62 lines
2.2 KiB
Python
62 lines
2.2 KiB
Python
import numpy as np
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from ..utils.utils import alt_conver,check_altitude
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def expo(alts,alt_type='geometric'):
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'''
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Estimate the air densities at given geometric or geopotential altitudes
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above the sea level using a exponential atmosphere model from
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Vallado, D. A. (2013). Fundamentals of astrodynamics and applications (4th Edition). Microcosm Press.
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Usage:
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rhos = expo(alts)
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or
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rhos = expo(alts,'geopotential')
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Inputs:
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alts -> [float list/array] altitudes, [km]
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Parameters:
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alt_type -> [string] type of altitudes, which may either be 'geopotential' or 'geometric'.
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Outputs:
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rhos -> [float array] densities at given altitudes, [kg/m^3]
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Reference:
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'''
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# Get geometric and geopotential altitudes
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zs,hs = alt_conver(alts, alt_type)
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# Base altitude for the exponential atmospheric model, [km]
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zb = np.array([0., 25, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120,
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130, 140, 150, 180, 200, 250, 300, 350, 400, 450,
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500, 600, 700, 800, 900, 1000])
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zb_expand = zb.copy()
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# Set the two endpoints of base altitude to a small enough and a large enough value respectively for extrapolation calculations.
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zb_expand[0],zb_expand[-1] = -np.inf,np.inf
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# Nominal density for the exponential atmospheric model, [kg/m³]
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rhob = np.array([1.225, 3.899e-2, 1.774e-2, 3.972e-3, 1.057e-3,
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3.206e-4, 8.770e-5, 1.905e-5, 3.396e-6, 5.297e-7,
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9.661e-8, 2.438e-8, 8.484e-9, 3.845e-9, 2.070e-9,
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5.464e-10, 2.789e-10, 7.248e-11, 2.418e-11,
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9.518e-12, 3.725e-12, 1.585e-12, 6.967e-13,
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1.454e-13, 3.614e-14, 1.170e-14, 5.245e-15,3.019e-15])
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# Scale height for the exponential atmospheric model, [km]
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ZS = np.array([7.249, 6.349, 6.682, 7.554, 8.382, 7.714, 6.549,
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5.799, 5.382, 5.877, 7.263, 9.473, 12.636, 16.149,
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22.523, 29.740, 37.105, 45.546, 53.628, 53.298,
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58.515, 60.828, 63.822, 71.835, 88.667, 124.64,181.05, 268.00])
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check_altitude(zs,(-0.611,1e3),'warning')
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inds = np.zeros_like(zs,dtype=int)
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for i in range(len(zs)):
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inds[i] = np.where((zs[i] - zb_expand) >= 0)[0][-1]
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rhos = rhob[inds]*np.exp(-(zs-zb[inds])/ZS[inds])
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return rhos |