Question

A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the sun and the earth in terms of the new unit if light takes 8 minutes and 20 seconds to cover this distance?

Answer 1

In, the given question to find out the distance between the sun and the earth in terms of the new unit, what we need to do is that, the distance between the Sun and the Earth is equal to the speed of light multiplied by the time it takes light to travel that distance.

Complete step by step answer:
In a vacuum, the speed of light is unity.
Speed of light = $1{\text{ }}unit$
Time taken = $t{\text{ }} = {\text{ }}8{\text{ }}min{\text{ }}20{\text{ }}s$
Let, us convert the given time in second

\Rightarrow \text{Time taken}= {\text{ }}480{\text{ }} + {\text{ }}20{\text{ }} \\\ \Rightarrow \text{Time taken}= {\text{ }}500{\text{ }}s$$ We know that, in order to find the distance between the Sun and the Earth, The distance between the Sun and the Earth$$ = \text{the speed of light} \times \text{time it takes light to travel that distance.}$$ So, if we add all of the values together, we get; $$ \text{Distance between the Sun and the Earth} = {\text{ }}1{\text{ }} \times {\text{ }}500 \\\ \therefore \text{Distance between the Sun and the Earth}= 500{\text{ }}units$$ **Hence, Distance between the Sun and the Earth is $$500{\text{ }}units.$$.** **Note:** The universal physical constant $$c$$ , or the speed of light in vacuum, is essential in many fields of physics. Its actual speed is $$299792458m{s^{ - 1}}$$ (about $$300000{\text{ }}kilometres{\text{ }}per{\text{ }}second$$ , or$$186000{\text{ }}miles{\text{ }}per{\text{ }}second$$ ). It's precise because a metre is defined as the length of the route taken by light in vacuum over a time interval of $$\dfrac{1}{{299792458}}{\text{ }}seconds$$ by international agreement. According to special relativity, the speed at which ordinary matter, energy, or any signal carrying information may travel through space is limited to $$c$$.