---

PIONEER ANOMALY AND COSMIC DECREASE OF GRAVITY
The modified Hubble-law

By Louis Nielsen
http://www.rostra.dk/louis

THE PIONEER-ANOMALY.
When all known forces acting on the Pioneer spacecrafts are taken into
consideration, a very small but unexplained force remains. It appears
to cause a constant sunward acceleration for both spacecraft.
It is observed that the Pioneer spacecrafts has a negative
acceleration-anomaly about
a(anomaly) = 8*10^(-10) m/s^2.

COSMIC DECREASE OF GRAVITY. THE MODIFIED HUBBLE-LAW.
In the following considerations about a modified Hubble-law where the
Hubble-function H(T) is determined by a decreasing gravitational
‘constant’ G according to the relation:

(1) H(T) = - (dG/dT)*(1/G) = (1/3)*(1/T)

In equation (1) (dG/dT) is the time derivative of the variable
decreasing gravitational ‘constant’ G and T is the actual age of the
Universe.
The mathematical connection between H(T) and T gives a hyperbola
curve.

The modified Hubble-law is given by:

(2) v(T) = H(T)*D(T)

In equation (2) v(T) is the radial velocity of an object at the time T
the actual age of the Universe and D(T) is the distance from an
observer to the object at the time T.

By differentiation of the velocity in equation (2) we get the
acceleration a(T) of the object at the time T when it is in a distance
D(T). We get:

(3) a(T) = (- 2/9)* (D(T)/T^2)

From equation (3) we see that the acceleration a(T) is negative. The
velocity v(T) of the object is decreasing.

We can rewrite equation (3) so we have a relationship between a(T),
v(T) and T. We get:

(4) a(T) = (-2/3)* (v(T)/T)

From equation (4) we see that the negative acceleration, the
deceleration, of a given object is inversely proportional to the
actual age T of the Universe and directly proportional to the actual
velocity v(T).

If T = 13*10^9 years = 4.1*10^17 sec and v(T) = 1*10^7 m/s (greater
than the real velocity) then we get a very small value for the
acceleration a(T) given by:

(5) a(T) = - 0.2*10^(-10) m/s^2

The value in (5) is of the order of the measured acceleration-anomaly.

Is the observed acceleration-anomaly of the Pioneer Probes caused by a
cosmic decrease of the gravitational ‘constant’ and maybe explained by
the above considerations?

Best regards
Louis Nielsen
Denmark
http://www.rostra.dk/louis

---

On Apr 26, 2:18 pm, Loui...@edu.herlufsholm.dk wrote:
> PIONEER ANOMALY AND COSMIC DECREASE OF GRAVITY
> The modified Hubble-law
>
> By Louis Nielsenhttp://www.rostra.dk/louis
>
> THE PIONEER-ANOMALY.
> When all known forces acting on the Pioneer spacecrafts are taken into
> consideration, a very small but unexplained force remains. It appears
> to cause a constant sunward acceleration for both spacecraft.
> It is observed that the Pioneer spacecrafts has a negative
> acceleration-anomaly about
> a(anomaly) = 8*10^(-10) m/s^2.
>
> COSMIC DECREASE OF GRAVITY. THE MODIFIED HUBBLE-LAW.
> In the following considerations about a modified Hubble-law where the
> Hubble-function H(T) is determined by a decreasing gravitational
> ‘constant’ G according to the relation:
>
> (1)  H(T) = - (dG/dT)*(1/G) = (1/3)*(1/T)
>
> In equation (1) (dG/dT) is the time derivative of the variable
> decreasing gravitational ‘constant’ G and T is the actual age of the
> Universe.
> The mathematical connection between H(T) and T gives a hyperbola
> curve.
>
> The modified Hubble-law is given by:
>
> (2)  v(T) = H(T)*D(T)
>
> In equation (2) v(T) is the radial velocity of an object at the time T
> the actual age of the Universe and D(T) is the distance from an
> observer to the object at the time T.
>
> By differentiation of the velocity in equation (2) we get the
> acceleration a(T) of the object at the time T when it is in a distance
> D(T). We get:
>
> (3)  a(T) = (- 2/9)* (D(T)/T^2)
>
> From equation (3) we see that the acceleration a(T) is negative. The
> velocity v(T) of the object is decreasing.
>
> We can rewrite equation (3) so we have a relationship between a(T),
> v(T) and T. We get:
>
> (4)  a(T) = (-2/3)* (v(T)/T)
>
> From equation (4) we see that the negative acceleration, the
> deceleration, of a given object is inversely proportional to the
> actual age T of the Universe and directly proportional to the actual
> velocity v(T).
>
> If T = 13*10^9 years = 4.1*10^17 sec and v(T) = 1*10^7 m/s (greater
> than the real velocity) then we get a very small value for the
> acceleration a(T) given by:
>
> (5)   a(T) = - 0.2*10^(-10) m/s^2
>
> The value in (5) is of the order of the measured acceleration-anomaly.
>
> Is the observed acceleration-anomaly of the Pioneer Probes caused by a
> cosmic decrease of the gravitational ‘constant’ and maybe explained by
> the above considerations?
>
> Best regards
> Louis Nielsen
> Denmarkhttp://www.rostra.dk/louis

Larger gravity.

---

Louis_N@edu.herlufsholm.dk writes:
> COSMIC DECREASE OF GRAVITY. THE MODIFIED HUBBLE-LAW.
> In the following considerations about a modified Hubble-law where the
> Hubble-function H(T) is determined by a decreasing gravitational
> ‘constant’ G according to the relation:
>
> (1) H(T) = - (dG/dT)*(1/G) = (1/3)*(1/T)
>
> In equation (1) (dG/dT) is the time derivative of the variable
> decreasing gravitational ‘constant’ G and T is the actual age of the
> Universe.

The actual measured limit to the time variation of "G" is
|(dG/dt)/G| < 9 x 10^{-13} (ref. Williams Turyshev & Boggs 2004).
Thus, your equation 1 cannot be correct, for reasonable ages of
the universe.

CM


References
J.G. Williams, S.G. Turyshev, D.H. Boggs, PRL. 93, 261101 (2004)
gr-qc/0411113.

---

--
This message is brought to you by Androcles
http://www.androcles01.pwp.blueyonder.co.uk/

<Louis_N@edu.herlufsholm.dk> wrote in message
news:1c5e632b-6dba-4566-8fe1-ccad14fe81ec@p25g2000hsf.googlegroups.com...
| PIONEER ANOMALY AND COSMIC DECREASE OF GRAVITY
The modified Hubble-law

| By Louis Nielsen
| http://www.rostra.dk/louis

| THE PIONEER-ANOMALY.
| When all known forces acting on the Pioneer spacecrafts are taken into
| consideration, a very small but unexplained force remains.


No it doesn't, the crank Einstein shift was applied where Doppler shift was
is
and remains appropriate.
The "unexplained" force is --- ya got ya sums wrong.

---

"Androcles" <Headmaster@Hogwarts.physics> writes:
> <Louis_N@edu.herlufsholm.dk> wrote in message
> news:1c5e632b-6dba-4566-8fe1-ccad14fe81ec@p25g2000hsf.googlegroups.com...
> | PIONEER ANOMALY AND COSMIC DECREASE OF GRAVITY
> The modified Hubble-law
>
> | By Louis Nielsen
> | http://www.rostra.dk/louis
>
> | THE PIONEER-ANOMALY.
> | When all known forces acting on the Pioneer spacecrafts are taken into
> | consideration, a very small but unexplained force remains.
>
>
> No it doesn't, the crank Einstein shift was applied where Doppler shift was
> is
> and remains appropriate.
> The "unexplained" force is --- ya got ya sums wrong.

This statement is incorrect. If the classical Doppler shift is used
instead of the relativistic one, the Pioneer solution actually becomes
much worse.

---

Well you found that the swing force may apply to rotating planets too,
not just spiral galaxies. This means that in any swinging rotation of
bodies around the center, there is always more gravity.

www.geocities.com/gmbajszar/BreakPedalEffect.htm

---

> Well you found that the swing force may apply to rotating planets too,
> not just spiral galaxies. This means that in any swinging rotation of
> bodies around the center, there is always more gravity.
>
> www.geocities.com/gmbajszar/BreakPedalEffect.htm

Let's expand on this. There is a gravitational field of the Sun which
formed a disk out along it's rotating equator. If that is true, then
regardless of the direction of the rotation of the planets around the
Sun as long as they have a Saturn ring distribution direction, on that
disk, gravity distributes unevenly. Check out this break pedal effect.

---

On 27 Apr, 18:33, Craig Markwardt
<craigm...@REMOVEcow.physics.wisc.edu> wrote:
> "Androcles" <Headmas...@Hogwarts.physics> writes:
> > <Loui...@edu.herlufsholm.dk> wrote in message
> >news:1c5e632b-6dba-4566-8fe1-ccad14fe81ec@p25g2000hsf.googlegroups.com...
> > |PIONEERANOMALYAND COSMIC DECREASE OF GRAVITY
> > The modified Hubble-law
>
> > | By Louis Nielsen
> > |http://www.rostra.dk/louis
>
> > | THEPIONEER-ANOMALY.
> > | When all known forces acting on thePioneerspacecrafts are taken into
> > | consideration, a very small but unexplained force remains.
>
> > No it doesn't, the crank Einstein shift was applied where Doppler shift was
> > is
> > and remains appropriate.
> > The "unexplained" force is --- ya got ya sums wrong.
>
> This statement is incorrect. If the classical Doppler shift is used
> instead of the relativistic one, thePioneersolution actually becomes
> much worse.

The classical (first order) Doppler shift was actually used by
Anderson et al. in their paper (see Eq.(15) in http://arxiv.org/abs/gr-qc/0104064
).

Thomas

---

This message is brought to you by Androcles
http://www.androcles01.pwp.blueyonder.co.uk/

"Thomas" <thomas.smid@gmail.com> wrote in message
news:7b80157e-d871-4366-896d-6554a70a9dd2@a1g2000hsb.googlegroups.com...
| On 27 Apr, 18:33, Craig Markwardt
| <craigm...@REMOVEcow.physics.wisc.edu> wrote:
| > "Androcles" <Headmas...@Hogwarts.physics> writes:
| > > <Loui...@edu.herlufsholm.dk> wrote in message
| >
>news:1c5e632b-6dba-4566-8fe1-ccad14fe81ec@p25g2000hsf.googlegroups.com...
| > > |PIONEERANOMALYAND COSMIC DECREASE OF GRAVITY
| > > The modified Hubble-law
| >
| > > | By Louis Nielsen
| > > |http://www.rostra.dk/louis
| >
| > > | THEPIONEER-ANOMALY.
| > > | When all known forces acting on thePioneerspacecrafts are taken into
| > > | consideration, a very small but unexplained force remains.
| >
| > > No it doesn't, the crank Einstein shift was applied where Doppler
shift was
| > > is
| > > and remains appropriate.
| > > The "unexplained" force is --- ya got ya sums wrong.
| >
| > This statement is incorrect. If the classical Doppler shift is used
| > instead of the relativistic one, thePioneersolution actually becomes
| > much worse.
|
| The classical (first order) Doppler shift was actually used by
| Anderson et al. in their paper (see Eq.(15) in
http://arxiv.org/abs/gr-qc/0104064
| ).

The correct Doppler shift is f' = f.(c+v)/c.

The "classical" Doppler shift (as it applies to a medium) is
f' = f. c/(c+v)
Ref: http://en.wikipedia.org/wiki/Doppler_effect

Both "relativistic" and "classical" would be wrong.

Doppler's full equation is
c+v
f' = f * ------
c+u

Where v the motion of the source relative to the medium
and u is the motion of the observer relative to the medium.
In the absence of a medium f = f . (c+v)/ c applies.

As usual, wackypedia is full of incomplete rubbish.

The "unexplained" force is --- ya got ya sums wrong.

---

Thomas <thomas.smid@gmail.com> writes:


> On 27 Apr, 18:33, Craig Markwardt
> <craigm...@REMOVEcow.physics.wisc.edu> wrote:
> >
> > This statement is incorrect. If the classical Doppler shift is used
> > instead of the relativistic one, thePioneersolution actually becomes
> > much worse.
>
> The classical (first order) Doppler shift was actually used by
> Anderson et al. in their paper (see Eq.(15) in [...]
> ).

You are incorrect. Quoting more of the text, "The observed, two-way
anomalous effect *can be expressed* to first order in v/c as ...."
(emph added.)

That the anomaly *can be expressed* in that fashion for reader
edification does not mean it was "actually used" that way in the
analysis. In fact, the *actual* Doppler analysis as described by
Moyer (Anderson's footnote 42) uses the fully relativistic
formulation.

The Anderson authors display their equation 15 to first order in v/c
because it is more instructive that way. The fully relativistic
expression is far more complicated and the anomalous contribution
would be difficult to discern.

CM