The astronomical unit (AU) is defined as the mean center-to-center distance from

Question

The astronomical unit (AU) is defined as the mean center-to-center distance from Earth to the Sun, namely 1.496x10^(11) m. The parsec is the radius of a circle for which a central angle of 1 s intercepts an arc of length 1 AU. The light-year is the distance that light travels in 1 y. (a) How many parsecs are there in one astronomical unit? (b) How many meters are in a parsec? (c) How many meters in a light-year? (d) How many astronomical units in a light-year? (e) How many light-years in a parsec?

Explanation / Answer

One AU = 1.496*10^11 m

From the definition given,
The arc length for 1 s central angle is 1 AU
The arc length for 360*60*60 s (360 degrees) central angle is
1.296*10^6 * 1.496*10^11 m = 1.938816*10^17 m
2(pi)R = 1.938816*10^17 m (Radius of the circle = parsec)
R = 3.0857*10^16 m

one parsec = 3.0857*10^16 m one light year = c*t = (3*10^8 m/s)*(3.156*10^7 s)        one light year = 9.468*10^15 m (a) 1Au/1 parsec = 1.496*10^11 m/3.0857*10^16 m      1Au/1 parsec = 4.85*10^-6                    1 AU = 4.85*10^-6 parsec (b)one parsec = 3.0857*10^16 m (c)one light year = 9.468*10^15 m (d)1 LY/1 AU = 9.468*10^15 m / 1.496*10^11 m     1 LY/1 AU = 6.33*10^4            1 LY = 6.33*10^4 AU (e) 1 parsec / 1 LY =  3.0857*10^16 m / 9.468*10^15 m      1 parsec / 1 LY = 3.26               1 parsec = 3.26 light years

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