# Random MOND theory / dark matter question(possibly really easy to answer)

1. Dec 11, 2006

So I was googling around and I happen to see several references to MOND theory, Modified Newtonian Dynamics.

Anyway, it proposes that there is this other new constant $$a_{0}$$ that is a very very very low acceleration that exists. Basically, as far as I can tell so far the whole idea is that under very very small acceleration F=ma breaks down.

so, a lot of sites reference this value of $$a_{0}$$ to be 1.2E-10 m/s/s

Now with that background in mind, here's my actual question.

Most of the sites mention that the original author of this concept remarked that if you take the age of the universe and see what speed something would be at after moving with this acceleration, the velocity equals the speed of light.

or in that person's words

"... the acceleration you get by dividing the speed of light by the lifetime of the universe. If you start from zero velocity, with this acceleration you will reach the speed of light roughly in the lifetime of the universe."

My question is What value for the age of the universe was this person using?? I can't seem to find it anywhere, and my calculations using the 13.7 billion year value(yes I converted to seconds first) doesn't come close to the speed of light when I work it out.

Anyone know what I'm talking about?

A brief intro to MOND theory can be found by googling around. Most of the sites say the same thing.

I just wanted to see if this value * age of universe really equalled the speed of light as we know it.

Thanks

2. Dec 11, 2006

### Garth

Hi lampshade and welcome to these Forums! Keep asking the questions, that is how we learn.

First some numbers:
Hubble Time, the inverse of Hubble's constant is equal to:

$$T_H = 0.98/h \times 10^{10} yrs. = 3.1/h \times 10^{17} secs.$$

A modern accepted value of h is 0.73.

i.e. Hubble's Constant $H = 73 km.sec^{-1}Mpsc^{-1}$

$H = 2.4 \times 10^{-18} sec^{-1}$

Therefore the value of Hubble Time is about 4.2 x 1017 secs.

The Hubble Acceleration (Hc) is therefore equal to 7.1 x 10-10 m.sec-2., which is within an OOM of a0, the MOND acceleration.

As a matter of interest note that the Pioneer Anomaly (PA) is equal to
ap = (8.74 ± 1.33) x 10-10 m.sec-2, which is much closer to the Hubble Acceleration!

The MOND acceleration might just have a connection with the PA. Just a thought.....

Garth

Last edited: Dec 11, 2006
3. Dec 11, 2006

Thanks

It took me a while to figure out that OOM meant Order of Magnitude, but I got it.

THANKS!

4. Dec 11, 2006

I'm also having a hard time calculating the theoretical value of the MOND acceleration.

I tried using universal gravitation, the veloctiy of the Earth as it orbits the sun, and the mass of the earth, but I got a value nowhere close in magnitude to what all these websites are saying the value of mond acceleration is.

Would you happen to know what the standard walkthrough is to find it?

Basically I've been using $$a = \dfrac{v^2}{r} = \sqrt{\dfrac{ a_{0} GM}{r^2}}$$

when I try this with 29785 m/s as the velocity of the Earth and use the mass of the Earth, like I said, I am orders of magnitude off. What's wrong with my thinking?

Where a sub 0 is the MOND Acceleration.

5. Dec 12, 2006

### Garth

The MOND acceleration is empirical, Milgrom found that value of a0 could explain the galactic rotation profile without invoking DM.

People had tried variations of Newton where the regime changed outside a certain radius, Milgrom tried changing the regime when the acceleration fell below a certain a0.

What might change the Newtonian acceleration below the MOND threshold? The Tensor-Vector-Scalar gravity (TeVeS) theory provides a possible mechanism. Actually I find the TeVeS rather complicated - it appears to me that it is simpler to accept DM!

Note: The Bullet Cluster appears to show DM is real although the TeVeS school claim that their theory also accounts for these observations.

Garth

Last edited: Dec 12, 2006