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Actually the angular size of Uranus seen from earth is almost a million times larger than a microbe seen from 90m (not that TFA was about seeing a single microb

Actually the angular size of Uranus seen from earth is almost a million times larger than a microbe seen from 90m (not that TFA was about seeing a single microbe, or seeing a microbe at all for that matter).

moralestapia 1y ago
Can we do the math? I know that burden's on me but I feel I might be wrong, my back of the napkin calculation puts them within 10-100x. 1 micrometer (1E-6) to 50,700 km (1E6) 90 meters (1E2) to 2.8 billion km (1E12) Edit: Oh yeah but size/distance does not decay linearly ...
- 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 ago
    2.2 × 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 ago
      Thanks. 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!"
- penteract 1y ago
  Angular size is proportional to size/distance, so the calculation you're trying to do is correct; however, 50700 km is more than 1e7 meters so the angular sizes differ by about 3 orders of magnitude.
dylan604 1y ago
A leading reason touted as evidence the moon landing was fake is that we can't see the stuff supposedly left on the moon. Once you start going into angular resolution and the physics of optics you've already lost the argument.
- outworlder 1y ago
  You don't "lose" an argument just because the other side doesn't have the attention span to understand what you are saying.
  - dylan604 1y ago
    Sure, but you'll never win. So whether you want to call it "lose" the argument or just apply "lose" to the amount of time and/or your own sanity, it's still a loss. You will definitely not be changing the other party's mind.

moralestapia 1y ago

Can we do the math? I know that burden's on me but I feel I might be wrong, my back of the napkin calculation puts them within 10-100x. 1 micrometer (1E-6) to 50,700 km (1E6) 90 meters (1E2) to 2.8 billion km (1E12) Edit: Oh yeah but size/distance does not decay linearly ...

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 ago
  2.2 × 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 ago
    Thanks. 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!"
penteract 1y ago
Angular size is proportional to size/distance, so the calculation you're trying to do is correct; however, 50700 km is more than 1e7 meters so the angular sizes differ by about 3 orders of magnitude.

dylan604 1y ago

A leading reason touted as evidence the moon landing was fake is that we can't see the stuff supposedly left on the moon. Once you start going into angular resolution and the physics of optics you've already lost the argument.

outworlder 1y ago
You don't "lose" an argument just because the other side doesn't have the attention span to understand what you are saying.
- dylan604 1y ago
  Sure, but you'll never win. So whether you want to call it "lose" the argument or just apply "lose" to the amount of time and/or your own sanity, it's still a loss. You will definitely not be changing the other party's mind.