Question

What is the speed of light in $\dfrac{AU}{h}$?

Answer 1

Hint: In order to answer this question, we will discuss a few things about light and we will also calculate the speed of light in different units.Light is electromagnetic radiation that the human eye can sense. Electromagnetic radiation has a broad variety of wavelengths, ranging from gamma rays with wavelengths less than $1\times {{10}^{-11}}\,m$ to radio waves with wavelengths measured in $meters$. The wavelengths visible to humans occupy a very small band within the wide spectrum, ranging from about $700nm$ (nm; billionths of a metre) for red light to about $400nm$ for violet light.

Complete answer:
As we all know that the speed of light in a vacuum is a fundamental physical constant, with a present agreed value of \[299,792,458\text{ }\dfrac{meters}{\sec ond}\] (\[186,282\text{ }\dfrac{miles}{\sec ond}\]). But what is its value if we want to measure it in the Astronomical unit? Before finding the value of light in this unit, we will have a small glimpse at what an Astronomical unit is: The astronomical unit (AU, or au) is a length unit that is effectively equal to the average, or mean, distance between Earth and the Sun, which is specified as \[149,597,870.7\text{ }kilometres\](\[92,955,807.3\text{ }miles\]).

It can also be thought of as the length of Earth's elliptical orbit around the Sun's semi major axis—that is, half of the maximum diameter. The astronomical unit is a convenient way to convey and relate distances between solar system objects, as well as to perform various astronomical calculations. Now, the speed of light in AU is,
Speed of light = $2.998\times {{10}^{8}}\dfrac{m}{s}$
In kilometres, the speed of light = $10.8\times {{10}^{8}}\dfrac{km}{h}$
\[1.50\times {{10}^{8}}km=1AU\] (average distance from earth to sun)
$\Rightarrow 1\dfrac{AU}{h}=1.50\times {{10}^{8}}\dfrac{km}{h}$, then
$\Rightarrow (?)\dfrac{AU}{h}=10.8\times {{10}^{8}}\dfrac{km}{h}$
On calculating,
$\therefore \dfrac{10.8\times {{10}^{8}}}{1.50\times {{10}^{8}}}=7.2\dfrac{AU}{h}$

Therefore the speed of light in units of $\dfrac{AU}{h}$ is $7.2\dfrac{AU}{h}$.

Note: The speed of light is constant in the whole universe in any frame of references from which it is measured. Remember to convert the value of the speed of light from meter per seconds to kilometres per hour, as it will be convenient to calculate after that in terms of astronomical units per hour.