Question

Light year is equal to

• A. 9.46 x 10\(^{15}\) m
• B. 9.46 x 10\(^{12}\) m
• C. 9.46 x 10\(^{8}\) m
• D. 9.46 x 10\(^{10}\) m

Hint:

Remember the order of magnitude for common astronomical distances. A light-year is a vast distance, on the order of 10\(^{15}\) meters or 10\(^{12}\) kilometers. An Astronomical Unit (AU, the distance from Earth to the Sun) is much smaller, about 1.5 x 10\(^{11}\) meters. A parsec is larger, about 3.26 light-years.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A light-year is a unit of astronomical distance. It is defined as the total distance that a beam of light, moving in a vacuum, travels in one Julian year (365.25 days). It is a unit of distance, not time.
Step 2: Key Formula or Approach:
The distance can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \] Step 3: Detailed Explanation:
The values needed for the calculation are:
\begin{itemize} \item Speed of light in vacuum (\(c\)) \(\approx 299,792,458 \text{ m/s} \approx 3 \times 10^8 \text{ m/s}\) \item Time (\(t\)) = 1 Julian year = 365.25 days \end{itemize} First, we need to convert the time from years to seconds:
\[ t = 365.25 \text{ days} \times 24 \frac{\text{hours}}{\text{day}} \times 60 \frac{\text{minutes}}{\text{hour}} \times 60 \frac{\text{seconds}}{\text{minute}} \] \[ t = 31,557,600 \text{ seconds} \] Now, calculate the distance:
\[ \text{Distance} = (299,792,458 \text{ m/s}) \times (31,557,600 \text{ s}) \] \[ \text{Distance} \approx 9,460,730,472,580,800 \text{ m} \] In scientific notation, this is approximately:
\[ \text{Distance} \approx 9.46 \times 10^{15} \text{ m} \] Step 4: Final Answer:
One light-year is equal to approximately 9.46 x 10\(^{15}\) meters. This matches option (A).