Using 1AU (mean earth-sun distance)=`1.5 xx10^(11)m` and parsec as distance at which 1AU subtends an angle of 1 sec of arc, find parsec in metres.

Astronomical distances are so large compared to terrestrial ones that much larger units of length are used for easy comprehension of the relative distances of astronomical objects. An astronomical unit (AU) is equal to the average distance from Earth to the Sun, 1.50xx10^(8)km . A parsec (pc) is the distance at which 1 AU would subtend an angle of 1 second of arc. A light year (ly) is the distance that light, traveling through a vacuum with a speed of 3.00xx10^(5) km/s, would cover in 1 year. Express a light - year and a parsec in kilometers.

Find the length which at a distance of 5280m will subtend an angle of 1' at the eye.

Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.

Suppose we invent a unit of mass which we shall call the caendish (C). One cavendish of mass is defined such that G = 1.0000(AU)^(3)//(yr^(2)C) . Our unit of length is the astronomical unit (AU) , the earth-sun distance -1AU = 1.496 xx 10^(11) m - and our unit of time is the year (yr) . (a) Datermine the conversion factor between C and kg. (b) Find the mass of the sun in C.

The principle of 'parallax' in section 2.3.1 is used in the determination of distances of very distant starts. The baseline AB is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth's orbit = 3xx10^(11)m . However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1" (second) of arc or so. A parsec is a conventent unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1" (second of arc) from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres ?