How long will it take for the earth to pass the center of the milky way

That is its impossible as our solar system orbits the center of the Milky-way (spinning at around 134 miles/sec). However the Sun will cross the galactic equator this year , like it does every year (twice , once in June and once in December)

Our Sun's orbit around the galactic center doesn't take us there. So, the quick answer is, never. However, if Sol's orbit is disturbed by another close pass of a massive star, our solar system could be hurdled toward oblivion in the galactic core. The speed at which we arrive would depend upon the encounter with the "Nemesis" star.

I hope this helps. Good luck.

Never, since we orbit about 2/3 of the way out from the center (26,000 light years). We're on our 20th or 21st orbit around the galaxy.
http://www.astrodigital.org/astronomy/so…
http://www.enchantedlearning.com/subject…

The Earth will never pass the centre of the Milky Way because the Sun is in a stable orbit 27,000 light years away from the centre.