It is believed that the universe began with
a big bang about 16 billion years ago. Neglecting the expansion of the universe, we can
reason that the most distant objects observable are no further than the distance light
could have traveled in 1.6 × 1010 years.
If the speed of light is 2.99792 × 108 m/s,
what is the maximum possible radius of the
observable universe?
Answer in units of m.

To determine the maximum possible radius of the observable universe, we can use the following approach:

### Step 1: Identify the given data
- **Time** (since the Big Bang): \( t = 1.6 \times 10^{10} \) years
- **Speed of light**: \( c = 2.99792 \times 10^8 \) meters per second (m/s)

### Step 2: Convert time into seconds
We need to convert the time from years to seconds because the speed of light is given in meters per second.

There are \( 365.25 \) days in a year, \( 24 \) hours in a day, \( 60 \) minutes in an hour, and \( 60 \) seconds in a minute. Thus, the conversion is as follows:

\[
\text{Time in seconds} = 1.6 \times 10^{10} \times 365.25 \times 24 \times 60 \times 60 \text{ seconds}
\]

### Step 3: Calculate the distance
The maximum distance light could have traveled (which is the radius of the observable universe) is given by the equation:

\[
\text{Distance} = \text{speed of light} \times \text{time}
\]

Substituting the values:

\[
\text{Distance} = (2.99792 \times 10^8 \, \text{m/s}) \times \text{Time in seconds}
\]

Now, let's calculate this.The maximum possible radius of the observable universe, based on the given data, is approximately \( 1.5137 \times 10^{26} \) meters.

Would you like more details on this calculation, or do you have any other questions? Here are some related questions:

1. How would the calculation change if the universe's expansion is taken into account?
2. What is the significance of the observable universe's radius in cosmology?
3. How does the finite speed of light limit our observations of the universe?
4. What are the implications of different cosmological models on the size of the observable universe?
5. How does the concept of the universe's age relate to the observable universe's radius?

**Tip:** The observable universe is just a portion of the entire universe, limited by the distance that light has traveled since the Big Bang.

It is believed that the universe began with a big bang about 16 billion years ago. Neglecting the expansion of the universe, we can reason that the most distant objects observable are no further than the distance light could have traveled in 1.6 × 10^10 years. If the speed of light is 2.99792 × 10^8 m/s, what is the maximum possible radius of the observable universe? Answer in units of m.

Find out how to calculate the maximum possible radius of the observable universe based on the distance light could have traveled in 16 billion years at the speed of light (2.99792 × 10^8 m/s). This problem involves physics and cosmology concepts, such as distance calculation and unit conversion, suitable for students in Grades 11-12 or undergraduate physics courses.

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