# I MOND -- Understanding Equations

#### Arman777

Gold Member
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

Gold Member
2018 Award
$F$ is likely the gravitational field, which is the force per unit mass of the object the force acts upon.

#### Arman777

Gold Member
$F$ 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

Gold Member
2018 Award
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:
$$F(r) = f(a(r)/a_0)GM/r^2$$

Staff Emeritus
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.

#### Arman777

Gold Member
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

Staff Emeritus
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.

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