Is 18.3 x10^-6 m/s^2 the value of the acceleration of the Earth Relative to the Milky Way barry center?

Answer 1

I thought a barycentre (as we spell it in England) was as between 2 objects and referred to the single point in space where the gravitational pull of each on the other were balanced.

Usually this point in space is inside the larger and more massive object (eg the star as regards a planet orbiting a star or eg the planet as regards a moon orbiting a planet).

In the Pluto - Charon system where their masses are similar, it is outside of Pluto's surface, but this is relatively unusual.

The barycentre, thus defined, is one of the foci of the elliptical orbit of each body.

HENCE I am a little puzzled (not to say bewildered) as to how one would work out a barycentre of 200-400 billion stars AND their entourages,

Perhaps you mean the Galactic Centre which in the case of the Milky Way is a Supermassive Black Hole in Sagittarius?

And would not the issue be the velocity and acceleration of the Sun (not the Earth which is not independent in these matters) wlth regard to the Galactic Centre, anyway?

My understanding is that Kepler's Second Law would apply (the Sun swept out equal areas in equal time) and therefore it would speed up when it was near perigalacticon (its closest approach to the Galactic Centre) and it would slow down when it was near apgalacticon (its furthest distance from the Galactic Centre) and so sometimes it would be accelerating (though not towards the Galactic Centre but tangentially to its orbit around it) and sometimes decelerating i.e. there would be no single rate of acceleration that applied throughout at all points of the orbit, as your question seems to imply. (It would constantly be changing.)

However the presence of dark matter (sic) near the centre of the Milky Way may well mean Kepler's Laws do not transpose well to it.

The other difficulty is that the semi-major axis of the Sun's orbit in the Milky Way is only known imprecisely as is the length of the Galactic Year (the time talen to complete one orbit) (225-250 million years),

The distance from the Sun to the galactic centre is now estimated at 26,000 ± 1400 light-years while older estimates could put our parent star as far as 35,000 light-years from the central bulge.

So even if I knew what you were really asking, this would be very hard to answer.

The best I can offer you is

(1) The orbital speed of the solar system around the galactic centre is 217 km/s, i.e. 1 light-year in circa. 1400 years, and 1 AU in 8 days.

(2) As is typical for many galaxies, the distribution of mass in the Milky Way is such that the orbital speed of most stars in the galaxy does not depend strongly on its distance from the centre. Away from the central bulge or outer rim, the typical stellar velocity is between 210 and 240 km/s.

Hence the orbital period of the typical star is directly proportional only to the length of the path traveled. This is unlike in the solar system where different orbits are also expected to have significantly different velocities associated with them, and is one of the major pieces of evidence for the existence of dark matter in the galaxy.

(3) many astronomers believe the galaxy is moving through space at approximately 600km per second relative to the observed locations of other nearby galaxies. Most recent estimates range from 130 km/s to 1,000 km/s.

If indeed the Milky Way is moving at 600 km per second, we are traveling 51.84 million km per day, or more than 18.9 billion km per year. For comparison, this would mean that each year, we are traveling about 4.5 times the distance that Pluto lies from the Earth (at its closest).

The Milky Way is thought to be moving in the direction of the constellation Hydra, and may someday become a close-knit member of the Virgo cluster of galaxies.

Answer 2

Interesting.

Let's lok at your definations first:

Barycenter:

The barycenter (or barycentre; from the Greek βαρύκεντρον) is the point between two objects where they balance each other. In other words, the center of gravity where two or more celestial bodies orbit each other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting around a point which lies outside the center of the greater body. For example, the moon does not orbit the exact center of the earth, instead orbiting a point outside the earth's center (but well below the surface of the Earth) where their respective masses balance each other. The barycenter is one of the foci of the elliptical orbit of each body. This is an important concept in the fields of astronomy, astrophysics, and the like (see two-body problem).

OK, in caluclating the barycenter between the earth and the center of the galaxy the amount from the center is (for all practical purposes) 0 distance from the center of the galaxy. The mass of the galaxy so overwhelms the mass of the earth that calculations become meaningless.

If you mean the barycenter of the galaxy as a whole, including all the different masses in the galaxy then the calculation become impossible since there are way to many unknowns.

So, let's just say the acceleration to the center of the milky way.

Now we are getting somewhere!

Now, the speed at which the solar system orbits the center of the milky way is about 700,000 km/hr (http://en.wikipedia.org/wiki/Orders_of_magnitude_%28speed%29) and the distance is 26,000 light years to 35,000 light years from the galactic center (http://en.wikipedia.org/wiki/Galactic_coordinate_system). Taking 31,000 light years as the distance (not exact, but close enough, you can calulate the acceleration.

Answer 3

Hi. I never worked that out before, but there is a lot of material outside of Earth's galactic orbit, so the problem is complex.

Answer 4

Seems awfully small considering the magnitude of the galaxy.