The escape velocities of two planets $$A$$ and $$B$$ are in the ratio $$1 : 2$$. If the ratio of their radii respectively is $$1 : 3$$, then the ratio of acceleration due to gravity of planet $$A$$ to the acceleration of gravity of planet $$B$$ will be:

For any planet, the escape velocity formula is
$$v_e = \sqrt{2\,g\,R}$$
where $$g$$ is the acceleration due to gravity on the planet and $$R$$ is its radius.

Given two planets $$A$$ and $$B$$, take the ratio of their escape velocities:
$$\frac{v_{eA}}{v_{eB}} = \sqrt{\frac{g_A R_A}{g_B R_B}} \quad -(1)$$

The problem states
$$v_{eA} : v_{eB} = 1 : 2 \; \Rightarrow \; \frac{v_{eA}}{v_{eB}} = \frac{1}{2}$$
and
$$R_A : R_B = 1 : 3 \; \Rightarrow \; \frac{R_A}{R_B} = \frac{1}{3}.$$

Substitute these ratios into equation $$-(1)$$:
$$\frac{1}{2} = \sqrt{\frac{g_A}{g_B} \cdot \frac{R_A}{R_B}}$$
$$\frac{1}{2} = \sqrt{\frac{g_A}{g_B} \cdot \frac{1}{3}}.$$

Square both sides to remove the square root:
$$\left(\frac{1}{2}\right)^2 = \frac{g_A}{g_B} \cdot \frac{1}{3}$$
$$\frac{1}{4} = \frac{g_A}{g_B} \cdot \frac{1}{3}.$$

Isolate the ratio $$\frac{g_A}{g_B}$$:
$$\frac{g_A}{g_B} = \frac{1}{4} \times 3 = \frac{3}{4}.$$

Therefore, the ratio of the acceleration due to gravity on planet $$A$$ to that on planet $$B$$ is $$\frac{3}{4}$$.

Option D is correct.