How far is the Earth/Sun above/below the galactic plane, and is it heading toward/away from it?

Question

How far is the Earth/Sun above/below the galactic plane, and is it heading toward/away from it? We know the Sun is orbiting the galactic center every 225 million years. But how far are we from the galactic plane, and is the inclination of the plane of the Sun's orbit around the galactic center, as compared to the galactic plane, known?

According to this drawing

the Sun is traveling approximately in the ecliptic plane. However, the ecliptic plane is steeply inclined to the galactic plane, so if this drawing is correct (from voyager.jpl.nasa.gov) then this would mean the plane of the Sun's orbit around the galactic center is also quite inclined. And thus my question, what is the distance to the galactic plane, are we heading toward/away from it, and what is the inclination of the orbital plane of our Sun/solar system to the galactic plane? 3 questions I guess.

Answer 1

Humphreys & Larsen (1995) suggest, using star count information, a distance of $20.5 \pm 3.5$ pc above the Galactic plane; consistent with, but more precise than the Bahcall paper referred to by Schleis.

Joshi (2007) is more guarded, investigating some systematic uncertainties in the estimation techniques and ends up with distances between 13 and 28 pc above the plane. This paper gives an excellent review of the topic in its first couple of pages.

The Sun moves at about 15-20 km/s with respect to a local standard of rest defined by the general motion of stars in our vicinity around the Galaxy. In three-dimensions, this "peculiar velocity" is $U=10.00 \pm 0.36$ km/s (radially inwards), $V=5.25 \pm 0.62$ km/s (in the direction of Galactic rotation) and $W=7.17 \pm 0.38$ km/s (up and out of the plane). (Dehnen & Binney 1998)

The Sun executes oscillations around its mean orbit in the Galaxy, periodically crossing the Galactic plane. I borrowed this illustration (not to scale!) from http://www.visioninconsciousness.org/Science_B08.htm to show this oscillatory motion. As the Sun is currently above the plane and moving upwards, and 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.

EDIT: An update. A new analysis by Karim & Mamajek (2016) yields a distance above the plane of $17.1 \pm 5$ pc and they provide a meta-analysis of previous analyses that gives a median distance of $17.4 \pm 1.9$ pc. They also refer to a paper by Schonrich et al. (2010) that gives the velocity away from the plane as $7.25 \pm 0.37$ km/s (though with an additional systematic uncertainty of 0.5 km/s).

Answer 2

According to this article, we are somewhere between 75 and 101 light years above the plane and getting closer. So we won't be crossing it for quite some time.

http://earthsky.org/astronomy-essentials/will-earth-pass-through-galactic-plane-in-2012

This page has references to the research in regards to the calculations.

http://www.nature.com/nature/journal/v316/n6030/abs/316706a0.html

Answer 3

The position data of the sun in the Milky Way is very important, and these data will provide the basis for the calculation of the gravitational wave energy.

This is a paper on gravitational waves, and its analysis is based on classical mechanics. https://www.academia.edu/93320245/Influence_of_gravitational_waves_on_planetary_orbits_4_1