Question

Taking one light year i equal to \[9.4 \times {10^{15}}m\]and one day is equal to \[86400s\], what will be the speed of light in light year per day if the speed of light in m/s is $3 \times {10^8}m/s$.

Answer 1

Hint:-Here we will use light year and one day in terms of m and second respectively then substitute them in the value of speed of light so that we can get the speed of light in light year per day

Complete step by step solution
The light-year is a unit of distance and is used to measure astronomical distances and is equivalent to about 9.46 trillion kilometres (9.46 x 10¹² km) or 5.88 trillion miles (5.88 x 10¹² mi).
Since speed of light is $ \Rightarrow 2.75 \times {10^{ - 3}}ly/day$ $3 \times {10^8}\dfrac{m}{s}$.............(1)
So here in the place of m we can substitute the value of the light year as 1m and in second we can substitute days as 1 second.
$\because 1ly = 9.46 \times {10^{15}}m$
So I m will be equal to $\dfrac{{1ly}}{{9.46 \times {{10}^{15}}}} = 1m$
And we have one day is equal to \[86400s\]
So, $\dfrac{{1day}}{{86400}} = s$
 Then from equation (1)
 speed of light in light year per day is
$ \Rightarrow 3 \times {10^8}\dfrac{{\dfrac{1}{{9.46 \times {{10}^{15}}m}}}}{{\dfrac{{1day}}{{86400}}}}$
$ \Rightarrow 2.75 \times {10^{ - 3}}ly/day$

Note:-The speed of light in vacuum air or in space is a universal physical constant used in many areas of physics. Its exact value is around  299792458 metres per second  which is approximately 300000 km/s, or 186000 miles/s. it is generally denoted by c. Speed of light in other medium like glass, water is less than
It was first demonstrated by Ole Christensen Rømer in 1676 that light travels at a finite speed (non-instantaneously) by studying the apparent motion of Jupiter's moon Io.