What is the length of the apogalacticon and perigalacticon of the Sun and Milky Way? The general terms seem to be apoapsis and periapsis.
My greatest efforts at Googling have failed miserably. If you can provide references as well, please do!
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According to this website we need another 15 million years to the perigalacticon.
Recall the Sun's motion ... 30 degrees toward the galactic centre from circular motion, and 23 degrees upward out of the galactic plane. We will be at perigalacticon (closest to the nucleus) in 15 million years. At apogalacticon the Sun is seven percent farther out.
This vertical oscillation cycles at 3.5 times per galactic year.
We are now about 27,000 lightyears away from the galactic center, close to the perigalacticon. The difference between apogalacticon and perigalacticon is a little more than 4,000 lightyears (15% of 27,000 lightyears). The 15% number is calculated from the 7% eccentricity of the orbit by $1.07/0.93=1.15~~$ according to the definition of eccentricity, and Kepler's 1st law.
user68441 is in error. We are not part of the Sagittarius Dwarf Elliptical Galaxy. Our velocity perpendicular to the galactic plane is only 4.95±0.09 km/s with respect to the Local Standard of rest.
Each cycle takes about 70 million years with an amplitude of 100pc (Matese et al. 1995), it will be roughly 30 million years before we cross the plane again.
Given the thickness of the disk is roughly 1000LY, the solar system will stay within the disk, unless perturbed by an interaction with another star.