Why is the ionic radius of sodium far smaller than its atomic radius?
The positive ion of sodium has its entire outer (valence) shell removed, which causes the ion to be smaller.
The sodium atom has a full first and second shell with one valence electron in the third shell. The size of the atom is established by the average distance from the nucleus to this electron.
When the positive sodium ion is formed, the outer electron is stripped away, leaving only the first and second shells. The distance from the nucleus to the second shell is smaller than the distance to the third shell.
There is also a small effect due to the reduced amount of electron repulsion as the number of electrons is reduce from 11 to 10.