Orbit around the Galactic Center

[Philosophaie]

The Galactic Center of the Milky Way is about 25,900 light years away from the solar system. Its mass is 4.31E6*(Mass of the Sun). What I would like to know is what is the elliptical, circular, or etc orbit around the singularity especially the vector v and vector r. And if there is one, the reference frame that is commonly used for this singularity?

 

[Matterwave]

You're talking about the orbit the Sun makes around the galactic center or the orbits of the stars near the center which orbit the supermassive black hole?

 

[Philosophaie]

I would like the orbit the Sun makes around the galactic center of the Milky Way Galaxy! All I need is just two vectors: the velocity of the Sun in the reference frame of the singularity and the radius of the Sun to the singularity in the reference frame of the singularity.

 

[Chronos]

Oh, the alignment between earth, sun and the galactic center is so exciting . . . what a bunch of crap. If the cubs win the world series in 2012, i might worry.

 

[D H]

I would like the orbit the Sun makes around the galactic center of the Milky Way Galaxy! All I need is just two vectors: the velocity of the Sun in the reference frame of the singularity and the radius of the Sun to the singularity in the reference frame of the singularity.

The solar system does not follow a Keplerian path (i.e., conic section) about the galaxy. Keplerian orbits arise in system comprising a single large central mass with all other objects having inconsequential mass. While the galaxy does have a large central mass, the mass of that singularity (~4.1 million solar masses) is but a small fraction of the total mass of the galaxy (~580 billion solar masses).