# MOND overview for beginners

1. Jan 22, 2006

### marcus

http://arxiv.org/abs/astro-ph/0601478
Modified Newtonian Dynamics, an Introductory Review
Riccardo Scarpa

To Appear in the proceeding of the "First crisis in cosmology" conference, published in the American Institute of Physiscs' proceedings series, Vol. 822. (includes 13 pages and 12 figures)

"By the time, in 1937, the Swiss astronomer Zwicky measured the velocity dispersion of the Coma cluster of galaxies, astronomers somehow got acquainted with the idea that the universe is filled by some kind of dark matter. After almost a century of investigations, we have learned two things about dark matter, (i) it has to be non-baryonic -- that is, made of something new that interact with normal matter only by gravitation-- and, (ii) that its effects are observed in stellar systems when and only when their internal acceleration of gravity falls below a fix value a0=1.2x10-8 cm s-2. This systematic, more than anything else, tells us we might be facing a failure of the law of gravity in the weak field limit rather then the effects of dark matter. Thus, in an attempt to avoid the need for dark matter, the Modified Newtonian Dynamics. MOND posits a breakdown of Newton's law of gravity (or inertia) below a0, after which the dependence with distance became linear. Despite many attempts, MOND resisted stubbornly to be falsified as an alternative to dark matter and succeeds in explaining the properties of an impressively large number of objects without invoking the presence of non-baryonic dark matter. In this paper, I will review the basics of MOND and its ability to explain observations without the need of dark matter."

2. Jan 25, 2006

### Galoot

Is the Pioneer anomaly -- i.e., the apparent deceleration (or more correctly heliocentric acceleration) of the Pioneers 10 & 11 outside the solar system -- evidence of, or at least consistent with, MOND?

3. Jan 25, 2006

### marcus

I have read discussions of that, but I can't confidently evaluate them---so I have to wait for someone else to respond.

That is, I have seen scientific papers which try to put Pioneer anomaly together with MOND in the same model, but I cannot recommend anything to you. It all seemed pretty iffy----like this and this are in the same ballpark so they might be related IF the anomally is actually real.

Hello Galoot, it is a good question. See if anyone else will respond to you, or give you a link to some scientific paper.

4. Jan 25, 2006

### Garth

Hi Galoot!

Yes it is - the MOND critical acceleration being OOM about the same as the PA, both are also approxiamtely equal to the Hubble acceleration HC (lots of room for 'hand waving'!)

Garth

Last edited: Jan 25, 2006
5. Jan 25, 2006

### Garth

Just to be specific:
http://arxiv.org/PS_cache/astro-ph/pdf/0112/0112069.pdf [Broken] by Mordehai Milgrom
The Pioneer anomaly is due to a constant acceleration of
aP = (8.74 ± 1.33) × 10−8 cm s−2
and the Hubble acceleration with h = 0.71, the present best accepted value:
Hc = 6.69×10−8 cm.sec-2.

Food for thought?

Garth

Last edited by a moderator: May 2, 2017
6. Jan 25, 2006

### matt.o

That looks like number games to me. Is there any physical basis behind the hubble constant time the speed of light being approximately equal to the anomolous pioneer acceleration (which I am not sure is constant in time anyway)?

7. Jan 26, 2006

### Chronos

The Pioneer anomaly is certainly interesting and potentially important. This is worth a look:

http://www.arxiv.org/abs/gr-qc/0512121
The Study of the Pioneer Anomaly: New Data and Objectives for New Investigation

8. Jan 26, 2006

### Garth

The Pioneer/Voyager acceleration is constant over the life-time of their journeys.

The PA may have prosaic components as well, i.e. gas leakage and anisotropic radiation emission. These have been suggested as a possible cause for the effect but have proven to be about an OOM too small. However subtract such a value from the PA and the remainder is consistent with Hc.

The reduced Pioneer anomaly
aP reduced = (8.74 - ~0.9 ± 1.33)×10−8cms−2 = (7.84 ± 1.33)×10−8cms−2
and the Hubble acceleration:
Hc = (6.69 ± 0.7)×10−8cms−2,
where I have included a possible 10% error in the determination of H.

There is a possible physical basis as this effect is predicted as a cosmological clock drift between atomic and ephemeris clocks in the alternative gravitational theory of Self Creation Cosmology.

Garth

Last edited: Jan 26, 2006
9. Jan 26, 2006

### Chronos

Observational evidence suggests the PA effect is not constant, which is part of the mystery:

http://www.arxiv.org/abs/gr-qc/0601055
What do the orbital motions of the outer planets of the Solar System tell us about the Pioneer anomaly?

10. Jan 27, 2006

### Garth

Not so; the definitive analysis of the effect is the Anderson et al. paper: Study of the anomalous acceleration of Pioneer 10 and 11
(emphasis mine)

The Iorio paper assumes that, because the effect was not detected closer than 20AU, it doesn't exist there, rather than that it was simply swamped by other forces such as solar radiation pressure.

The fact that outside this range the effect is constant is important.

If it were a gravitational effect, a modification of the GR Schwarzschild field, then it would most probably be dependent on r. It is not. Therefore we can conclude it is not an artefact of the Sun's field.

As it is just a little larger than cH the most probable explanation is that (most of) the PA is cosmological in nature.

Garth

Last edited: Jan 27, 2006
11. Jan 27, 2006

### matt.o

Hmm, I remember seeing a graph in a presentation that showed what I though were some wiggles indicating some periodicity, but they may have been within the errors. I was just fitting with my eye.

12. Jan 29, 2006

### jgraber

However, one of these two terms should have a minus sign.
The cosmological constant term(CC} is an acceleration, both the Pioneer affect(PA), and MOND are decellerations. Stated in other words, CC is a repulsion and results in an expansion, MOND and PA are attractions and result in keeping clusters together or slowing down the escape of the Pioneer spacecraft.

MOND is usually stated to not apply inside the solar system due to absolute values of the acceleration. Scarpa's recent suggestion that MOND could apply inside the solar system, based on the NGC 6171 results, seems to be in contradiction with Iorio's PA paper, also referenced by Garth. According to my calculations, MOND( and PA) produces bigger effects than the null results obtained by Adelberger, but the geometry would be different, so I do not currently think there is a conflict here, but the question merits deeper study.
Jim Graber

13. Jan 29, 2006

### Garth

Hi Jim!

Yes, you do have to look at the sign. A straightforward explanation of the PA as cosmic acceleration on a local scale goes the 'wrong way' as you point out.

However if, as I have argued, the PA is cosmological in origin then it is inconsistent with GR. We have to look again for a modification of GR that will explain the PA correctly.

The first thing to realise is the PA is not a measurement of an acceleration; it is in fact a doppler measurement, which is interpreted as being caused by an anomalous sunwards acceleration. That is, the negative doppler shift of the radio signals from the receeding spacecraft decreased more quickly than expected by a blue shift rate:
ap/c ~ (2.94 +/- 0.44) x 10-18 sec-1. (See Nieto et al. The Pioneer Anomaly: The Data, its Meaning, and a Future Test )

(Note: Hubble constant in these units is (h = 0.71):
H = 3.24h x 10-18 sec-1 = 2.30 x 10-18 sec-1)

One possible explanation that does fit, as I posted above, is that it is caused, not by an anomalous deceleration of the spacecraft, but by an anomalous increase in clock rate. That is, it is caused by an atomic clock rate increase as compared to the ephemeris clock determining the spacecraft trajectory. (See Peter Ostermann's eprint; Relativity theory and a Real Pioneer Effect)

Is there a physical basis for such a clock drift?

In the published, and about to be tested, theory of Self Creation Cosmology particle rest masses ma and the Gravitational 'constant' G vary inversely to each other so that Gma is constant. In the cosmological case the ephemeris clock, i.e. orbital period, maintains a constant rate while the atomic clock 'speeds up' relative to it because atomic masses are increasing.
In SCC (but not GR):

$$m_a(t) = m_0 \exp{(Ht)}$$

and as

$$\nu = \nu_0\frac{m_a(t)}{m_0}$$

then

$$\frac{\nu'}{\nu} = H$$

as is observed in the PA.

Garth

Last edited: Jan 30, 2006