Question

Astronomical unit $(AU)$is the average distance between the earth and sun, approximately $1.5 \times {10^8}km$. The speed of light is about $3.0 \times {10^8}$m/s. the speed of light in astronomical unit per minute is
(A) $0.012AU/\min $
(B) $0.12AU/\min $
(C) $1.2AU/\min $
(D) $12.0AU/\min $

Answer 1

Hint: The astronomical unit is a unit of length, roughly the distance from earth to the sun and equal about $150$million kilometers. The actual distance varies as earth orbits the sun, from a maximum to a minimum and back again once each year.

Complete step by step answer:
We convert meters to astronomical unit, and seconds to minutes, using
$ 1000m = 1km \\
  1AU = 1.50 \times {10^8}km \\
  60s = 1\min \\
$
Thus, $3.0 \times {10^8}m/s$becomes
$\left( {\dfrac{{3.0 \times {{10}^8}m}}{8}} \right)\left( {\dfrac{{1km}}{{1000m}}} \right)\left( {\dfrac{{60s}}{{\min }}} \right) = 0.12AU/\min $
Astronomical unit: a unit of measurement equal to $149.6$million kilometers, the mean distance from the center of the sun. terrestrial planet.
A light year is the distance light travels in one year, while AU, otherwise known as an astronomical unit, is the distance between the sun and the earth. A light year is approximately $9.5 \times {10^{12}}km$. An AU is $149600000km$. As you can probably tell, an AU is much shorter than a light year.
Hence, the correct option is (B) $0.12AU/\min $

So, the correct answer is “Option B”.

Note:
$1672$ the Italian-born French astronomer Gian Domenico Cassini made a reasonably close estimate of the astronomical unit based on a determination of the parallax displacement of the planet Mars-and thus its distance to earth. One of the most important of these is the astronomical unit. It is a unit of length approximating the sun earth distance which is of convenient use in astronomy. Beyond the solar system distance in astronomy are so great that using the au becomes too cumbersome.