PDS_VERSION_ID = PDS3
RECORD_TYPE = STREAM
OBJECT = TEXT
INTERCHANGE_FORMAT = ASCII
PUBLICATION_DATE = 2019-06-01
NOTE = "Description for Venus Climate Orbiter (VCO,
also known as PLANET-C and AKATSUKI) RS data
calculation including calibration"
END_OBJECT = TEXT
END
calculation to derive the current product
=========================================
This file is created by extracting texts from [IMAMURAETAL2011].
Schematic diagram of radio occultation experiments
--------------------------------------------------
The following two diagrams, global view and close-up view, show the
geometric relation among the Earth, Venus, Akatsuki, Venusian Atmosphere,
and ray path of the transmitted wave using Ultra-Stable Oscillator from
Akatsuki. Note that the bending of the ray path for each is exaggerated.
global view
-----------
(2) The wave propagates through the Venusian atmosphere
and the ray path of the wave is bended.
..------------..
.'' _______ ``.
/ ..'' ``.. \
/ .'' ray path ``. \
|.' _______ `.|
.' / \ `.
.' | | | | `. .__
.' | | Venus | | `. |`. (1) transmission
.' | | | | `. `. of the wave
Earth | \_______/ | `. `.
\ / `. `.
(3) The wave \ / Akatsuki
is received `. .'
by ground ``-------------''
station at the Earth.
close-up view
-------------
asymptotes
`. .'
`. .'
`. .'\
`x' | ``alpha''
.' `. /
.------.'-----`.--------.
.-' .' `. `-. Venus' atmosphere
.-' .' `. `-.
.-' .' `. `-.
/ .'__..------+------..__`. \
.' ..'' ray path | ``.. `.
/ .' | `. .__
| .'\ | ``r0'' /`. |`. transmission
.' \ ..--------|-------.. / `. `. of the wave
.' \ ' Venus | ` / `. `.
ray path .' \ body | / `. `.
.' \ | / ray path `. `.
.' \ | / `.
.' \ | / to Akatsuki
.' ``a'' \ | / ``a''
to Earth \ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\|/
+
center of Venus
Note that the variables -- that are enclosed with `` '' -- are described
in the next section.
Variables, equations, and the parameters used
---------------------------------------------
-- variables --
name label name if any description
----- --------------------- ------------------------------------------
r_0 RADIUS (L3) distance of the ray from the center of
Venus at closest approach to Venus
alpha BENDING_ANGLE (L3) asymptotic bending angle for a radially
symmetric atmosphere.
a IMPACT_PARAMETER (L3) ray impact parameter
n REFRACTIVE_INDEX (L3) refractive index
mu REFRACTIVITY (L3) refractivity
-- equations --
n(r0) * r0 = a (Bouguer's rule) eq. (1)
where r0 is function of a.
/inf 1 dn 1
alpha = -2a | --- -- ------------------------- dr eq. (2)
/r_0 n dr sqrt( (n * r)**2 - a**2 )
where dn/dr is partial derivative.
1 /inf [ a / ( a ) \ ] dalpha
ln n(r) = - -- | ln [ --- + | (---)**2 - 1 |**(1/2) ] ------ da
PI /a_1 [ a_1 \ (a_1) / ] da
eq. (3)
where a_1 is function of r. ``alpha'' and ``a'' are calculated from
the measured atmospheric Doppler shift and the reconstructed velocity
and position vectors of the spacecraft and the ground stations.
The refractivity mu is related to the refractive index by
mu = (n-1) x 10**6 eq. (4)
and mu is the sum of the contributions from the neutral atmosphere and
the ionosphere:
beta * N_e
mu = V * N - ---------- * 10**6 eq. (5)
f**2
where V is the refractive volume, N is the number density of the
neutral atmosphere, beta = e**2/(8*pi**2*epsilon*m_e) ~ 40.3 m**3 s**-2
with e, epsilon and m_e being the elementary charge, dielectric constant
in vacuum and electron mass, respectively, c is the speed of light, N_e
is the number density of electrons, and f is the frequency of the
carrier signal. On the assumption that the neutral atmosphere is well
mixed, we adopt a constant V of 1.81 x 10**-17 m**3 based on the
composition of 96.5% CO2 and 3.5% N2 using the constants given in
[FJELDBO&ESHLEMAN1968]. The neutral and ionospheric contributions are
separated in altitude (see results of [PAETZOLDETAL2007]). This enables
us to retrieve the vertical profiles of the neutral atmospheric density
N and the electron density N_e separately.
The vertical profile of the neutral atmospheric pressure, p(r), is
derived from the density profile N(r) by integrating the equation of
hydrostatic equilibrium:
/ r_top
p(r) = p(r_top) + m | N(r') * g(r') dr' eq. (6)
/ r
where m is the mean molecular mass, g is the acceleration due to
gravity, and r_top is the adopted upper boundary. The ideal gas law
relates p(r_top) to the atmospheric temperature T at this height as
p(r_top) = N(r_top) * k * T(r_top), eq. (7)
where k is the Boltzmann's constant. The boundary condition required
for the integration is the value T(r_top). The temperature profile
T(r) is calculated from N(r) and p(r) using the ideal gas law. The
influence of the adopted T(r_top) on the calculated T(r) is almost
negligible except at the uppermost 10 km [PAETZOLDETAL2007,
TELLMANNETAL2009].
The received signal power varies during each occultation experiment
due to atmospheric defocusing and absorption. The former must be
taken into account when retrieving the vertical distribution of
absorbing materials from the observed signal power.
Atmospheric defocusing is caused by the radial gradient of the
refractive index. The defocusing loss is estimated by [ESHLEMAN1973]
L = ( cos alpha - D (d alpha / d a) )**-1 eq. (8)
where D is the distance from the spacecraft to the crossing of the
ray asymptotes.
Once the defocusing loss is estimated as a function of time from
trajectory information and the relationship between alpha and a from
the Doppler measurements, one may calculate the total atmospheric
absorption from the time series of the received signal power. This
time series is converted to a height profile of the absorptivity with
the aid of ray tracing on the assumption of a spherically symmetric
atmosphere [JENKINS&STEFFES1991, JENKINSETAL1994]. The absorption due
to CO2, N2, and SO2 is removed from the absorptivity profile based on
its dependence on the ambient pressure and temperature. The remaining
absorption will be principally due to H2SO4 vapor.
-- Summary of the assumed parameters --
Venus radii: 6052 km
GM: 3.24858592 x 10**5 km**3 s**-2
V: 1.81 x 10**-17 m**3