Calculating the Observable Universe in Centimeters

When discussing the vastness of the observable universe, it's often useful to translate distances into more familiar units. Specifically, converting the diameter of the observable universe into centimeters can provide a sense of scale that is easier to grasp.

The Observable Universe - Defined and Calculated

Current estimates suggest that the diameter of the observable universe is approximately 93 billion light years. This diameter is based on the particle horizon, which approximates the present diameter of all structures we can observe. While a light year is defined as the distance light travels in one year, which is about 9.5 trillion kilometers, it's helpful to break down this figure into centimeters.

Here is the step-by-step calculation to convert the observable universe's diameter into centimeters:

Step-by-Step Calculation

We start with the diameter of the observable universe in light years:

93.5 billion light years

We know that 1 light year is approximately 9.5 trillion kilometers:

1 kilometer is 1000 meters:

1 meter is 100 centimeters:

The conversion can then be calculated as follows:

93.5 x 10^9 x 9.5 x 10^12 x 1000 x 100 93.5 x 9.5 x 10^26

888.25 x 10^26 cm

In simpler terms, this is 88 followed by 27 zeroes. This number is increasing, but the exact rate is faster than the speed of light, meaning the observable universe's diameter is expanding continuously.

Additional Context

To further understand the scale, you can use scientific notation for the calculation:

94E9 x 31.5E6 x 30E9

Where E9 means 9 zeros for a billion, etc. This calculation helps to represent the enormous distances involved.

It's important to note that the value of the observable universe's diameter is increasing every second. However, due to the finite speed of light, the measurements we have are as of a certain point in time.

Defining Distance in the Observable Universe

Before we can provide an exact number, we need to define what we mean by “is.” No one can lay a large number of rulers end-to-end from here to the farthest observable point, as the observable universe is always expanding, and we cannot lay out rulers that fast due to the speed of light and the changing universe. Therefore, we have to define distance in indirect ways such as angular diameter distance, luminosity distance, light-travel distance, and proper distance.

For example, the proper radius of the observable universe is 46.5 billion light years, which translates to:

46.5 billion light years x 365.25 days/year x 24 hours/day x 3600 seconds/hr x 299792458 m/s x 100 cm/m 4.40 x 10^28 cm

And for the proper diameter, we simply double the radius:

8.8 x 10^28 cm

This value aligns with the approximate 8.70387203477e28 cm mentioned in the text.

Conclusion

The observable universe's diameter, when converted into centimeters, is an immensely large number, underlining the vastness of the cosmos. Understanding these conversions and measurements can help us appreciate the scale of the universe and the challenges of measuring such vast distances accurately.