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Solid body does not flow like fluid, the Navier-Stokes Equations doesn't seem to be applicable in such case. However, the equation can be used to calculate the critical mass for the self-gravity of a solid body to overcome its resistant forces so that it assumes a hydrostatic equilibrium (nearly round) shape. Solid body actually has | ||

## Figure 21 Deformation of Solid Body |
## Figure 22 Geometric Shape [view large image] |
elastic property, that makes it to deform in response to the external force as shown by the deformation of the moon by the gravitational tug of a planet in Figure 21. |

Since there is no flow in solid body

The external force per unit mass is just the gravitational force (per unit mass):

The pressure gradient in terms of the spherical coordinate r is:

p = dp / dr = B / r ---------- (29)

where B = stress/(% volume compression) = dp/(V/V) is the Bulk modulus, the value of which ranges from 0.02 x 10

Substituting Eq.(28) and (29) into Eq.(27) yields:

GM / r

There are 3 possible cases for the development of geometric shape :

Case 1: GM / r

Case 2: GM / r

Case 3: GM / r

Eq.(30) can be simplified further, if we assume uniform distribution of matter:

B = GM

Table 01 lists some solid objects have (or have not) sufficient gravitational strength to develop a spherical shape (to overcome the elastic resistance of the material).

Object | Type | Mass M (gm) | Radius or Size r (cm) | B (10^{12}dynes/cm^{2}) |
Geometric Shape |
---|---|---|---|---|---|

Neutron Star | Star | 0.2 - 6.0x10^{33} |
~1.0x10^{6} |
~ 10^{22} - Super-hard |
Spherical |

Mercury | Planet | 3.6x10^{26} |
1.1x10^{8} |
14.4 | Spherical |

Venus | Planet | 5.7x10^{27} |
5.7x10^{8} |
5.2 | Spherical |

Earth | Planet | 6.0x10^{27} |
6.0x10^{8} |
4.5 | Spherical |

Moon | Satellite | 7.2x10^{25} |
7.8x10^{7} |
2.3 | Spherical |

Mars | Planet | 6.6x10^{26} |
3.0x10^{8} |
0.9 | Spherical |

Pluto | Dwarf Planet | 1.2x10^{25} |
1.2x10^{8} |
0.01 | Spherical |

Phobos | Satellite of Mars | 1.0x10^{19} |
2.7x10^{6} |
N/A | Irregular |

Deimos | Satellite of Mars | 1.8x10^{18} |
1.5x10^{6} |
N/A | Irregular |

Itokawa | Asteroid | 3x10^{13} |
5.4x10^{4} |
N/A | Irregular |

Comet | Planetesimal | ~6x10^{15} |
~6x10^{4} |
N/A | Irregular |

Human | Living Organism | ~10^{5} |
~2x10^{2} |
N/A | Definitely not Spherical |

Neutron | Composite Particle | 1.67x10^{-24} |
~10^{-13} |
N/A | Unknown |

Electron | Elementary Particle | 9.1x10^{-28} |
~10^{-16} |
N/A | Unknown |

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