Consider the case of a pure gas planet where the hydrostatic law is dpdz=−ρ(z)Gm(z)/z2: , where G is the gravitational constant and m(z)=4π∫z0ρ(ζ)ζ2dζis the planetary mass up to distance z from the center of the planet. If the planetary gas is perfect with gas constant R, determine ρ(z) and p(z) if this atmosphere is isothermal at temperature T.
Answers
Answer:
In fluid mechanics, hydrostatic equilibrium or hydrostatic balance (also known as hydrostasy)[1][2] is the condition of a fluid at rest. This occurs when external forces such as gravity are balanced by a pressure-gradient force.[3] For instance, the pressure-gradient force prevents gravity from collapsing Earth's atmosphere into a thin, dense shell, whereas gravity prevents the pressure gradient force from diffusing the atmosphere into space.
Hydrostatic equilibrium is the current distinguishing criterion between dwarf planets and small Solar System bodies, and has other roles in astrophysics and planetary geology. This qualification means that the object is symmetrically rounded into an ellipsoid shape, where any irregular surface features are due to a relatively thin solid crust. In addition to the Sun, there are a dozen or so such non-satellite objects confirmed to exist in the Solar System, with others possible.