Comparing Scales: A Bacterium on Earth vs. Earth in the Universe
The universe is vast and incomprehensible in its scale, while microscopic organisms like bacteria exist in an equally mind-boggling world of the infinitely small. By comparing these extremes, we can gain a humbling perspective on our place in the cosmos. Using some fascinating calculations, let’s explore the relationship between the volume of a single bacterium and the Earth, and how Earth’s volume compares to the known universe. Spoiler alert: Earth is far smaller in the universe than a bacterium is on Earth!
The Volume of a Bacterium
To understand this comparison, let’s first calculate the volume of a single bacterium. For simplicity, we’ll model it as a cylinder.
- Length of the bacterium: 0.001 mm (1 micron)
- Radius of the base: One-sixth of the length, or 0.00015 mm
Using the formula for the volume of a cylinder:
Volume = π × r2 × h
Substituting the values:
Volume = 3.14 × (0.00015)2 × 0.001 = 0.00000000007065 mm3
This simplifies to 7.065 × 10-11 mm3, or when converted to cubic kilometers:
7.065 × 10-29 km3
The Volume of Earth
Next, let’s consider Earth’s volume, which is well-documented:
Earth's Volume = 1.08321 × 1012 km3
This is the scale we’ll compare the bacterium to, as well as Earth to the known universe.
Comparing the Bacterium to Earth
The ratio of the volume of a bacterium to Earth’s volume can be calculated as:
Bacterium-to-Earth Ratio = (7.065 × 10-29) / (1.08321 × 1012) = 6.5 × 10-41
In other words, the bacterium’s volume is 1 part in 1041 of Earth’s volume. That’s a number with 40 zeros before it—an almost incomprehensibly small fraction!
The Volume of the Known Universe
Now, let’s look at the known universe. Its estimated volume is:
Universe's Volume = 1.031 × 1070 km3
Compared to this, Earth’s volume is minuscule. The ratio of Earth’s volume to the universe is:
Earth-to-Universe Ratio = (1.08321 × 1012) / (1.031 × 1070) = 1.05 × 10-58
This means Earth’s volume is just 1 part in 1058 of the universe’s volume.
Earth’s Relative Scale vs. a Bacterium
To compare the two ratios—the bacterium-to-Earth ratio and the Earth-to-universe ratio—we divide them:
Comparison = (6.5 × 10-41) / (1.05 × 10-58) = 6.1 × 1017
This result tells us that Earth’s proportion of the universe is about 600 quadrillion (600,000,000,000,000,000) times smaller than the proportion of a bacterium to Earth.
What Does This Mean?
This calculation highlights the staggering scale of the universe:
- A bacterium’s presence on Earth is minuscule, yet it’s vastly larger in proportion than Earth’s presence in the universe.
The human mind struggles to grasp scales this extreme. While we can comprehend the smallness of a bacterium or the vastness of Earth, putting these into
the context of the entire universe reveals just how insignificant we truly are.
A Humbling Perspective
This comparison offers more than just numbers—it offers perspective. Despite our achievements, ambitions, and conflicts, Earth is a tiny dot in a cosmic ocean, and the things we consider “large” pale in comparison to the grand scale of the universe.
And yet, even in this immensity, life thrives in the smallest forms, like bacteria, reminding us of the profound complexity and beauty of existence.
