Exploring starlight：練習問題

In a simple Hertzsprung-Russell (H-R) diagram, where would a star like our Sun be located during its current evolutionary phase?

A Cepheid variable star is observed to have a period of \(20\) days. How do astronomers use this information to determine the distance to the star's host galaxy?

An astronomer observes a star with an apparent magnitude (\(m\)) of \(+1.4\) and a distance of \(25\) pc. Using the distance modulus formula \(M = m + 5 - 5 \log_{10} d\), calculate the absolute magnitude (\(M\)) of the star.

An astronomer measures the heliocentric parallax (\(p\)) of a nearby star as \(0.125\) arcseconds ("). Calculate the distance to this star in parsecs.

Which of the following describes the relationship between the surface temperature of a star and its spectral classification in the Harvard system?

Describe the specific role of an aperture synthesis system (array) in radio astronomy and why this technique is necessary for obtaining high-resolution images.

Explain why infrared telescopes are often placed at high-altitude locations or in space, focusing on the specific components of the Earth's atmosphere that interfere with observations.

A star has an apparent magnitude of \( m = 1.4 \) and is located at a distance of \( d = 25 \text{ pc} \). Calculate the absolute magnitude \( M \) of the star using the formula \( M = m + 5 - 5 \log_{10} d \).

A student observes a star and determines its surface temperature is approximately \(3,500\) K.

(a) Identify the most likely spectral type (O, B, A, F, G, K, or M) for this star and state its typical colour.
(b) On a sketch of a Hertzsprung-Russell (H-R) diagram, describe where this star would be located if it were a Red Supergiant compared to its location if it were a Main Sequence star. Mention both the luminosity (y-axis) and temperature (x-axis) positions.

The star Procyon has a measured heliocentric parallax of \(0.286\) arcseconds.

(a) Calculate the distance to Procyon in parsecs (pc). Use the relationship \(d = \frac{1}{p}\).
(b) Convert this distance into light years (l.y.), given that \(1\text{ pc} = 3.26\text{ l.y.}\).
(c) Procyon is part of a binary system. Explain how an astronomer can deduce the orbital period of an eclipsing binary star from its light curve, and describe one feature of the light curve that indicates the stars have different surface temperatures.