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Chapter 17: Problem 34

Suppose that a dim star were located 2 million AU from the Sun. Find (a) the distance to the star in parsecs and (b) the parallax angle of the star. Would this angle be measurable with present-day techniques?

Short Answer

Expert verified
The distance to the star is approximately 9.7 parsecs. The parallax angle for the star is approximately 0.103 arcseconds. This parallax angle is near the limit of precision but still could be measurable with present-day techniques, although with a degree of uncertainty.

Step by step solution

01

Understand AU and parsec

The Astronomical Unit (AU) is the distance from the Sun to the Earth. This is about 150 million kilometers. The parsec (pc) is the distance at which the mean radius of the earth's orbit subtends an angle of one second of arc, or about 3.086 x 10^16 meters, or about 3.26 light-years.
02

Conversion of AU to parsecs

Given 2 million AU, we want to convert this to parsecs. Using the fact that 1 parsec = 206,265 AU we find that the distance is \(\frac{2,000,000}{206,265} \approx 9.7 parsecs.\)
03

Parallax angle calculation

The parallax angle is given by the relationship \(p=\frac{1}{d}\) where p is the parallax angle in arcseconds and d is the distance in parsecs. Using the distance calculated in step 2, \(d = 9.7 parsecs\), we get that the parallax angle \(p = \frac{1}{9.7} \approx 0.103 arcseconds.\)
04

Assess measurability

The current limit of accuracy with ground-based measurements is around 0.01 arcseconds. In principle, therefore, a parallax of 0.103 arcseconds could be measurable with present-day techniques, although it would be at the limit of precision and thus subject to a degree of uncertainty.

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Most popular questions from this chapter

Some giant and supergiant stars are of the same spectral type (G2) as the Sun. What aspects of the spectrum of a G2 star would you concentrate on to determine the star's luminosity class? Explain what you would look for.

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