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Betelgeuse (in Orion) has a parallax of 0.00451 + 0.00080 arcsec,as measured by the Hipparcos satellite. What is the distance to Betelgeuse, and what is the uncertainty in that measurement?

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Betelgeuse, the bright red star in the constellation of Orion the Hunter, is in the end stage of its stellar life. Astronomers have long thought it will someday explode to become a supernova. In late 2019 and early 2020, Betelgeuse generated a lot of
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We have that  the distance to Betelgeuse, and the uncertainty in that measurement is

  • [tex]d=(221.7\pm39.33)pc[/tex]
  • Uncertainty U = 0.00080

From the Question we are told that

Betelgeuse (in Orion)  has a parallax of 0.00451 + 0.00080

Generally

[tex]Distance\ in\ parsecs =\frac{ 1}{(parallax\ measured\ in\ arcseconds}[/tex]

Where

Parallax [tex]P =0.00451[/tex]

Uncertainty [tex]U = 0.00080[/tex]

Generally the equation for the distance  is mathematically given as

[tex]d=(\frac{1}{P}pc\pm(\frac{U}{P}*100\%))[/tex]

Therefore

[tex]d=(\frac{1}{0.00451}pc\pm(\frac{0.00080}{0.00451}*100\%))[/tex]

[tex]d=(221.7\pm39.33)pc[/tex]

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