Solution:

The acceleration due to gravity \( g \) on the surface of a spherical planet can be calculated using the formula:

\[
g = \frac{GM_p}{R_p^2},
\]

where:
- \( G \) is the gravitational constant,
- \( M_p \) is the mass of the planet,
- \( R_p \) is the radius of the planet.

Given that the diameter \( D_p = 2R_p \), we can express the radius as \( R_p = \frac{D_p}{2} \).

Substituting this into the formula gives:

\[
g = \frac{GM_p}{\left(\frac{D_p}{2}\right)^2} = \frac{GM_p}{\frac{D_p^2}{4}} = \frac{4GM_p}{D_p^2}.
\]

Thus, the acceleration due to gravity experienced by the particle near the surface of the planet is:

\[
g = \frac{4GM_p}{D_p^2}.
\]