I am not sure what you are inferring, but the solar system does not move independent of its position in the galaxy on locale. It is called the 2nd Law of Celestial Dynamics. You are inferring, for some reason, the solar system breaks away, all of it, the 9 planets, the Asteroids, The Oort Cloud and the Kuiper Belt, and somehow we "pass" through to the core of the galaxy?
Or, you are saying we are going to go to the galactic "plane". This is also impossible and a meaningless statement. The Galactic plane is just that. We, our solar system, is revolving around the center of the Milky Way Galaxy, making one orbit every 230,000,000 (230 million) years.
The equation for validation for this is as follows, where N=orbital velocity x distance/position on local:
N=£∆.32n/∫–(∆230/ç∂

≠Vn∑ø«C/Pi≈/µ
Lastly, The photo above is from HST and is taken in gamma, infrared, and red shift laurex, which sees through dust and other diffusions. It is an accurate image of the Milky Way's galactic core. You are in error.
This is what I do for a living.
Hope that is helpful.
Robert