Is 0.026 the Key to Unveiling a New Exoplanet's Characteristics?

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The discussion revolves around the oscillation of Barnard's star, which is suggested to have an amplitude of 0.026 arcseconds over a 25-year period, potentially indicating the presence of an orbiting planet. Participants are questioning the meaning of the 0.026 arcseconds, with some suggesting it represents the angular size related to the star's orbit around its center of mass. The distance to Barnard's star is noted as 1.83 parsecs, which is crucial for calculating the mass and radius of the hypothesized planet's orbit. There is also a focus on how the star's motion can be interpreted in terms of its position relative to other stars and the center of mass of the system. Understanding these parameters could lead to insights into the characteristics of the potential exoplanet.
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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?
 
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shirin said:
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.
 
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?
 
shirin said:
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.
 
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