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I Take the diameter AB of the Earth's orbit as 3 x 10 km and consider a star S at a distance d, such that SA = SB and the angle ASB = 2 arcseconds. Calculate d. This is the distance unit of one parsec. Relate it to one light year.

I Take the diameter AB of the Earth's orbit as 3 x 10 km and consider a star S at a distance d, such that SA = SB and the angle ASB = 2 arcseconds. Calculate d. This is the distance unit of one parsec. Relate it to one light year.

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used in the rest of this book. Exercises I Take the diameter AB of the Earth's orbit as 3 x 108 km and consider a star S at a distance d, such that SA = SB and the angle ASB = 2 arcseconds. Calculate d. This is the distance unit of one parsec. Relate it to one light year. 2 Given that the Sun takes ~2 × 108 years to make a circular orbit around the Galactic Centre, staying at a distance of 10 kpc, estimate the mass of the Galaxy contained within the solar orbit, assuming that it is spherical and ignoring any effects of mass lying outside the orbit. (You may use Newtonian dynamics and gravitation.) 3 A galaxy has a visible mass of 101 Mo and a flat rotation curve extending to 25 kpc at the level of 150 km s-1. What is the ratio of its dark-matter mass to its visible mass? 4 Compute the gravitational energy of a pair of colliding galaxies, each of mass 10"Mo, separated by a distance of ~10 kpc and compare it with the energy requirements of a powerful radio source. What conclusion do you arrive at from such a comparison? Using a Hubble constant given by ho = 0.6, place an approximate upper limit on the angular size of a quasar of redshift z = 0.2 if it exhibits a time variability on the scale of I h. (Use the argument that no physical effect travels in a material object faster than light.) Use the energy density of the microwave background given in Table 1.3 to estimate its temperature, assuming that it has a blackbody form.
Transcribed Image Text:used in the rest of this book. Exercises I Take the diameter AB of the Earth's orbit as 3 x 108 km and consider a star S at a distance d, such that SA = SB and the angle ASB = 2 arcseconds. Calculate d. This is the distance unit of one parsec. Relate it to one light year. 2 Given that the Sun takes ~2 × 108 years to make a circular orbit around the Galactic Centre, staying at a distance of 10 kpc, estimate the mass of the Galaxy contained within the solar orbit, assuming that it is spherical and ignoring any effects of mass lying outside the orbit. (You may use Newtonian dynamics and gravitation.) 3 A galaxy has a visible mass of 101 Mo and a flat rotation curve extending to 25 kpc at the level of 150 km s-1. What is the ratio of its dark-matter mass to its visible mass? 4 Compute the gravitational energy of a pair of colliding galaxies, each of mass 10"Mo, separated by a distance of ~10 kpc and compare it with the energy requirements of a powerful radio source. What conclusion do you arrive at from such a comparison? Using a Hubble constant given by ho = 0.6, place an approximate upper limit on the angular size of a quasar of redshift z = 0.2 if it exhibits a time variability on the scale of I h. (Use the argument that no physical effect travels in a material object faster than light.) Use the energy density of the microwave background given in Table 1.3 to estimate its temperature, assuming that it has a blackbody form.
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