# Rotational velocity due to Dark matter

I was wondering if we can predict the rotational velocity due to dark matter in this way:

Consider that we theoretically derived the rotational velocity of a galaxy ($$v_{the}$$). Then from experiment we got some other rotation velocity ($$v_{obs}$$). Then can we subtract these two velocities to obtain the rotational velocity due to dark matter ($$v_{dar}$$).

If not, how can we derive $$v_{dar}$$ by $$v_{the}$$ and $$v_{obs}$$?

• Yes, this is essentially the method, though of course using the complete formulas. – Javier Jun 17 at 20:49
• You mean $v_{obs}$-$v_{the}$=$v_{dar}$ just confirming – The One Eye Triangle Jun 17 at 21:11

Radial acceleration is $$v^2/r$$ and this is proportional to the total mass enclosed within the orbit. Adopting a rough Keplerian approximation $$\frac{v^2}{r} = \frac{G}{r^2}\sum_i M_i,$$ where $$M_i$$ are the masses of the various components (baryonic, dark).
If I understand correctly, your "theoretical" rotation curve arises from considering only baryonic matter, whereas the observed speed corresponds to $$v$$ in the equation above. If so, then $$v^2_{\rm obs}\simeq v^2_{\rm the} + v^2_{\rm dark}\ .$$