3 ms·
I was lazy and asked Claude, although I didn't check the math. ** Uranus subtends a much greater angle than a microbe at 90 meters. Let me work this out: Micr
by HarHarVeryFunny 1y ago
I was lazy and asked Claude, although I didn't check the math.
**
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.
- penteract 1y ago2.2 × 10⁻⁸ radians is 0.0045 arcseconds [1]. That answer is off by 3 orders of magnitude. [1] https://frinklang.org/fsp/frink.fsp?fromVal=2.2*10%5E-8+radians&toVal=arcseconds#calc https://frinklang.org/fsp/frink.fsp?fromVal=2.2*10%5E-8+radi...
- moralestapia 1y ago:O So what would be the difference on magnitude between the bacteria and Uranus, then? Edit: nvm, I just read your other comment.
- HarHarVeryFunny 1y agoThanks. That was the latest greatest Sonnet 4.5 ... not quite great enough evidentially. I just asked it to "check the radians to arcsec conversions", and it realized the error.
- moralestapia 1y ago"You're absolutely right!"