I MOND -- Understanding Equations

  • Thread starter Arman777
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I am reading an article written by Sanders and McGaugh In the article, the first equation is written as $$F = f(r/r_0)GM/r^2~~~(1)$$

where ##x = r/r_0##
Then it goes like if
$$f(x) =
\begin{cases}
1 & \text{if } x <<1 \\
x & \text{if } x >>1
\end{cases} $$

So the equation becomes

$$F =
\begin{cases}
GM/r^2 & \text{if } x <<1 \\
GM/rr_0 & \text{if } x >>1
\end{cases} $$

Then he defines the force acting on the particle ##m## as

$$F = ma\mu(a/a_0)$$

However in the wikipedia its claimed that


$$F = \frac {GMm} {\mu(a/a_0)r^2} $$

My first question is what is this ##F## ? It cannot be force since the units do not match. Is it acceleration ?

Or in (1) ##m## is taken as 1 ?

The wiki equation and the equation (1) are the same ?
 
Last edited:

kimbyd

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##F## is likely the gravitational field, which is the force per unit mass of the object the force acts upon.
 
1,476
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##F## is likely the gravitational field, which is the force per unit mass of the object the force acts upon.
I see. Then should we use ##\mu(a/a_0)## or ##\mu(r/r_0)## ? Is there a difference ? For instance if I write $$F = f(r/r_0)GM/r^2=f(a/a_0)GM/r^2$$ Is this true ?
 

kimbyd

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I see. Then should we use ##\mu(a/a_0)## or ##\mu(r/r_0)## ? Is there a difference ? For instance if I write $$F = f(r/r_0)GM/r^2=f(a/a_0)GM/r^2$$ Is this true ?
I think the difference between the two is just notation. You can always re-express a function in terms of different parameters if you want. With the above, if ##F## is a function of ##r##, then the second equation written out fully would be:
$$F(r) = f(a(r)/a_0)GM/r^2$$
 

Vanadium 50

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In the article, the first equation
Did you actually read the paper? The first equation is not MOND, and the first two pages of the paper explain why it's not MOND.
 
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Did you actually read the paper? The first equation is not MOND, and the first two pages of the paper explain why it's not MOND.
I was reading but I missed that sentence I think. Okay thanks
 

Vanadium 50

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I missed that sentence I think
first two pages
Two pages are more than a sentence. When you find yourself in a hole, it's best to stop digging. Given that this whole thread is based on reconciling two equations that aren't even supposed to be the same, I am going to ask it be closed.
 

Doc Al

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On that note, thread closed.
 

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