Sun's orbital elements I have the orbital elements of an asteroid's heliocentric motion (the orbit has non-zero inclination and is elliptical). But I want to simulate the motion of the sun around the asteroid. So without having the sun's ephemeris, and given only the asteroid's orbital elements, how can I determine an equivalent orbital elements for the sun's motion around the asteroid?

Edit:
I realize that the question wasn't clear enough based on the comment. So, what I am trying to do is to numerically solve the two body problem equation in the inertial frame. In the classic two-body problem 2nd order ODE, in my case, the position vector is defined from the centre of the asteroid to the sun, which is absolutely valid and upon integration gives me the position an velocity for the sun with respect to an inertial frame centred at the asteroid. My question is concerned with the initial conditions to begin the numerical integration. As of now I determine the initial state vector for the Sun from some random orbital elements. But to perform a more realistic simulation, Is it possible to determine the real orbital elements for the asteroid-centric motion of the Sun from a given set of orbital elements of a heliocentric-motion of the asteroid? I hope I was clear and not made this more confusing.
Strictly speaking the Sun's motion is going to be dominated by the gas giants and the planets and one asteroid is going to have negligible effect on it compared to those.

However if we assume there are no other items we can get an approximate idea of the effect.

You can use the similarity of the orbits.  The Sun ( in this simplified model ) follows a complimentary orbit around the center of mass of the two bodies.

The distances you have for the size of the obit scale like this :

$$r_1 = \frac \mu m_1 r$$

$$r_2 = \frac \mu m_2 r$$

where $\mu$ is the reduced mass :

$$\mu = \frac { m_1 m_2 } { m_1 + m_2 }$$

And as you can see $r = r_1 + r_2$ is the distance between the two bodies.

Now as you can see from those equations, the most massive body moves the least.

The mathematics comes from the way the standard two body problem is solved.

It might be instructive for you to compare the effect of your asteroid to that of Jupiter or Earth.