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

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Discussion Overview

The discussion revolves around the interpretation of the oscillation amplitude of Barnard's star, specifically the value of 0.026 arcseconds, and its implications for understanding the potential presence of an exoplanet. Participants are exploring the theoretical aspects of this oscillation in relation to the star's orbit and the characteristics of any orbiting planet.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question whether the 0.026 arcseconds refers to the angular size of 2*a of the star's orbit around the center of mass.
  • Others suggest that 0.026 arcseconds is a measurement as observed from Earth, indicating potential oscillatory motion of the star.
  • There is uncertainty about the meaning of the term "oscillates with an amplitude of 0.026 arcsec," with participants proposing different interpretations regarding the nature of the star's motion.
  • One participant discusses the implications of the star's movement in relation to the center of mass and the calculation of the moment arm based on the arclength and distance.

Areas of Agreement / Disagreement

Participants express varying interpretations of the meaning of 0.026 arcseconds and its implications for the star's motion. There is no consensus on the exact interpretation or significance of this value.

Contextual Notes

Some participants note the presence of symbols that appear as boxes, indicating potential formatting issues in the original problem statement. The discussion also highlights the need for clarity on the definitions and assumptions related to angular measurements and orbital mechanics.

shirin
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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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