One parsec is equal to

Options

A. `10^(-7)` m
B. `10^(-6)` m
C. `3.08 xx 10^(16)` m.
D. `3.08 xx 10^(-16)` m .

Answer

To find out how many meters are in one parsec, we can follow these steps:

### Step 1: Understand the Definition of a Parsec
A parsec is a unit of length used in astronomy to measure large distances. It is defined as the distance at which one astronomical unit subtends an angle of one arcsecond.

### Step 2: Relate Parsec to Light-Years
1 parsec is equivalent to approximately 3.26 light-years.

### Step 3: Convert Light-Years to Meters
To convert light-years to meters, we need to know the speed of light and the number of seconds in a year.

1. **Speed of Light**: The speed of light is approximately \(3 \times 10^8\) meters per second.
2. **Time in One Year**:
- Days in a year: 365.25 (including leap years)
- Hours in a day: 24
- Seconds in an hour: 3600

Therefore, the total number of seconds in one year is:
\[ \text{Seconds in a year} = 365.25 \times 24 \times 3600 \]

### Step 4: Calculate the Total Seconds in One Year
Calculating the total seconds:
\[ 365.25 \times 24 = 8766 \text{ hours} \]
\[ 8766 \times 3600 = 31,557,600 \text{ seconds} \]

### Step 5: Calculate the Distance of One Light-Year in Meters
Now, we can calculate the distance of one light-year:
\[ \text{Distance of 1 light-year} = \text{Speed of light} \times \text{Time in one year} \]
\[ = (3 \times 10^8 \text{ m/s}) \times (31,557,600 \text{ s}) \approx 9.461 \times 10^{15} \text{ meters} \]

### Step 6: Calculate the Distance of One Parsec in Meters
Now, we can find the distance of one parsec:
\[ 1 \text{ parsec} = 3.26 \text{ light-years} \approx 3.26 \times (9.461 \times 10^{15} \text{ m}) \]
\[ \approx 3.08 \times 10^{16} \text{ meters} \]

### Conclusion
Thus, one parsec is equal to approximately \(3.08 \times 10^{16}\) meters.

### Final Answer
**1 parsec is equal to \(3.08 \times 10^{16}\) meters.**