The distance between celestial bodies is expressed in terms of light years, where 1 light year is the distance travelled by light in one year and is equal to 9.46X 1017centimetres. If light takes 499 seconds to travel from the Sun to the Earth, which of the following is the closest to the distance, in million kilometres, between the Earth and the Sun?a)100b)1000c)10,000d)100,000e)125,000Correct answer is option 'A'. Can you explain this answer?

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The distance between celestial bodies is expressed in terms of light years, where 1 light year is the distance travelled by light in one year and is equal to 9.46 X 10¹⁷centimetres. If light takes 499 seconds to travel from the Sun to the Earth, which of the following is the closest to the distance, in million kilometres, between the Earth and the Sun?

a)
100
b)
1000
c)
10,000
d)
100,000
e)
125,000

Correct answer is option 'A'. Can you explain this answer?

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The distance between celestial bodies is expressed in terms of light y...

Given:

1 light year = Distance travelled by light in 1 year = 9.46 x 10¹⁷centimeters
Time taken by light to travel from Sun to Earth = 499 seconds

To find: The option that is closest to the distance, in million kilometers, between Sun and Earth

Approach:

To answer the question, we need to find the approximate distance between Sun and Earth
- Note that the 5 answer choices are quite far apart in magnitude. Therefore, we’ll be able to use Estimation and Rounding aggressively. All we need here is an idea of the order of the magnitude of the distance between Sun and Earth (whether this distance is in hundred millions or thousand millions or ten thousand millions of kiometers).
From the definition of light year, we get the distance travelled by light in 1 year. So, using the Unitary Method, we’ll be able to find the distance travelled by light in 499 seconds (and thus, the distance between Sun and Earth)
- One thing that we must be careful about when working out this solution – we must use one unit of time (either years or seconds) and one unit of distance (either centimeters or kilometers) in our solution.
- Working Out:
- Expressing the given information in a single Distance unit and a single Time unit
  - Since the answer choices are in units of (millions of) kilometers, it’ll be wise for us to convert the distance given in centimeters into kilometers. (If you want to do vice-versa, that is, if you want to convert kilometers into centimeters, then you may later have to do 5 such conversions – 1 for each answer choice and therefore, that will be more time-consuming)

For Time, let’s convert 1 year into seconds:
- 1 year = 365*24*60*60 seconds
  - = 36*24*36*10³ seconds approx.
  - (Note: we’re not simplifying this expression very much here because we’ll do all the simplifications together after we’ve deduced an expression for the distance between Earth and Sun)

Finding the approximate distance between Earth and Sun
- From the definition of light year, we know that:

Thus, distance between Earth and Sun =
We’ll now simplify the above expression for distance by using estimation and rounding:
Since the question asks for the distance in units of million kilometers, let’s now express the above distance in million kilometers:

Therefore, 1.25*10⁸ kilometers =

= 1.25*10² million kilometers
= 125 million kilometers approx.
- Thus, we see that the order of distance between the Sun and the Earth is hundred million kilometers.

Looking at the answer choices, we see that the correct answer is Option A

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The distance between celestial bodies is expressed in terms of light years, where 1 light year is the distance travelled by light in one year and is equal to 9.46X 1017centimetres. If light takes 499 seconds to travel from the Sun to the Earth, which of the following is the closest to the distance, in million kilometres, between the Earth and the Sun?a)100b)1000c)10,000d)100,000e)125,000Correct answer is option 'A'. Can you explain this answer?

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