<DOC>
<DOCNO>
548
</DOCNO>
<TITLE>
the contraction of satellite orbits under the influence
of air drag . pt .iv with scale height dependent on
altitude .
</TITLE>
<AUTHOR>
king-hele,d.g., and cook,g.e.
</AUTHOR>
<BIBLIO>
rae tn.space 18, 1962.
</BIBLIO>
<TEXT>
  the effect of air drag on satellite
orbits of small eccentricity e
was studied in part i (tech. note
gw 533), on the assumption that
atmospheric density varies exponentially
with distance r from the earth's
centre, so that the 'density scale height'
h, defined as, is
constant .  in practice h varies with height
in an approximately linear
manner, and in the present note the theory
is developed for an atmosphere
in which h varies linearly with r .  equations
are derived which show how
perigee distance and orbital period vary
with eccentricity, and how
eccentricity varies with time .  expressions
are also obtained for the lifetime
and air density at perigee in terms
of the rate of change of orbital
period .  the results are also presented
graphically .
  the results are formulated in two
ways .  the first is to specify the
extra terms to be added to the constant-h
equations of part i .  the second
the best constant value of h for
use with the equations of part i .  for
example, it is found that the
constant-h equations connecting perigee
distance (or orbital period) and
eccentricity can be used unchanged without
loss in accuracy, if h is taken
as the value of the variable h at a height
above the mean perigee height
during the time interval being considered,
where, and
decreases from to 0 as e decreases
from 0.02 to 0 .  similarly the
constant-h equations for air density at
perigee can still be used if h is
evaluated at a height above perigee,
where, and
decreases to zero as e decreases from
constant-h equations can still be used
if h is evaluated at the scale height
below the initial height .  variation of
h with altitude has a small effect
on the lifetime - about 3 - and on the
e-versus-time curve .
</TEXT>
</DOC>
