Question

The distance travelled by the Earth in one orbit around the Sun is about 580,000,000 miles. Earth makes one complete orbit around the Sun in one year. Of the following, which is closest to the average speed of the Earth, in miles per hour as it orbits the Sun?
a) 66000
b) 93000
c) 210000
d) 420000

Answer 1

Hint: In this question, we are given the distance travelled by the Earth in one orbit and the time it takes to complete one orbit. As the average speed is the ratio of distance travelled and time taken and as we are asked to find the average speed in miles per hour, we should first convert the time taken in terms of hours. Thereafter, we can use the above formula for speed and use the values to obtain the required answer.

Complete step by step solution:
It is given that the distance travelled by the Earth in one orbit around the Sun= 580,000,000 miles
And it is also given that the time taken to complete one orbit= 1 year
We know that the formula for speed is given by
$\text{Average Speed=}\dfrac{\text{Distance Travelled}}{\text{Time Taken}}.......................(1.1)$
As we are asked to find the speed in miles per hour, we should first convert the time taken in terms of hour.
We know that, as one year consists of approximately 365 days and one day consists of 24 hours,
No. of hours in one day=24
$\Rightarrow $ No. of hours in one year= No. of hours in 365 days= No. of hours in one day$\times $365= $24\times 365=8760........................(1.2)$
As it is given that the distance travelled by Earth in 1 year is 580,000,000 miles, using this value and (1.2) in (1.1), we obtain
$\text{Average Speed=}\dfrac{580000000\text{ miles}}{8760\text{ hours}}\approx 66210.04\text{ miles/hr}$
Thus, the average speed is 66210.04 miles per hour which is closest to 66,000 from the options given in the question. Thus, option(a) is the correct answer.

Note: We should note that in equation (1.1), the time taken in the formula should be the time taken to travel the distance in the numerator. For example, the average speed would be the same if in (1.1), we used the distance travelled by the Earth in 2 orbits and the time taken for the Earth in two orbits. This is because, this would just introduce a factor of 2 in the numerator and denominator and the average speed would be the same as obtained in the solution.