It seems that we know the rotation curve inside the sun\'s galactic orbit fairly

Question

It seems that we know the rotation curve inside the sun's galactic orbit fairly accurately. Then wouldn't we be able to just take the derivative* of this to get the DM density profile at smaller radii? What then is the primary reason we can't distinguish between different profiles like pseudo-isothermal, NFW etc?

a) Is it uncertainty in the rotation curve? If so what is the source of this uncertainty? b) Uncertainty in the amount of luminous matter? Source?

Something else?

I can see why the profile is uncertain at larger distances from the galactic center since the rotation curve is uncertain there, but why is it uncertain in the region where the rotation curve is known more precisely?

*Well, square, multiply by r and take the derivative, but you get the idea

Explanation / Answer

The average dark matter density in the universe is about the mass of 1 hydrogen atom per cubic metre. If we take this density we can work out how the mass of the dark matter within e.g. the orbit of Jupiter compares to the mass of the Sun.

The distance of Jupiter from the Sun is about 800,000,000,000 metres (I say about because it's orbit is elliptical), so the mass of dark matter within it's orbit is 2

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