Question

How much time will it take for the solar radiation to reach Mars?

(A)10 min
(B)12.6 min
(C)15 min
(D)14.8 min

Answer 1

Hint : In order to solve this question, we are going to first what distance the light needs to travel to cover the orbital radius of Mars. Then, by using the standard value of the speed of the light, we can very easily determine the time taken by the solar radiation to reach the planet Mars.
If $s$ is the distance which a planet covers with the speed $v$ , then, the time taken is given by
$t = \dfrac{s}{v}$

Complete Step By Step Answer:
In this question, the distance which is required by the light to travel is equal to the orbital radius of the Mars which is equal to $2.28 \times {10^{11}}m$ where for approximately circular orbits the orbital radius is the distance from an object in space to the body which it is orbiting.
Now, as we know that the speed with which the light travels in the vacuum is given by the value $3 \times {10^8}m{s^{ - 1}}$
Thus, the time taken by the solar radiation to reach the planet Mars is calculated as
$t = \dfrac{{2.28 \times {{10}^{11}}m}}{{3 \times {{10}^8}m{s^{ - 1}}}} = 0.76 \times {10^3}s \\\ \Rightarrow t = 760s$
Converting this time into minutes, we get
$\Rightarrow t = 12\min 40s = 12.67\min$
Hence, option $(B)12.6\min$ is the correct answer.

Note :
In orbital mechanics, the Hohmann Transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii around a central body in the same plane. The Hohmann transfer often uses the lowest possible amount of propellant in traveling between these orbits, but bi-elliptic transfers can use less in some cases.