## 4 Calculation Results and Analysis  
Some parameters are computed in this section, which include gravity potential, total gravitational acceleration, tangential acceleration, and surface slope with respect to local gravity level. Practically speaking, the potential on the surface is the minimum energy for landing on the asteroid from infinity or leaving the asteroid to infinity. Internal gravitational acceleration determines the stress and strain of the structure of asteroid. Outside acceleration determines the orbits of a probe. Slope is important for the analysis of dust motion on the surface of an asteroid because the tangent of this angle is equal to the steady friction coefficient of dust on its surface. As a byproduct, the calculation of the overall mean minimum slope can be an constraint of the free density parameter. The surface gravity magnitude is used to calculate the landing and take off of a probe on the asteroid. When we calculate the orbit around an asteroid, the landing and taking off, or the hopping on surface, we often meet the following kind of problems: (1) When do we have to use the time-consuming polyhedral method? (2) When can we use the fast spherical harmonic model? (3) How do we simply choose a good enough order and degree of spherical harmonic model? Rather than consider the abstract definition of the exterior Brillouin sphere, though it is sometimes regarded as the circumscribing sphere, \(r=0.879\) km for  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Castalia** & \multicolumn{3}{c}{**Rectangle (1.7 \(\times\) 0.9 \(\times\) 0.8)**} \\ \hline
**n** & **m** & **C\({}_{mm}\)** & **S\({}_{mm}\)** & **C\({}_{mm}\)** & **S\({}_{mm}\)** \\ \hline
0 & 0 & 1.000000000000000 & 0 & 1.000000000000000 & 0 \\
1 & 0 & \(-\)0.00014168122220 & 0 & 0.000000000000000 & 0 \\
1 & 1 & \(-\)0.00004075795821 & \(-\)0.000002282770478 & 0.0000000000000000 & 0.00000000000000000 \\
2 & 0 & \(-\)0.1047383593850 & 0 & -0.10240642551483 & 0 \\
2 & 1 & 0.00005077855278 & \(-\)0.00001641325376 & 0.00000000000000 & 0.00000000000000000000 \\
2 & 2 & 0.147471731853537 & -0.000007350942982 & 0.152450260149168 & 0.00000000000000000000000 \\
3 & 0 & \(-\)0.01992884455238 & 0 & 0.00000000000000000 & 0 \\
3 & 1 & \(-\)0.03410426627931 & 0.00074227942951 & 0.0000000000000000 & 0.00000000000000000000 \\
3 & 2 & 0.01165825781331 & 0.00224122654733 & 0.00000000000000000 & 0.00000000000000000000 \\
3 & 3 & 0.01779196117460 & -0.01186045941413 & 0.0000000000000000 & 0.0000000000000000000000 \\
4 & 0 & 0.03501656662646 & 0.0175424640102 & 0 \\
4 & 1 & 0.002602002008679 & 0.00163584922657 & 0.0000000000000000 & 0.0000000000000000000000 \\
4 & 2 & \(-\)0.04830393903696 & 0.00311423803618 & \(-\)0.039143149995087 & 0.0000000000000000000 \\
4 & 3 & 0.00690976107455 & -0.00383406677217 & 0.00000000000000000 & 0.0000000000000000000000 \\
4 & 4 & 0.04473930002048 & -0.01216108958396 & 0.019151577641493 & 0.0000000000000000000 \\
5 & 0 & 0.02398903330765 & 0 & 0.00000000000000000 & 0.000000000000000000000 \\
5 & 1 & 0.03681372375277 & -0.00231269356380 & 0.0000000000000000 & 0.00000000000000000000000000 \\
5 & 2 & \(-\)0.022854269738 & -0.00181873143701 & 0.000000000000000000 & 0.00000000000000000000000000 \\
5 & 3 & \(-\)0.02349704830265 & 0.00997187133947 & 0.000000000000000000 & 0. Castalia [8; 9], in this paper, we use the direct parameter, mean reference radius \(r_{0}\), to find some criteria to answer above practical questions. We also apply the conventional polyhedral model [7] without much modification of the algorithm to calculate the gravitational acceleration inside an asteroid without considering the internal Brillouin shpere. This could be a surprise for most researchers. We also use this polyhedral model to compute the gravitational acceleration on the surface of asteroid without using the special type interior/exterior spherical Bessel gravity fields [8]. In this circumstance, the polyhedral method also works well, which is known by very few researchers.