Transcript From the Pioneer-flyby anomalies to an alternative cosmology

From the Pioneer-flyby anomalies to an alternative cosmology.
Mike McCulloch.
Honorary Fellow, University of Exeter, U.K.
[email protected]
Talk for Cosmo-08
at the University of Wisconsin, Madison, 26th August 2008
Outline:
Reasons, and a method, for modifying inertia (MiHsC)
MiHsC predicts a minimum acceleration: c2/R (dark energy?)
MiHsC predicts the Pioneer anomaly (when unbound)…
and the flyby anomalies (using mutual accelerations)
First attempts at a cosmology.
Conclusions
The Pioneer anomaly may imply a modification of inertia
Pioneer 10 & 11 after gravity-assist flybys show an unexplained extra
acceleration of 8.7x10-10 m/s2 towards the Sun (Anderson et al., 1998)
No mundane explanation so far (Anderson et al., 2002)
Earth, 1973
Jupiter
Saturn
Pioneer
The Pioneer have anomalous accelerations, but not the planets.
The anomalies began when the spacecraft became unbound.
These are easier to explain with a modification of inertia.
How to reduce inertia for very small accelerations: Milgrom’s break
Hawking (1974) showed black
hole event horizons radiate at
a temperature T
c3
T
8 GMk
Haisch et al. (1994) derived inertia
from part of the Unruh radiation.
Accelerations (a) too, cause
event horizons that radiate at
temperature T (Unruh, 1976)
Acc
a
T
2 ck
Milgrom (1999): for low acc Unruh
waves are longer than the Hubblescale so inertia collapses (MOND).
Magnetic Lorentz
force: looks like
inertia.
Universe’s edge
Milgrom (1999) can’t explain the Pioneer anomaly: the accelrtn’ is too high!
More gradual: a Hubble-scale Casimir effect (McCulloch, 2007)
The wavelength λ of the Unruh radiation varies as
A rocket accelerates
within the
observable
universe
Observable Universe
4 2  c 2
m 
a
This can be
modelled as a
Hubble-scale
Casimir effect.
Doesn’t fit
It sees Unruh
waves (red lines)
The inertial
mass varies as:
Fits
At low accelerat’ns
the Unruh waves
are longer, and fewer
fit into the Hubble-scale.
(see the dashed red line)
  2c 2 
mi  mg 1 

a



Modified inertia
by a Hubblescale Casimir
effect (MiHsC).
Consequences of Modified inertia by a Hubble-scale Casimir effect.
Has MOND-ish behaviour:
Equiv Prin
F=ma 1
MOND
Mi / mg
MiHsC
  2c 2 
mi  mg 1 

a



Putting this into Newton’s laws we
get an equation of motion:
F  mi a 
GMmg
r2
a0
g
Acceleration
GM  2 c 2
a 2 
r

GM
c2
a  2  0.99 
r

Even when M=0, acceleratn ~ cH ~ c2/Θ (cosmic acceleration, dark energy?)
MiHsC agrees with the Pioneer anomaly (unbound)
Observed values are shown as error
bars. Average a=8.7x10-10 ms-2.
Predicted:
GM  2 c 2
a 2 
r

Outside 12 AU, the Pioneer Anomaly is
predicted without adjustable parameters
(some dependence on choice of Θ)
Inside 10 AU it doesn’t agree.
Here the Pioneer were bound?
Published in:
McCulloch, 2007. MNRAS, 376, 338-342
(arXiv:astro-ph/0612599)
The flyby anomalies, Anderson et al. (2008)
Unexpected speed-up of Earth flyby
craft by a few mm/s (dv) seen by:
Antreasian & Guinn (1998)
Anderson et al. (2008).
dv
Not: relativistic frame dragging
computer error, engine firing, tides,
Solar wind, geoid error.
Lammerzahl et al. (2006)..
dv
14
Anderson et al. (2008) found
the following empirical formula:
dv  3106 v (cos1  cos2 )
Anomaly (mm/s)
12
10
8
6
4
2
0
-2
er
es
se
ng
i
et
ta
M
Ro
s
Ca
ss
in
NE
AR
G
al
-2
-4
G
al
-I
and said the cause may be
‘something to do with rotation’…
What if we consider all the local mutual accelerations in MiHsC?
A spacecraft on an equatorial approach
sees slightly larger mutual accelerations.
So its inertial mass is slightly larger
  2c 2 
mi  mg 1 

a



Acceleration of a point mass
Earth’s rotation
On a polar exit trajectory
We have smaller mutual accelerations
So inertia reduces
By cons of mtum, speed increases
Reminiscent of E.Mach?
Does it work?..
Using mutual accelerations, MiHsC predicts the flyby anomalies
Conservation of momentum for craft & Earth before (1) and after (2) flyby
  2c 2 
mi  mg 1 

a



m1ev1e  m1v1  m2v2e  m2v2
me
 2c 2  v2 v1 
v2  v1  dv 
(v1e  v 2 e ) 
  
mg
  a2 a1 
a is the average mutual
acceleration, including
the Earth’s rotation:
0.07  ve2
a
cos 
R
 2 Rc 2  v2 cos 1  v1 cos  2 
dv 


0.07ve2  cos 1 cos  2

Where Φ = latitude
 cos 1  cos  2 
dv  3 10  v  

cos

cos


1
2 
Derived
dv  3106  v  (cos 1  cos 2 )
Observed
7
The observed flyby anomalies (◊), and those predicted by MiHsC (+)
The MiHsC theory agrees in 3 out
of 6 cases.
Not as accurate as the empirical
formula of Anderson et al. (2008),
but MiHsC has no adjustable
parameters.
A good test: flybys of other planets
because their Rs and ves are different.
 2 Rc 2v  cos 1  cos  2 
dv 


0.07ve2  cos 1 cos  2 
Mission name
Published in:
McCulloch (2008) MNRAS-letters,
389 (1), L57-60 (arXiv/0806.4159)
The maximum mass for a black hole from MiHsC (McCulloch, 2007)
A black hole’s Hawking temperature is:
c3
T
8 GMk
T
Using Wien’s law λ=βhc/kT gives

M
16 GM 
c2
2
Assume Hawking waves larger than
the observable universe can’t exist (λ=Θ):
c 2
M 2
 4.8  0.4 1052 kg
4 G 
The mass of the observable
universe is observed to be:
310521 kg
So can we model the observable universe as a black hole?
A simple MiHsC cosmology  steady state + hot early universe
The universe’s mass derived
from MiHsC:
c3
M
2GH
c
c
M 2

4 G  8GH
2
Is similar to Hoyle’s (1948)
steady state formula
3
The steady state theory was rejected because it didn’t predict a hot
early universe (CMB), but MiHsC does predict a hot early universe:
c 2
M 2
4 G 
c3
T
8 GMk
hc 
T
4k 
An example: when T=3000K, the Hubble-diameter Θ is 2mm. The
acceleration attributed to dark energy can be derived from the above
mass formula. McCulloch 2009?, submitted to MNRAS-Letters…
Conclusions
The model: MiHsC, without adjustable parameters, agrees with the following:
1.
2.
3.
4.
5.
Cosmic acceleration: c2/R
The Pioneer anomaly (when unbound) arXiv: astro-ph/0612599
The flyby anomalies (using mutual accelerations) arXiv:0806.4159
The mass of the observable universe
A Steady State theory, with a hot early universe.
MiHsC does not agree with:
1. Planetary orbits, Earth-bound equivalence principle tests (boundedness?)
To do:
1. Why does boundedness matter? Or does it?
2. Model galaxies/clusters with MiHsC and mutual accelerations
3. Set up a more direct test in the lab! (eg, see: arXiv:0712.3022)
Many thanks to the Royal Astronomical Society
& the Institute of Physics’s C.R.Barber trust fund for travel grants.