How can the small angle formula be used to measure the physical size of a star?

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Discussion Overview

The discussion revolves around the application of the small angle formula to measure the physical size of stars, particularly focusing on how to determine the angular size of a star like Betelgeuse, which is located 600 light years away. Participants explore the theoretical and practical aspects of measuring angular size and the challenges associated with distant stars.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant explains that the small angle formula relates the angular size of an object to its physical size and distance from the observer, questioning how to find the angular size of Betelgeuse.
  • Another participant suggests using a right triangle to conceptualize the measurement, indicating that the angle at the observer's position is half the angular size and can be calculated using the inverse tangent function.
  • This participant notes that if the distance to the star and its angular size are known, the radius of the star can be derived using the tangent of the half-angle.
  • A later reply points out the difficulty in measuring the angular size of most stars, stating that they appear as points even with the best telescopes, and mentions that only a few stars are close enough to measure their parallax due to Earth's orbit.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of measuring the angular size of stars, with some suggesting methods while others highlight the limitations posed by distance.

Contextual Notes

There are unresolved assumptions regarding the measurement techniques and the specific conditions under which angular sizes can be determined for distant stars.

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Basically this formula relates the angular size of an object (how big the object appears to an observer), the actual physical size d of the object, and the distance D from the observer to the object.

So let's say i want to find the physical size of Betelgeuse. As a scientist figuring this out, how would you find theta, or angular size of a star 600 light years away, and what is the angular size actually measuring?
 
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I'm not sure what you're asking. It's simple enough to draw a right triangle with one leg as the line from the observer to the center of the star, and the other leg as a radius of the star, taken perpendicular to the first line. The angle at the observer's end is half the angular size (since we're looking at the radius and not the diameter), which you get get using the inverse tangent.

If you know the distance to the star and its angular size, which you measure optically, the you can get the radius of the star by using the tangent of the half-angle.

The angles in such cases are very small of course ...
 
thank you for clearing that up for me
 
unfortunately stars are too far away. Even in the best telescope they are points with no angular size. There are a few stars which are close enough to measure their paralax as the Earth moves in its orbit.
 

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