Orbit Decay Characteristics Due to Drag

Parsons, W. D.

doi:10.2514/8.6411

Cited by 10 publications

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“…can be integrated to give r 2 (d6/dt) -h (a const) (4) This relation is used to change the independent variable from Uo0by The perturbed form of Eq. (8), assuming that drag is canceled by thrust, gives …”

Section: Discussionmentioning

confidence: 99%

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Analytic solution of the synergetic turn.

Parsons

1966

Journal of Spacecraft and Rockets

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Nomenclature a = acceleration normal to flight path, g's A = aerodynamic reference area, ft 2 CD = D/qA, drag coeff (D = drag, Ib)-acceleration of gravity on earth, 32.2 fps h = altitude measured from earth's surface, naut mile, or angular momentum lot Ii -zer° an d first-order modified Bessel function, respectively m = mass, slugs Q = right-hand side of differential Eq. (9) q = dynamic pressure = pF 2 /2, psf r -radial distance from earth's center = R + h, naut mile R = earth's radius, 3440 naut mile t = time, sec V = velocity, fps W = weight = mg, Ib X, Y, Z = radial, planer, and lateral forces, respectively, Ib a.= angle of attack, rad l/f3 = atm scale height, naut mile A = perturbation quantity y = r" 1 , (naut mile)" 1 = lateral spherical coordinate, measured from unperturbed orbital plane, rad p -density, slugs/ft 3 a-= -2/3r 0 (ATYy 0 )retro, or (-1/2)0 Ar, Eq. (20) 6 = polar spherical coordinate measured in unperturbed orbital plane from apogee, rad 8 = inclination of thrust axis from flight path, deg Subscripts o = initial or unperturbed orbital condition R = at earth's surface

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Section: Discussionmentioning

confidence: 99%

“…. + (4) Combining the foregoing equations, one obtains for the t If p 2 = 0 and m = 0, then (0)° is understood to be 1; this accommodates the case where the incoming energy illuminates the bottom directly without previously undergoing a reflection.…”

Section: Methods Of Calculationmentioning

confidence: 98%