Anomalous accelerations of Pageos satellite and application of theory to predict perturbations in mean motio

Kissel, K. E.

Smith, D. E.

English

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D. E. SMITH
K. E. KISSELL
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X-553-71-338
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ANOMALOUS ACCELERATIONS
OF THE PAGEOS SPACECRAFT
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AUGUST 1971
	
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ANOMALOUS ACCELERATIONS OF THE PAGEOS SPACECRAFT
D. E. Smith
Geo3ynamics Branch
Trajectory Analysis and Geodynamics Division
and
K..^ Kissell
General Physics Research Laboratory
Aerospace Research Laboratories, AFSC
Wright-Patterson Air Force Base, Ohio
August 1971
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GODDARD SPACE FLIGHT CENTER
Greenbelt, Maryland
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ANOMALOUS ACCELERATIONS OF THE PAGEOS SPACECRAFT*
D. E. Smith
K. E. Kissell
ABSTRACT
Observational studies of PAGEOS have indicated that the balloon satellite ex-
periences very large periodic accelerations whenever the orbit intersects the
Earth's shadow. In 1969 the amplitude of these anomalous accelerations was
about 10 -4 revolutions per day 2 with a period of 10 to 15 days and caused along-
track deviations of the spacecraft from its expected position of 20 to 40 km. It
has been suggested by Professor I. Shapiro of the Massachusetts Institute of
Technology that these accelerations are abnormal solar radiation pressure
perturbations caused by the non-sphericity of the spacecraft and its rotational
motion on its axis.
During 3 months in 1969 the dynamical behavior of PAGEOS on its axis and the
detailed shape of the balloon were determined by the USAF Aerospace Research
Laboratories at Wright-Patterson AFB from photometric observations by new
methods. These studies showed that PAGEOS is not spherical but ellipsoidal
with major and minor axes approximately 34 meters and 27 meters, respectively
and rotating about a minor axis which is itself precessing.
These results on the dynamical behavior of PAGEOS have been used in a new
theory of radiation pressure perturbations developed at Goddard Space Flight
Center that includes the effects of spacecraft attitude, rotational behavior and
specular and diffuse reflection and used to predict the acceleration of PAGEOS
for 3 months in 1969. The predictions, based on the observed rotational motion,
a specular reflectivity of 85% and a spacecraft mass of 55 kg, show that the new
theory computes the observed anomalous accelerations of PAGEOS to about 10-5
revolutions per day 2 , or better than 10%. This is believed to be one of the first
demonstrations of coupling between the rotational motion of a spacecraft on its
axis and the dynamics of its orbit.
*Paper presented at Working Group 1, COSPAR, Seattle, Washington, June 1971.
•	 111
0ANOMALOUS ACCELERATION.: OF THE PAGEOS SPACECRAFT
INTRODUC'T'ION
Satellites of large cross-sectional area to mass ratio are known to be strongly
perturbed by the forces of solar radiation pressure. Such radiation pressure
= forces indirectly caused the demise of Echo I in 1968.
	 Studies (1, 2) of the be-
-- havior of two other inflation-deployed spacecraft, the 2.5-meter diameter
sphere 1963-30D (DASH 2) and the 30-meter diameter sphere 1966-56A
-_ (PAGEOS), both Ln high polar orbits, have demonstrated that our present theo-
retical treatment of radiation pressure indeed goes far in explaining the im-
portant secular and long period changes to the orbit. 	 How-ver, these same
studies also indicate that bot!i balloon spacecraft undergo accelerations that
cannot be explained by the ncrmal treatment of radiation pressure. Neither
can these anomalous perturbations be explained by Earth-reflected radiation
pressure, air drag, or luni-:solar gravitational effects.
	 Since these satellites
were launched for study of high-altitude air drag and geodetic position, it is
important that their orbital motions be well understood.	 These anomalous per-
turbations, recognized in 19 ,39, are evidenced by regular motion of the space-
craft alternately ahead and then behind the position in its orbit to be expected
on the basis of the most complete, normal theory. Such accelerations affect,
- therefore, the mean motion of the spacecraft in its orbit.
This paper reports on the perturbations in mean motion predicted by a new
theoretical treatment of radiation-pressure which accounts for non-isotropic
°i scattering of solar radiation from a rotating ellipsoidal body and a comparison
of these perturbations with the observed mean motion of the PAGEOS space-
craft during a time interval when the rotational dynamics had been determined
by a new method; namely, photoelectric photometry. 	 The theory necessarily
incorporates the orientation for and precessional movement of the rotation axis
of the satellite.	 This development is similar to that given by Shapiro (3) for the
radiation pressure effects on a cylindrical satellite. 	 We will show that there
exists a coupling between the spin and orbital dynamics of the low mass-to-area
satellites if their scattering is isotropic and that the effect is noticeable in the
orbital behavior.
DISCUSSION OF THE OBSERVED PERTURBATIONS
A polar orbit at an altitude of about 4000 km intersects the Earth's shadow for
a period of approximately 3 months followed by an almost equal period of full
sunlight until the orbit again enters the Earth's shadow as the Earth moves
s
6around the sun. This behavior is observed for both DASH 2 and PAGEOS.
During the all-sunlight period, in agreement with theory, virtually no long-
period or secular mean-motion perturbations of these spacecraft were detecta-
ble in these studies. As soon as the orbits entered the shadow, however, a
large perturbation due to solar radiation pressure was observed as expected.
Unfortunately, the character of the acceleration of both s pacecraft, during every
shadow period, differed significantly from what was anticipated. In addition, to
the normal radiation pressure perturbations, there appeared to be a very large
periodic perturbation with an amplitude nearly as large as the normal pertur-
bation. The period of the effect on DASH 2 was many weeks during the first
shadow period after launch and steadily decreased so that four years after
launch, the period of the ai,omalous acceleration for DASH 2 had reached
2 weeks. Three years after launch the period for PAGEOS was about 11 days.
Since the PAGEOS launch in 1966, the OPOS Observatory of the USAF Aerospace
Research Laboratories at Wright-Patterson AFB, Ohio, has been making photo-
electric brightness measurements of the spacecraft (4) as part of a program to
explore the capabilities of passive optical photometry for the remote-sensing
of spacecraft properties. By utilizing the variations with time of the sunlight
scattered from the PAGEOS aluminized outer surface, it has been possible to
deduce, during certain periods, the spin rate, spin-axis orientation and preces-
sion, and the shape of the balloon (5). These studies indicate that the PAGEOS
balloon has gradually become prolate and that it is spinning about a minor axis
with a period varying between 190 and 350 seconds. In addition, the spin axis is
found to be precessing at varying rates about an axis that always points toward
the sun. Figure 1 shows the location of the rotation axis during the period
August-December 1969. It is to be noted that the spin axis precessed very
rapidly, at about 25 deg/day daring August., increasing to 45 deg/day at the be-
ginning of November, then dropping again to 25 deg/day in late November. The
angle between the spin and precession axes was about 65 degrees. The physical
cause of this dynamical behavior of PAGEOS on its axis remains unexplained,
but, because its precession axis appears locked to the sun, the forces of solar
radiation pressure might well be the driving mechanism.
THEORETICAL ANALYSIS
The possibility h2a been exauuined theoretically (6) that the anomalous orbital
accelerations are coupled with the non-sphericity of the balloon and its observed
rotational behavior. In particular, a theory has been elaborated for the effect of
solar radiation pressure on the orbit of an ellipsoidal-shaped spacecraft, spin-
ning about an axis that is processing and including the effects of both diffuse and
specular reflection of sunlight from the satellite's surface. The essential
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modification made to the normal treatment of radiation pressure is that account
was taken of the direction in which sunlight is reflected from the satellite. In
the normal treatment it is assumed that the reflected radiation is symmetric
about the satellite-to-sun line so that the acceleration is always directed away
from the sun: this is obviously true for spheric:.tl satellites but is not true, in
general, for an ellipsoid. Under these circumstances there is a "Sideways"
component to the radiation pressure force which causes additional perturbations
of the orbit, analogous to the lateral accelerations of a tacking sailboard.
APPLICATION OF THE THEORY
This theory has now been tested numerically against orbital data obtained from
the Smithsonian Astrophysical Observatory. The positions of the spin a.\is of
PAGEOS obtained by the .Aerospace Research Laboratories, together with their
estimate of the prolate shape of the spacecraft and of its reflective properties
were used to compute the acceleration of the spacecraft between July and
October 1969. During most of this time the orbit of PAGEOS intersected the
Earth's shadow and large perturbations of the orbital mean motion were ob-
served. The accelerations computed from the normal an,f modified theories
together with the acceleration observed by the Smithsonian Astrophysical Ob-
servatory are shown in Figure 2. The spn.eecraft parameters used in the com-
putation of the balloon's behavior were: polar radius 1.,'..0 meters; major equa-
torial radius 17 meters: minor equatorial radius 13.5 meters; mass 55 kgm;
spec, Jar albedo 0.85, diffuse albedo 0.0.
The agreement between the theory and observations is clearly evident in
Fignire 2. It' should be noted that the theory does not indicate any perturbation
of the acceleration when the orbit is fully in sunlight, .. result in agreement
with the theory for a spherical satellite. When the orbit is partially shadowed,
an oscillation caused l;y the precession of the spin axis about the sun is clearly
evident as is the steadily increasing rate of precession. The differences be-
tween the theory and t'he observations suggest that the root-ineali-square of the
residuals is about 101n of the amplitude of the perturbation after allo '.Wing for
an apparent phase drift. The residuals are comparable in magnitude to the
slight accelerations actually observed during periods when the orbit is in
complete sunlight.
CONCLUSIONS
We believe the agreement obtained between the new theory and the observations
is one of the first der.ionstrations of coupling between the rotational dynamics
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•of a spacecraft about its center of mass and the orbital dynamics of the
spacecraft about the Earth. The perturbing acceleration produces large along-
track oscillations of the PAGEOS spacecraft which, during July to September
1969, had an amplitude of 20 to 40 km with a period ranging from 10 to 15 days.
Such large perturbations have considerable impact on she quality of orbit deter-
mination and prediction. For the topocentric observer these were errors of
0.5 to 1.0 degrees in apparent position.
A problem deserving further work is the torquing mechanism of the rotation
and precession of these spacecraft.. Only a beginning exists in the suggestion
by Mar and Vigneron (7) of the Canadian Defense Research Telecommunications
Establishment of a thermal distortion mechanism to allow torquing of the
Echo II spacecraft.
REFERENCES
1. K. Fea, in "Dynamics of Satellites 1969", Bruno Morando, Ed. (Springer-
Verlag, New York, 1970), pp. 295-302.
2. K. H. Fea and D. E. Smith, Planet. Space Sci., Vol. 18, 1499 (1970).
3. I. I. Shapiro, in "Dynanics of Satellites 1962", M. Roy, Ed. Academic Press,
New York 1963, p. 271-272.
4. R. C. Vanderburgh, in "Proceedings of University of Miami Symposium on
Optical Properties of Orbiting Satellites", D. Duke, and K. Kissell, Eds
(Aerospace Research Labs Report ARL 69-0078, May 1969), pp. 201-225
(AD 692,742).	 i
5. R. C. Vandcrburgh and K. E. Kissell, Planet. Space Sci., Vol. 19, pp. 223-
231 (1971).
6. D. E. Smith and K. H. Fea, NASA, Goddard Space Flight Center X-Document
550-70-92 (19;0).
7. 11ar, J. and F. 11. Vigneron, in "Trajectories of Artificial Celestial Bodies",
Jean Kovalevsky, Ed. (Springer-Verlag, New York 1966) pp. 151-163.
6


Anomalous accelerations of the Pageos spacecraft

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