Long-Distance and Wide-Area Detection of Gene Expression in Living Bacteria

**

Uranus subtends a much greater angle than a microbe at 90 meters. Let me work this out: Microbe from 90 meters:

A typical bacterium is about 1-5 micrometers (let's say 2 μm = 0.000002 meters) Angular size = (size / distance) in radians = 0.000002 / 90 ≈ 2.2 × 10⁻⁸ radians Converting to arcseconds: ≈ 0.0000046 arcseconds

Uranus from Earth:

Uranus is about 2.6-3.2 billion km from Earth (depending on orbital positions) Its diameter is about 51,000 km At closest approach, Uranus subtends approximately 3.7 arcseconds Even at its farthest, it's still around 3.3 arcseconds

So Uranus appears about 800,000 times larger in angular size than a bacterium at 90 meters away! This is why we can see Uranus through telescopes (and technically with the naked eye under perfect conditions, though just barely), but we absolutely cannot see individual bacteria without a microscope—the angle they subtend is far, far too small for our eyes to resolve.