The Smithsonian/NASA
Astrophysics Data
System
Home Help Sitemap NASA According to thestr Search
Fulltext Article
Find Similar Articles
Full record info
According to the strict solution of GR there is
no the un-modeled anomalous acceleration of
Pioneer
Chen, Shao-Guang
38th COSPAR Scientific Assembly. Held 18-15 July 2010, in Bremen, Germany, p.2
According to the definition of force f = d (m v) /d t = m (d v / d t) + v (d m / d t ) and the
change in masses ( the exchange of momentum-energy tensors bwtween two bodies Tμυ
via the field tμν ) deduced by Bondi from Einstein equation ( H.Bondi, Proc. R. Soc.
London A 427, 249, 1990 ), we get a new gravitational equation: f GR = f P + f C , f P =
-G (m M /r 2 ) (r /r), f C = -G (m M / r 2 ) (v /c) (1). The deductive process is: First if
mass is invariable, which implies that the mass may produce the gravitational field but
the gravitational field should not lead to the change in mass, i.e., the mass should be an
invariable parameter and the fourth dimension momentum i E/c should be entirely
independent of three-dimension momentum P. In other words, the energy and the
momentum should not compose the four-dimension momentum-energy vector and
tensor. Thus, the gravitational equation is no longer a nonlinear but a linear one and
Einstein equation should be reduced to Newtonian law: f GR = f P = -G (m M /r 2 )
(r /r). Second according to the mass-energy relation we get: dm /dt = dE /c2 dt, where E
= EK + m0 c2 , then from the conservation of four dimension momentum-energy vector
P 2 -(E/c) 2 = 0, we obtain: dE/dt = c dP/dt, dm/dt = dP/c dt = f P /c, f C = v (dm/dt) = v
(f P /c) = -G (m M /r 2 ) (v /c). Then, we educe Eq.(1) from the special relativity when
the mass is variable. In Eq.(1) the gravitational mass is just the inertial mass and the
equivalent principle come absolutely into existence. Einstein equation can also be
deduced from Eq.(1) and is equivalent to Eq.(1). Now the nonlinear gravitation
problems can be solved with the one by one substitute method of masses solved by
alone f P and alone f C in Eq.(1), e.g., from one loop Σf P • d s = 0, the energy loss of
celestial body running one loop by f C is a typical dipole radiation and a gravitational
wave of dipole radiation is predicted.When mass-point B nearing mass-point A, the
masses MA and MB will change, when third mass-point C nearing A and B, MA and
MB cum force f AB between A and B will again change. Then in GR the gravitational
linear superposition principle has not to hold, the relative decrease ratio of nonlinear
superposition to linear superposition is defined as a self-shielding coefficient q of the
aggregate body of many mass-points M. The more the mass accumulated, the stronger
the self-shielding effect is, larger the coefficient q is. When (d m /d t) = 0, f GR = f P
and q=0, the invariable mass maintains the linear superposition principle. When v=0,
only f GR = f P , the static Newtonian law also needs to be modified with q: f = -(1 -q )
The Smithsonian/NASA
Astrophysics Data
System
Home Help Sitemap NASA According to thestr Search
w 页码，1/2(W)
http://adsabs.harvard.edu/abs/2010cosp...38.3849C 2011/5/13
G m M r/r 3 , q = K M / r2 = K D L S / r 2 (2), where M / r 2 is the gravitational field
strength produced by body M on testing mass m , D and L are the density and the
thickness respectively, S is the cross section. K is the section of unit mass determined by
experiments. The problems of dark matter, dark energy and fifth kind force etc can all be
explained with Eq.(2). The radio tracking data from Pioneer 10/11 shows an anomalous
Doppler frequency drift that can be interpreted as an un-modeled anomalous
acceleration directed towards the sun of AP = (8.74 ± 1.33)•10-8 cm / s2 at heliocentric
distances 20 AU to 70 AU reported by Anderson et al. In the navigation of Pioneer
spacecraft Anderson et al used the parameterized post-Newtonian (PPN) approximation.
AP is drawn from the departure of the observational data for a navigation model. The
correction by PPN approximation to Newtonian law does not include the first order item
(v/c) of the velocity between Pioneer spacecraft and the sun, only includes the second
order items (v2 /c2 ) of the velocities between bodies. The velocities v of celestial
bodies and spacecrafts are in the order of magnitude of 10 km /s. Thus, v/c is about
3•10-5 and v2 /c2 is about 1•10-9 . Under the observational accuracy of 1•10-8 , the
conclusion of PPN approximation is nearly the same as that of Newtonian law.
Therefore, AP is essentially the conclusion of Newtonian law. The force f C exerted on
Pioneer 10/11 by the sun cannot directly produce the acceleration because f C is based
on the change in the mass and the invariable velocity v. But in PPN approximation the
mass of the spacecraft is an invariable parameter. Thus, the variance rate in momentum f
C can only be resulted from the change of the velocity. The change in velocity caused
by f C at heliocentric distances 20AU is equivalent to an acceleration directed towards
the sun: AGR = 6.25•10 -8 cm /s 2 (3). AGR caused by f C is the primary reason of AP .
In their data fitting equation Anderson et al have considered almost all the influences on
the spacecraft's movement such as the solar radiation pressure ASP , the variance in
spacecraft's mass by the whiffing thruster fuel consumption and the radioisotope
thermoelectric generator thermal fuel consumption etc. But they have not considered the
influence on the spacecraft's movement by the primary item AGR . Because the
acceleration AGR is caused by the Bondi's change in masses in GR, therefore, the bug
of the model is the reason of AP . In strict solution of GR, there is no un-modeled
anomalous acceleration. The attitude-control maneuver is frequently needed to keep the
communication antenna of the spacecraft pointing to the earth. The whiffing thrust
acceleration AW T of attitude-control maneuvers and the decrease rate ζ in mass of
spacecraft by whiffing thruster fuel consumption or by the leak of gasses are unknown
beforehand. The values of AW T and ζ can only be inferred from data-fitting afterwards.
Furthermore, both AW T and ζ will affect each other. Then we cannot obtain an accurate
value of AW T , i.e., an exact value of AP cannot be obtained by the data fitting. At
heliocentric distances 20 AU to 70 AU the interval between two attitude control
maneuvers is about half-year, which makes very few data of whiffing thrust available. In
the navigation software for data fitting, "AW T " and " ζ " deduced from data within 20
AU are used as the input parameters in the range from 20 AU to 70 AU. Thus, the data
fitting value of AW T should not decrease with the augment of distance and should be
larger than its actual value. Therefore, AP should not decease with the augment of
distance and the value of AP should be larger than the value of AGR . Otherwise, in the
navigation software for data fitting, the absorption/reflection coefficient κ of the
spacecraft's surface will influence the solar radiation pressure ASP . κ is taken to be
1.71, which is likely larger than its actual value. Thus, the ASP obtained by data fitting
will be larger than its actual value, and it makes AP (directing towards the reverse
direction of ASP ) larger than its actual value. It also is one of the reasons why the value
of AP is larger than the value of AGR .
The ADS is Operated by the Smithsonian Astrophysical Observatory under NASA Grant
NNX09AB39G
w 页码，2/2(W)
http://adsabs.harvard.edu/abs/2010cosp...38.3849C |