21st Century Astronomy (fifth Edition)
5th Edition
ISBN: 9780393603330
Author: Laura Kay, Stacy Palen, George Blumenthal
Publisher: W. W. Norton & Company
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Chapter 16.2, Problem 16.2CYU
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Let's calculate how much mass will be lost by the Sun during the course of its main-sequence lifetime. While it is on the main sequence, a star converts about 10% of the hydrogen initially present into helium (remember that it is only the core of the star that is hot enough for fusion). During nuclear fusion, the Sun converts about 0.7% of the core hydrogen mass into energy. The total mass of the Sun is 2 × 1030 kg. How many kilograms of mass will be converted to energy during the main sequence stage of the Sun's life? What is the ratio of this lost mass to the Earth's mass (6 × 1024 kg)? In other words, how many Earths of mass will be turned into energy?
A Crude Analysis:
In about 5 billion years, the Sun is going to look a lot different. Our
sun is going to turn into a red-giant, a bigger star whose core
temperature is much higher than the Sun's current core temperature
(you will learn about the red giants in the coming weeks). Assume
the core temperature of the red-giant phase of the Sun does not go
beyond 100 million degrees.
Do you think the temperature is high enough for helium fusion to
occur? Note that this question is about helium fusion not hydrogen
fusion. How are you going about proving your claim?
Question: What temperature in degrees Kelvin must the red-giant
sun be at to allow for the helium-helium interactions to take place
not considering the Quantum Mechanical effects (i.e. what
temperature would allow helium atoms to breach the helium-helium
potential wall without help from Quantum Mechanics)? Use wolfram
alpha to find the values for the constants. Round your answer to two
decimal places.
Your answer i [ Select ]
1.47…
a) At solar maximum sunspots might cover up to 0.4% of the total area of the Sun. If the sunspots have a temperature of 3800 K and the surrounding photosphere has a temperature of 6000 K, calculate the fractional change (as a percentage) in the luminosity due to the presence of the sunspots.
b) A star of the same stellar class as the Sun is observed regularly over many years, and a time series of its bolometric apparent magnitude is collected. What would be the signal in this time series which indicated that the star had a magnetic dynamo similar to the Sun? Briefly describe two or three possible sources of other signals which could confuse the interpretation of the data.
Chapter 16 Solutions
21st Century Astronomy (fifth Edition)
Ch. 16.1 - Prob. 16.1CYUCh. 16.2 - Prob. 16.2CYUCh. 16.3 - Prob. 16.3CYUCh. 16.4 - Prob. 16.4CYUCh. 16.5 - Prob. 16.5CYUCh. 16 - Prob. 1QPCh. 16 - Prob. 2QPCh. 16 - Prob. 3QPCh. 16 - Prob. 4QPCh. 16 - Prob. 5QP
Ch. 16 - Prob. 6QPCh. 16 - Prob. 7QPCh. 16 - Prob. 8QPCh. 16 - Prob. 9QPCh. 16 - Prob. 10QPCh. 16 - Prob. 11QPCh. 16 - Prob. 12QPCh. 16 - Prob. 13QPCh. 16 - Prob. 14QPCh. 16 - Prob. 15QPCh. 16 - Prob. 16QPCh. 16 - Prob. 17QPCh. 16 - Prob. 18QPCh. 16 - Prob. 19QPCh. 16 - Prob. 20QPCh. 16 - Prob. 21QPCh. 16 - Prob. 23QPCh. 16 - Prob. 24QPCh. 16 - Prob. 25QPCh. 16 - Prob. 26QPCh. 16 - Prob. 27QPCh. 16 - Prob. 28QPCh. 16 - Prob. 29QPCh. 16 - Prob. 30QPCh. 16 - Prob. 31QPCh. 16 - Prob. 32QPCh. 16 - Prob. 33QPCh. 16 - Prob. 34QPCh. 16 - Prob. 35QPCh. 16 - Prob. 36QPCh. 16 - Prob. 37QPCh. 16 - Prob. 38QPCh. 16 - Prob. 39QPCh. 16 - Prob. 40QPCh. 16 - Prob. 41QPCh. 16 - Prob. 42QPCh. 16 - Prob. 43QPCh. 16 - Prob. 44QPCh. 16 - Prob. 45QP
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- Select all of the statements about the main sequence stage in the life of a star that are TRUE: All stars spend the majority of their lives in the main sequence stage. Most stars lose a significant amount of mass while they are on the Main Sequence. Different stars spend a different amounts of time (number of years) in the main sequence stage, depending on the characteristics they were born with. Main sequence stars are rare in the Galaxy, so we are lucky to be living around one. During the main sequence stage, energy to power the star is provided by the fusion of hydrogen.arrow_forwardOnly about 11% of the initial Hydrogen in the Sun is in the core where it is hot enough to burn. What was the total mass of the initial H in the core of the Sun?arrow_forwardOnly about 11% of the initial Hydrogen in the Sun is in the core where it is hot enough to burn. What was the total mass of the initial H in the core of the Sun? (Mass of the Sun is 1.989 × 10^30 kg)arrow_forward
- For a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W). (Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)arrow_forwardThe Sun’s luminosity (or power) is 4 x 1026 Watts (=J/s). How many kilograms of hydrogen must be fused every second to maintain this luminosity? (hint: work backwards from the energy per second to the mass released to the amount of hydrogen required, using the results from the previous question.) The Sun’s mass is ~2x1030 kg. If 10% of this is Hydrogen available in the core, how long will the Sun be able to continue fusing hydrogen at this rate? This is considered the Sun's "lifetime". If the Sun is 4.6 billion years old (and assuming it's power output is constant), how many years does it have left?arrow_forward1. The mass of the Sun is about 2x10³0 kg. The Sun was about 72% hydrogen when it first formed. About 11% of the total amount of the Sun's hydrogen is available for fusion within the Sun's core. [3 points] (a) What is the total mass of hydrogen available for fusion, in kg? (b) The Sun fuses about 600 billion kg of hydrogen each second. Calculate how long the Sun's initial supply of hydrogen can last. Give your answer in both seconds and years. Hint: use the result you calculated in part (a). (c) We know that our Solar System is about 4.5 billion years old. Using your calculation above, how much longer do we have until the Sun runs out of hydrogen?arrow_forward
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