If light takes 5 yr to reach the Earth from a Star. Find the distance between that Star and the Earth in km.

Options

A. `3xx10^(8)`
B. `15xx10^(8)`
C. `4.73xx10^(13)`
D. `9.3xx10^(12)`

Explanation

To find the distance between the star and the Earth given that light takes 5 years to reach Earth, we can follow these steps:

### Step 1: Understand the relationship between distance, speed, and time
The basic formula for calculating distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 2: Identify the speed of light
The speed of light (C) is approximately:
\[ C = 3 \times 10^8 \text{ meters/second} \]

### Step 3: Convert the speed of light to kilometers
Since we need the distance in kilometers, we convert the speed of light from meters to kilometers:
\[ 1 \text{ km} = 1000 \text{ m} \]
Thus,
\[ C = 3 \times 10^8 \text{ m/s} = \frac{3 \times 10^8}{1000} \text{ km/s} = 3 \times 10^5 \text{ km/s} \]

### Step 4: Convert time from years to seconds
We know that:
- 1 year = 365 days
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds

Therefore, the total time in seconds for 5 years is:
\[ \text{Time} = 5 \text{ years} \times 365 \text{ days/year} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} \]

Calculating this step-by-step:
1. Calculate the number of days in 5 years:
\[ 5 \times 365 = 1825 \text{ days} \]
2. Calculate the number of hours in 1825 days:
\[ 1825 \times 24 = 43800 \text{ hours} \]
3. Calculate the number of minutes in 43800 hours:
\[ 43800 \times 60 = 2628000 \text{ minutes} \]
4. Calculate the number of seconds in 2628000 minutes:
\[ 2628000 \times 60 = 157680000 \text{ seconds} \]

### Step 5: Calculate the distance
Now, we can substitute the values into the distance formula:
\[ \text{Distance} = C \times \text{Time} \]
\[ \text{Distance} = (3 \times 10^5 \text{ km/s}) \times (157680000 \text{ seconds}) \]

Calculating this:
1. Multiply the speed of light by the time:
\[ \text{Distance} = 3 \times 10^5 \times 157680000 \]
\[ \text{Distance} = 4.73328 \times 10^{13} \text{ km} \]

### Final Answer
The distance between the star and the Earth is approximately:
\[ \text{Distance} \approx 4.73 \times 10^{13} \text{ km} \]

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