## P

Usually, one or more profiles of p(z) will be specified to a project, a nominal profile and two extremes (as for the entry analysis). A very crude profile can be generated with the assumption of constant temperature and composition, such that in hydrostatic equilibrium the atmosphere follows an exponential law, with p(z) = p(0) exp(-1) (4.3)

 (kg m"3) (s) Venus 8.9 90 740 44 64.4 4 4225 Earth 9.81 1 288 29 1.21 8.4 28 296 Mars 3.7 0.007 200 44 0.02 10.2 141 72 Jupiter 24.9 2 180 2.3 0.31 26.1 90 290 Saturn 10.4 1 120 2.1 0.21 45.7 70 650 Titan 1.35 1.5 94 28 5.37 20.7 5 4125 Uranus 10.4 1 75 2.3 0.37 26.1 53 491 Neptune 13.8 1 70 2.8 0.48 15.1 54 281

where p(0) is the surface density and H is the e-folding distance, or density scale height, given (for an ideal gas) by

where R is the universal gas constant, 8314Jkg—1 K—1, T the absolute temperature and M the relative molecular weight of the atmosphere. For Earth, the scale height is 8314X288/(9.8X28), equal to ~8.7km.

The time to fall through the bottom scale height is ~H/Vt(0), and each additional scale height above takes a factor ~ e—a5 = 0.6 times as long. Typically, planetary probes descend through about four scale heights, corresponding to a variation of ~100 in density.

If released from rest (as, for example, when a parachute line is cut) the vehicle will reach a new terminal velocity with a characteristic timescale of ~V/g.

Atmospheric temperatures vary significantly with altitude. In thin atmospheres (essentially, stratospheres) where absorption of sunlight at high altitude is the controlling factor, temperatures may increase or stay roughly constant with height, and there is relatively little vertical motion. Below some altitude, however, temperatures are controlled by the vertical transport of heat from either the hot depths of the giant planets, or the surface where sunlight is absorbed. In this tropospheric regime, temperatures fall with increasing altitude, often at a roughly linear rate that is equal to or below the adiabatic lapse rate, dT/dz = r = — g/cp, where cp is the specific heat of the gas; for Earth in dry air, r = —9.8/1000 10 K km— .

Table 4.1 gives parameters for the planets, together with typical speeds and timescales.  