Finding the planet mass from Barnard's star oscillation amplitude

[shirin]

There is a problem:
"The distance of Barnard’s star is 1.83 pc and mass 0.135 M. It has been suggested that it oscillates with an amplitude of 0.026"

in 25 year periods. Assuming this oscillation is caused by a planet, find the mass and radius of the orbit of this planet."
My question is what is 0.026"? Is it the angular size of 2*a of the star's orbit?

 

[Astronuc]

There is a problem:
"The distance of Barnard’s star is 1.83 pc and mass 0.135 M. It has been suggested that it oscillates with an amplitude of 0.026"

in 25 year periods. Assuming this oscillation is caused by a planet, find the mass and radius of the orbit of this planet."
My question is what is 0.026"? Is it the angular size of 2*a of the star's orbit?

I imagine that the 0.026'' is 0.026 arcseconds as measured by the observer on earth. One has a distance to the star of 1.83 pc.

There are some symbols that appear as boxes.

 

[shirin]

I don't know what it means that "the star oscillates with an amplitude of 0.026 arcsec"?
Does it mean that the angular size of its elliptical orbit (2a) around center of mass is 0.026? or whatelse?

 

[Astronuc]

I don't know what it means that "the star oscillates with an amplitude of 0.026 arcsec"?
Does it mean that the angular size of its elliptical orbit (2a) around center of mass is 0.026? or whatelse?

If a star is moving back and forth against the field of stars, then it means the star is revolving about some moment around the center of mass. At one time it is in one position, then in half the period, it is 0.026 arcsec from that position - diametrically opposed. The shorter arm is the one between COM and heavier mass.

Knowing the arclength and distance, one can calculate the moment arm of the star, or distance from the system's COM.