(I) The parallax angle of a star is 0.00029^∘ . How far away...

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Key Concepts

Parallax

Parallax is the apparent shift of an object's position when observed from two different points. In astronomy, it is especially useful because the small angular displacement measured as Earth orbits the Sun provides a basis for determining the distance to nearby stars. The basic idea is that the closer the object, the larger its apparent shift against distant backgrounds, which allows astronomers to calculate its distance using geometric relationships.

Parsec as a Distance Unit

A parsec is a unit of measurement used in astronomy, defined as the distance at which 1 astronomical unit (AU) subtends an angle of one arcsecond. This unit conveniently arises from the geometry of Earth's orbit and stellar parallax, allowing astronomers to directly convert parallax angle measurements in arcseconds to distances in parsecs using the formula d = 1/p, where d is the distance in parsecs and p is the parallax angle in arcseconds.

Unit Conversion (Degrees to Arcseconds)

Converting angular measurements between units is crucial in astronomy because parallax angles are often very small. Typically, parallax is expressed in arcseconds for computational convenience. Since one degree is equal to 3600 arcseconds, converting a parallax angle from degrees to arcseconds ensures that the distance formula d = 1/p is used correctly with consistent units.

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