An attempt was made to use GEOS-C spacecraft height, as measured by the onboard radar altimeter, for an improved determination of the earth's gravitational field and for the determination of the variation of the physical surface of the oceans. Two tracking system approaches to accurately determine the spacecraft height (orbit) are described and their results stated. These are satellite-to-satellite tracking (SST) and ground-laser tracking (GLT). Height variations can be observed in the dm-regions using SST and in the m-region using present GLT

Vonbun, F. O.

English

NASA Technical Reports Server

4SATELLITE HEIGHT DETERMINATION USING
SATELLITE-TO-SATELLITE TRACKING AND GROUND LASER SYSTEMS
F. O. Vonbun
NASA/Goddard Space Flight Center
Trajectory Analysis and Geodynamics Division
Mission and Data Operations Directorate
6
The height of the GEOS-C spacecraft is one of the
more important parameters for earth and ocean dy-
namics and geodesy. It is the intent to utilize
this parameter, as measured by the onboard radar
altimeter, for an improved determination of the
earth's gravitational field and for the determina-
tion of the variation of the physical surface of
the oceans.
Two tracking system approaches to accurately de-
termine the spacecraft height (orbit) are described
and their results stated. These are satellite-to-
satellite tracking (SST) and ground-laser tracking
(GLT). Height variations can be observed in the
dm - regions using SST and in the m-region using
present GLT.
i. INTRODUCTION
The GEOS-C spacecraft will be the first one Lo make a
connection between the National Geodetic Satellite Program
and hopefully a new program, namely the Earth and Ocean
Dynamics Satellite Applications Program.
The major difference between GEOS-C and the two previous
spacecraft', GEOS-A and -B, is that this one carries a radar
altimeter and a satellite-to-satellite tracking system. I Both
are major experiments needed for future applications programs
in the area of earth and ocean dynamics. 2
Altimeter "data with errors of, say, ±3 to ±5 m will be
used for a more rigorous analysis, as done in the past, of
the earth gravity field and the variations of the physical
surface of the sea (gravity anomalies, geostrophic equilib-
rium of the sea, wind loading, storm surges, etc.). One of
the main advantages of height information for orbit and thus
gravity field analysis is the large number of data points
6-1
N78-15375
https://ntrs.nasa.gov/search.jsp?R=19730006648 2020-03-17T07:41:50+00:00Z
iobtainable (2 per second), their high accuracy and extremely
good along track distribution. For the determination of the
ocean height and its variations, the altimeter is at present
the only capable instrument.
As is the case for all measurements made, a zero adjust-
ment or an initial calibration will have to be performed by
each of the pertinent experimenters. The SST and GLT for
altimeter calibration and along track evaluation will be
briefly discussed.
II. ATS-F AND GEOS-C SATELLITE TO SATELLITE TRACKING
The ATS-F spacecraft will track, as shown in figure i,
the GEOS-C using a ~2000 MHz SST which measures range and
range rate sums. I With such a system, the orbits of ATS-F
and GEOS-C can be determined simultaneously with a high de-
gree of accuracy. In addition, after an initial independent
determination of the GEOS-C height (using, say, a radar, or
a laser ground or shipborne station), the SST will be able
to'_ollow" the GEOS-C spacecraft in a phase-locked fashion
over half the earth. Thus a constant "watch" can be kept on
the altimeter independent of any ground support. This is im-
portant if the height is to be used to check the variation
of the physical surface of the ocean, say from the U.S. to
Europe. The SST, as presently configured, should be able to
"detect" satellite height variations in the submeter level,
figure 2. Please note that only systems errors are included
which are of primary importance at this time. It is clear
that these system errors have to be smaller by a factor of 5
to i0 as compared to those expected from the eventual
experiments.
Figure 3 shows the height differences of GEOS-C orbit
due to different gravity fields as used in present day accu-
rate orbit determination. The fields used are the NWL and
the SAO fields. S _ Variations in the order of tens of meters
6-2
@
do occur. Improvements made in the meantime may reduce these
values by a factor of 3 to 5. Nevertheless this indicates
that for the GEOS-C, at least at the beginning of the flight
evaluation period, only relative height variations in the
submeter level will be detectable. S In other words, one can
only determine these variations consistent with one particular
gravity field used in the orbit determination process.
These considerations do not hold for the variation of
the physical sea surface. A trench (5 to I0 m over i00 to
200 km) can and will be fairly easy to detect. This holds
true for other variations in the height of the ocean surface
(tides, storm surges). Figure 4 shows a mathematically sim-
plified trench profile (Puerto Rico trench) and the expected
height variations (Ah = 15 m, Ah = 1.6 m/s). I Since the
satellite orbit will certainly not follow this kind of a
profile and the altimeter can be "watched" from the ATS for
any eventual drifts, such profiles should be fairly easy de-
tectable with the GEOS-C altimeter system as configured.
The contribution of the SST to the analysis of the
gravity field, and in particular to the determination of
anomalies, is out of the content of this paper and is dis-
cussed in references 5, 6, and 7.
III. GEOS-C LASER GROUND TRACKING
In addition to the SST approach, precision GLT systems
will be used as an additional method of determining the "real"
height of the GEOS-C spacecraft independent of the dynamics
of the orbit.
As shown in figure 5, three precision ground laser sta-
tions are planned to be used in the Caribbean area. The sta-
tions will be near the sea (for ease of level determination)
at Key West, Canal Zone, and Antigua to form a good three-
dimensional triangle (station distances commensurate with
satellite height) of near optimum conditions. It is assumed
that the uncertainty of the sea surface over this area is
6-3
approximately two meters. Using these three stations, the
height of the spacecraft can be determined completely indepen-
dent of the orbital dynamics earth gravity field and its
rather large uncertainties, as shown in figure 3. Figure 6
depicts the height errors of the spacecraft as a function of
the ground track. 8 Please see also for comparison figure 5
showing the ground track and the position of the spacecraft
(time ticks) relative to the three ground stations_ It can
be seen (fig. 6) that over a rather large subsatellite track
(500 to i000 km), the spacecraft height can be de_termined
with these laser systems to within two to three meters. Please
note that this assumes that the relative errors are ±5 to 10 m
in longitude and latitude, and ±2 m in height for Key West and
Antigua and zero (arbitrary reference) for the Canal Zone.
The present (i0 cm in the future) tracking system's
capabilities of 30 cm (noise, bias) of the laser systems are
far below the errors considered_ so they do not constitute a
limit. On the contrary, they enable one to determine relative
_ntersite distances from 30 to 50 cm. This result was ob-
tained during the recent Goddard Polar Motion Experiment as
reported in reference 9. Thus, the errors of five meters, as
shown in figure 6, for the error of the intersite distances
can be reduced considerably by the method used for the Polar
Motion Experiment which in turn will reduce the depicted
height errors. This, of course, assumes that the problems
associated with the reflection from the sea surface have been
_olved to a compatible accuracy.
In conclusion it can be stated: Both methods, the SST as
well as the GLT can be used, under the conditions stated, to
determine the height of the GEOS-C spacecraft with errors com-
_=nsurate of the radar altimeter. It should be noted that
both methods are rather independent of the final choice of the
orbit.
6-4
}I
/i!_
!
approx:::mately two meters. Using these three stations, the
helgh: =f the spacecraft can be determined completely indepen-
dent _ _he orbital dynamics earth gravity field and its
rather _mrge uncertainties, as shown in figure 3. Figure 6
depict_ :he height errors of the spacecraft as a function of
the gro,u_d track, e Please see also for comparison figure 5
showing :he ground track and the position of the spacecraft
(time =_ks) relative to the three ground stations, It can
be see= _i_ig. 6) that over a rather large subsatellite track
(500 to _00 km), the spacecraft height can be determined
with the_ laser systems to within two to three meters. Please
note tham _his assumes that the relative errors are ±5 to lO m
in iongi=:_e and latitude, and ±2 m in height for Key West and
Antigua a:L_ zero (arbitrary reference) for the Canal Zone.
The _:esent (i0 cm in the future) tracking system's
capabili=±_ of 30 cm (noise, bias) of the laser systems are
far below :_e errors considered, so they do not constitute a
limit. O= :he contrary, they enable one to determlne relative
interslte distances from 30 to 50 cm. This result was ob-
_alned duri-_g the recent Goddard Polar Motion Experiment as
reported im meference 9. Thus, the errors of five meters, as
shown in f£_ure 6, for the error of the intersite distances
can be reduced considerably by the method used for the Polar
Motion Experi_ent which in turn will reduce the depicted
height errorg- This, of course, assumes that the problems
associated wi_h the reflection from the sea surface have been
solved to a c_mpatible accuracy.
In conci:Lsion it can be stated: Both methods, the SST as
well as the GLT can be used, under the conditions stated, to
4etermlne the _height of the GEOS-C spacecraft with errors com-
n_usurate of =[ne radar altimeter. It should be noted that
both methods are rather independent of the final choice of the
orbit.
6-4
iI
I
REFERENCES
DeWitt, R. N. (1962), Derivations of expressions describing
the gravitational field of the earth, Technical Memoran-
dum #K-35/62, U.S. Naval Weapons Laboratory, Dahlgren,
Virginia.
Gaposchkln, E. M., and K. Lambeck (1970), 1969 Smlthsonian
standard earth, SAO, Special Report #315, May.
Mueller, P. M., and H. L. Sjorgeu (1968), MASCONS:
mass concentrations, Science, 161, 680-684.
Lunar
NASA (1970), Earth and ocean dynamics satellite applications
program, April i (Washington, D. C.) (Preliminary Issue).
Schwartz, C. R. (1970), Gravity field refinement by satellite-
to-satellite Doppler tracking, Contract Number NGL 36-
008-093, OSURF Project Number 2514, December, Ohio State
University, Report Number 147.
Vonbun, F. O. (1971), The ATS-F/NIMBUS-E tracking experiment
Presented at the 48th IAU Symposium, May 9-15, Morioka,
Japan.
Vonbun, F. O. (1971), Geodetic satellite mission and GEOS-C
spacecraft, Space Res. XI, Academy Verlag, Berlin,
457-467.
6-5
/\
i
/
/
/
/
/
6-6 !
I
I
I
I
I
I
!
I
I
I
0
Z
o
"0
r_
_!!ii_ii_iii!!i_iiiiiiiiiiii!iii!ii_iiiiiiiii_iiiiiii_iiiii_i_ii_ii_ii_:::`
..:.::_:_!_iii_iii!iiii!iiiiiiiii_iiiiiiiiiiii_i!iiiii_i_ii_iiiiiiiii!iiiii_:. o
':::iii!i!iiiiiii!iiii!!iii!iiiiiiiiiiii_i!iiii!iiii!i_ii!_ii_i_: 00
'":'::i:iiii!iiiiiiiiiiii!ii:!:i:i:i:iiiii!iiii!iiii!!iiiii!::.... 0
========================:i:i:!::::::: ::::::::::::::::::::::::::::: I_
• "'"::::i:!:i:i:i:!:::::i:i:i:i:i::i:iiii_'i:i:i:i:!:i:i:!:i:!:i:i::.. r_
_...._..Q:_ =============================================================================_r_,,_,_,__iiiiiiii _
_ _ :::::::::::::::::::::::::::::::::::::::::::::
--..I -.I "'"::::!iiii!iiiii!iiiiiiiiiiiii!iii!iii!ii!iiii!iii:i:i:i::..
 iiiiiiiiiiiiiiiiiiiiiiiiiiii!i!iiii 
r_ '":'::i:i:!:!:!:i:i:i:i:!:i:i:i:i:i:i:i:!:i:i:::i:::...
_ _iiiiiiiiiiiiii!iiiiiiiiiiii!iiii!__,
0
0
0
I I I I I I I I I
C_ GO I",- _0 _ _ or) C_I
0 0 0 0 0 0 0 0 C)
0 I._ ia, I
Z
C_ i,-- 0
_1_ w i-
z
0
6-?
A
E
v
,q
0
0
oq
r_
uj L.-
i3_ .==i
I--.Z
c.._ om
u.i ,,_
C..30|
oO! ==.
_l.iJ
C.._
A
E
<3
I....
f.-
E
C_ o
OCt'>
""
,-4 II
X N
C_
00
m
133
o
l I I I I
CO C_I ,-.4 ,...4 @,,I CO
I I I
6-8
-@,
C_
<k_
:!
i
HEIGHT H T " "" -
, t=O / _" t=TI--" = T ;
- - / _ ,'*I"7_] , n_" _"////////.,"/
- " - ----.e-- - ' _ . ' .... "_ -
L w
|_ _-_
W
T=_
V
=" v e sin_/ GEOS-C HEIGHT VELOCITY e<<l
Y = 7 sin( t +-_-) TRENCH PROFILE (Approx.)
. h [2T_ 2_r _r
=T.-f-. cos(-i-_+_-) _.c.._.G._ v_oc._¥
_'• =- _---, -_-sin t+ _--)TRENCH HEIGHT ACCELERATION
FOR GEOS-C:
WITH h=15m, w=210km, T=30 sec, v--'7 km/s e=0.0322
• • 30 • • "° "HM_=2 m/s, YMAX= 1.6 m/s, YMAX=0.34 m/s 2
= 3.4.10-2g
Figure
_6-9
/i
Z
I,a,,I
I,,I.I
I,"-
I,,z,,i
l,Ji,J
c/}
c/}
II
c/)
IjJI
i,i
Z
Z
0
P_
0
o
0
o
,%
6-10
r_
_ _- or; _
6-11
:,!i
,j
i
II
6-12
L_ 0
II
0
0
0
0
0
0
0
0
m0
6-13


Satellite height determination using satellite-to-satellite tracking and ground laser systems

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server