#### Arman777

Gold Member

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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 ?

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 ?

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