14. Astronomy and cosmology A.md

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Understand: What is meant by the term 'luminosity' in the context of stars? Answer: In the context of stars, luminosity refers to the total power of radiation emitted by a star. It is a measure of a star's total energy output per unit of time, often expressed in watts.

Recall and Use: How is the inverse square law used to calculate radiant flux intensity in terms of the luminosity of a source? Answer: The inverse square law is used to calculate the radiant flux intensity (F) in terms of the luminosity (L) of a source using the formula , where \(d\) is the distance from the source. According to this law, the intensity of the radiation decreases with the square of the distance from the source.

Understand: What is a 'standard candle' in astronomy? Answer: A 'standard candle' in astronomy is an object of known luminosity. These objects are used as benchmarks or reference points to measure astronomical distances. By comparing the known luminosity of a standard candle with its observed brightness, we can calculate the distance to the object.

Understand: How are standard candles used to determine distances to galaxies? Answer: Standard candles are used to determine distances to galaxies by comparing the known luminosity of the standard candle with its observed brightness. The apparent brightness of an object decreases with increasing distance. Therefore, by knowing the luminosity of the standard candle, we can calculate the distance to the galaxy using the inverse square law.

Recall and Use: How is Wien’s displacement law used to estimate the peak surface temperature of a star? Answer: Wien's displacement law states that the wavelength of the peak radiation emitted by a black body is inversely proportional to its temperature. The law is often written as . By measuring the wavelength of the peak radiation from a star, we can estimate the surface temperature of the star using this law.

Use: How is the Stefan–Boltzmann law used? Answer: The Stefan–Boltzmann law relates the total energy radiated per unit surface area of a black body to its absolute temperature. The law is often written as , where \(L\) is the luminosity, \(\sigma\) is the Stefan-Boltzmann constant, \(r\) is the radius of the star, and \(T\) is the temperature.

Use: How can Wien’s displacement law and the Stefan–Boltzmann law be used together to estimate the radius of a star? Answer: Wien's displacement law can be used to estimate the temperature of a star, and the Stefan–Boltzmann law can then be used to estimate the radius of the star. By measuring the wavelength of the peak radiation from a star, we can estimate the surface temperature of the star using Wien's law. Then, knowing the luminosity and temperature of the star, we can calculate the radius of the star using the Stefan–Boltzmann law.

Understand: What does it mean when the lines in the emission spectra from distant objects show an increase in wavelength from their known values? Answer: When the lines in the emission spectra from distant objects show an increase in wavelength from their known values, it means that the light from these objects has been redshifted. This is a phenomenon caused by the Doppler Effect, where the frequency (and thus the wavelength) of light changes due to the relative motion between the source of the light and the observer. In this case, the increase in wavelength indicates that the distant objects are moving away from us.

Use: How is the formula used for the redshift of electromagnetic radiation from a source moving relative to an observer? Answer: This formula is used to calculate the redshift of electromagnetic radiation. Here, is the change in wavelength, is the original wavelength, is the change in frequency, is the original frequency, is the velocity of the source relative to the observer, and is the speed of light. The change in wavelength or frequency is directly proportional to the velocity of the source, and this relationship is used to calculate the redshift.

Explain: Why does redshift lead to the idea that the Universe is expanding? Answer: The redshift of light from distant galaxies indicates that these galaxies are moving away from us. This observation, which is consistent across the vast majority of galaxies we can observe, leads to the conclusion that the Universe is expanding. The more distant a galaxy is, the greater its redshift, which implies that it is moving away from us at a faster rate. This suggests that all galaxies are moving away from each other, indicating an overall expansion of the Universe.

Recall and Use: How is Hubble’s law expressed and how does it support the Big Bang theory? Answer: Hubble's law is expressed as , where is the recessional velocity of a galaxy, is the Hubble constant, and is the distance to the galaxy. Hubble's law states that the further a galaxy is from us, the faster it is moving away, which supports the idea of an expanding Universe. This observation is a key piece of evidence for the Big Bang theory, which posits that the Universe started from a very hot, dense state and has been expanding ever since.