2}\,
\frac{d^2\hat{e}_{r'}}{dt^2}$$

The fact that the transverse component varies as ##\frac{1}{r}## seems fairly obvious to me since what matters is just the angle through which the charge moves as seen from the distant observer. However, I'm not sure how to show what he claims for the radial component. Can someone help me see clearly why this is true?