Question

How long will it take to reach mars from the earth?

A. 5 days
B. 6 days
C. 60 days
D. 80 days

Answer 1

Hint: To reach mars from earth, one must first escape the gravitational pull exerted by the earth. If an object is released from the surface of earth with the escape velocity, the object will escape the earth’s gravity and then it can reach mars. Divide the distance between mars and earth by the escape velocity from earth to find the time.

Formula used:
$\text{time = }\dfrac{\text{distance}}{\text{speed}}$

Complete step by step answer:
Every object in the universe is attracted by the gravitational force of another object. Hence, small objects like us are bound to the gravity of a larger body like planet earth.
We humans are constantly being pulled by the gravitational force of the earth. If we want to reach another planet like Mars, then we have to escape the gravitational force exerted by Earth.
For a given object to escape the gravity of the earth, it must be released from the surface of the earth with a velocity equal to or greater than the escape velocity. If the object is launched with the escape velocity, it will have enough energy to overcome the gravitational pull.
The value of escape velocity for earth is equal to v =$11200m{{s}^{-1}}$.
The average distance between the earth and the mars is d = $7.8\times {{10}^{10}}m$.
Let the time to reach mars from earth be t.
Therefore, by using the formula $\text{time = }\dfrac{\text{distance}}{\text{speed}}$, we get $t=\dfrac{d}{v}=\dfrac{7.8\times {{10}^{10}}}{11200}=6964286s$.
Divide the time t by $3600\times 24$ to convert it into days.
 $\Rightarrow t=\dfrac{6964286}{3600\times 24}\approx 80days$.
Hence, it will take about 80 days to reach mars from earth.

So, the correct answer is “Option D”.

Note:
Although when a body is released with a velocity equal to or greater than the escape velocity, it escapes from the gravitational pull, but it does not travel with a constant velocity. We have assumed that the average speed will be close to the escape speed. Also, travelling in a straight line path from one planet to another is not preferable and hence in real life it takes more time to cover such distances.