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Chapter 15: Problem 52

The Sun took 30 million years to evolve from a collapsing cloud core to a star, with 10 million of those years spent on its Hayashi track. It will spend a total of 10 billion years on the main sequence. Suppose the Sun's main- sequence lifetime were compressed into a single day. a. How long would the total collapse phase last? b. How long would the Sun spend on its Hayashi track?

Short Answer

Expert verified
The collapse phase would last 0.072 hours, and the Hayashi track would last 0.024 hours.

Step by step solution

01

- Define the Compression Ratio

We are compressing the Sun's main-sequence lifetime of 10 billion years into a single day (24 hours). The compression ratio is therefore \ \( \frac{1 \text{ day}}{10 \text{ billion years}} \).
02

- Determine the Duration of the Collapse Phase in a Day

The total collapse phase took 30 million years. To find its duration in a compressed day: \( 30 \text{ million years} \times \frac{1 \text{ day}}{10 \text{ billion years}} = \frac{30 \text{ million}}{10 \text{ billion}} \text{ days} = 0.003 \text{ days} \). To convert days into hours, multiply by 24: \ \( 0.003 \text{ days} \times 24 \text{ hours/day} = 0.072 \text{ hours} \).
03

- Determine the Duration of the Hayashi Track Phase in a Day

The Hayashi track phase lasted 10 million years. To find its duration in a compressed day: \ \( 10 \text{ million years} \times \frac{1 \text{ day}}{10 \text{ billion years}} = \frac{10 \text{ million}}{10 \text{ billion}} \text{ days} = 0.001 \text{ days} \). To convert days into hours, multiply by 24: \ \( 0.001 \text{ days} \times 24 \text{ hours/day} = 0.024 \text{ hours} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sun's lifecycle
The Sun's lifecycle is a fascinating journey that showcases the evolution of a massive body of gas and plasma. Initially, it starts as a collapsing cloud core consisting mainly of hydrogen gas. This phase takes around 30 million years.
The gravity pulls the gas inward, eventually forming a protostar. Once it reaches enough pressure and temperature at the core, nuclear fusion ignites, converting hydrogen into helium.
This marks the beginning of the main sequence phase. Eventually, when it exhausts its fuel, the Sun will evolve into a red giant and finally shed its outer layers to form a planetary nebula, leaving behind a white dwarf.
Hayashi track
The Hayashi track represents a critical phase in the early life of the Sun and other similar stars. This phase involves the star contracting and radiating energy, but not yet initiating nuclear fusion. For our Sun, this phase lasted 10 million years.
During this phase, the star's temperature remains roughly constant while its luminosity increases. It's named after the Japanese astrophysicist Chushiro Hayashi, who described this phase.
The evolution during the Hayashi track is crucial as it leads the star towards the main sequence, where it achieves hydrostatic equilibrium and sustains fusion reactions at its core.
main sequence
The main sequence is the most stable and longest-lasting phase in the Sun's lifecycle. For our Sun, it will spend approximately 10 billion years in this phase.
During this time, the Sun fuses hydrogen into helium through nuclear fusion at its core, radiating energy that we perceive as sunlight. This period is marked by a balance between gravitational forces pulling inward and pressure from fusion pushing outward, which keeps the star stable.
Eventually, as the Sun exhausts its hydrogen fuel, it will leave the main sequence and enter the later stages of its lifecycle, leading to the formation of a red giant.

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Most popular questions from this chapter

Table 13.1 indicates that the ratio of hydrogen atoms \((\mathrm{H})\) to carbon atoms (C) in the Sun's atmosphere is approximately 2,\(400: 1 .\) It would be reasonable to assume that this ratio also applies to molecular clouds. If \(2.6-\mathrm{cm}\) radio observations indicate \(100 M_{\circ}\) of carbon monoxide (CO) in a giant molecular cloud, what is the implied mass of molecular hydrogen \(\left(\mathrm{H}_{2}\right)\) in the cloud? (Carbon represents \(^{3} / 7\) of the mass of a CO molecule.)

You can think of a brown dwarf as a failed star-that is, one lacking sufficient mass for nuclear reactions to begin. What are the similarities and differences between a brown dwarf and a giant planet such as Jupiter? Would you classify a brown dwarf as a supergiant planet? Explain your answer.

Molecular hydrogen is very difficult to detect from the ground, but astronomers can easily detect carbon monoxide (CO) by observing its 2.6 -cm microwave emission. Describe how observations of CO might help astronomers infer the amounts and distribution of molecular hydrogen within giant molecular clouds.

Molecular clouds fragment as they collapse because a. the rotation of the cloud throws some mass to the outer regions. b. the density increases fastest in the center of the cloud. c. density variations from place to place grow larger as the cloud collapses. d. the interstellar wind is stronger in some places than others.

In astronomy, the term bipolar refers to outflows that a. point in opposite directions. b. alternate between expanding and collapsing. c. rotate about a polar axis. d. show spiral structure.
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