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1.A cloud of neutral hydrogen is moving towards us at a speed of 70 kilometers per second. At what wavelength would one observe the radio spectral line characteristic of neutral hydrogen?
2. The filament in a regular incandescent light bulb reaches a temperature of 2900 k when it's on.
a. calculate the wavelength at which the blackbody radiation from this filament is most intense.
b. what type of light (e.g., ultraviolet, optical, infrared, radio) is a photon of this wavelength?
c. In light of your answer to part b explain why incandescent light bulbs are not a very efficient way to produce optical light.
3. If the ring nebula is a light-year in diameter and is expanding at a velocity of 15 km/s, typical of planetary nebular, how old is it?
4. The crab nebula is now 1.35 pc in radius and is expanding at 1400 km/s. About when did the supernova occur?
5. The supernova remnant Cassiopeia A is expanding in radius at a rate of about 0.5 second of arc per year. Doppler shifts show that the velocity of expansion is about 5700 km/s. How far away is the nebula?
6. If a neutron star has a radius of 10 km and rotates 716 times a second, what is the speed of the surface at the neutron star's equator in terms of the speed of light?
7. Suppose that a neutron star has a radius of 10 km and a temperature of 1,000,000 k. How luminous is it?
8. A certain telescope has an effective 10'x10' field of view that is recorded using a ccd chip having 2048 x 2048 pixels. What angle on the sky corresponds to 1 pixel? What would be the diameter of a typical seeing disk (1'' radius), in pixels?
9. Radio spectroscopy observations show us neutral hydrogen gas in the interstellar medium. Given the measured density of such hydrogen in the cloud, how big a volume would be required to contain one solar mass of such gas?
10. The Sun took 30 million years to evolve from a collapsing cloud core to a star. It will spend a total of 10 billion years on the main sequence. Suppose w were to compress the Sun's main sequence lifetime into just a single year. How long would the total collapse phase last?
11. The mean densities of stars can vary by enormous factors. For purposes of illustration, calculate the mean densities in units of average solar density for each of the following:
a. The supergiant star Betelqeuse, with a mass of 10 solar masses and a radius of 300 solar radii.
b. A 1.4 solar masses white dwarf, with a radius of 5 x 10 to the 7th power m.
c. A 1.4 solar mass neutron star, with a radius of 2 x 10 to the 4th power m. Assume that the radius of the sun is 7.0 x 10 to the 8th power m.
12. Estimate the main sequence lifetime for a 100 solar mass, 10 solar mass, 1 solar mass, 0.1 solar mass, and a 0.01 solar mass main sequence star. When a star goes through the main-sequence phase, does its luminosity remain constant? Explain.
13. With the aid of the mass-luminosity relation (L/Lsun)= (M/Msun)3.5 power of 10 and the Hertzsprung-Russell diagram, tabulate the luminosities (in units of the solar luminosity) and approximate surface temperatures of stars of 50, 1.0, and 0.1 solar masses.
14. Consider a model for the star DSCHUBBA, the center of the star in the head of the constellation Scorpious, consisting of a spherical blackbody with a surface temp. of 28,000 K and a radius of 5.16 x 10 to the 9th power m. If the star is located at a distance of 180 pc from Earth, determine the following for the star:
a. Luminosity
b. Energy flux density at the star's surface
c. Energy flux density at Earth's surface and compare with the solar constant
d. Peak wavelength, the wavelength symbol max
2. The filament in a regular incandescent light bulb reaches a temperature of 2900 k when it's on.
a. calculate the wavelength at which the blackbody radiation from this filament is most intense.
b. what type of light (e.g., ultraviolet, optical, infrared, radio) is a photon of this wavelength?
c. In light of your answer to part b explain why incandescent light bulbs are not a very efficient way to produce optical light.
3. If the ring nebula is a light-year in diameter and is expanding at a velocity of 15 km/s, typical of planetary nebular, how old is it?
4. The crab nebula is now 1.35 pc in radius and is expanding at 1400 km/s. About when did the supernova occur?
5. The supernova remnant Cassiopeia A is expanding in radius at a rate of about 0.5 second of arc per year. Doppler shifts show that the velocity of expansion is about 5700 km/s. How far away is the nebula?
6. If a neutron star has a radius of 10 km and rotates 716 times a second, what is the speed of the surface at the neutron star's equator in terms of the speed of light?
7. Suppose that a neutron star has a radius of 10 km and a temperature of 1,000,000 k. How luminous is it?
8. A certain telescope has an effective 10'x10' field of view that is recorded using a ccd chip having 2048 x 2048 pixels. What angle on the sky corresponds to 1 pixel? What would be the diameter of a typical seeing disk (1'' radius), in pixels?
9. Radio spectroscopy observations show us neutral hydrogen gas in the interstellar medium. Given the measured density of such hydrogen in the cloud, how big a volume would be required to contain one solar mass of such gas?
10. The Sun took 30 million years to evolve from a collapsing cloud core to a star. It will spend a total of 10 billion years on the main sequence. Suppose w were to compress the Sun's main sequence lifetime into just a single year. How long would the total collapse phase last?
11. The mean densities of stars can vary by enormous factors. For purposes of illustration, calculate the mean densities in units of average solar density for each of the following:
a. The supergiant star Betelqeuse, with a mass of 10 solar masses and a radius of 300 solar radii.
b. A 1.4 solar masses white dwarf, with a radius of 5 x 10 to the 7th power m.
c. A 1.4 solar mass neutron star, with a radius of 2 x 10 to the 4th power m. Assume that the radius of the sun is 7.0 x 10 to the 8th power m.
12. Estimate the main sequence lifetime for a 100 solar mass, 10 solar mass, 1 solar mass, 0.1 solar mass, and a 0.01 solar mass main sequence star. When a star goes through the main-sequence phase, does its luminosity remain constant? Explain.
13. With the aid of the mass-luminosity relation (L/Lsun)= (M/Msun)3.5 power of 10 and the Hertzsprung-Russell diagram, tabulate the luminosities (in units of the solar luminosity) and approximate surface temperatures of stars of 50, 1.0, and 0.1 solar masses.
14. Consider a model for the star DSCHUBBA, the center of the star in the head of the constellation Scorpious, consisting of a spherical blackbody with a surface temp. of 28,000 K and a radius of 5.16 x 10 to the 9th power m. If the star is located at a distance of 180 pc from Earth, determine the following for the star:
a. Luminosity
b. Energy flux density at the star's surface
c. Energy flux density at Earth's surface and compare with the solar constant
d. Peak wavelength, the wavelength symbol max
