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Comment by RationPhantoms | Hacker News Reader

Genuinely asking, do you think that could be solved by having better orbital visualizations?

Not the poster, but the issue is one of scale.

Any visualization that showed a full orbit in a visual field that a human can see at once, necessarily has to exaggerate the size of the satellite or it would be completely impossible to see the satellite at that same scale. By millions or even billions of times.

A GPS satellite in medium orbit has an orbital diameter of around 45, 000 km but is only a little over 5 meters in size. A ratio of roughly 10,000,000 to 1.

If you had a visualization a meter wide of its orbit, the satellite to scale would be less than a micron in size. Completely invisible.

The same problem comes up with those ‘topology of the earth’ maps that try to show how things like depth of the oceans, height of the Himalayas, etc. on a globe.

They have to dramatically exaggerate the actual altitude differences for them to be perceptible. [https://www.quora.com/If-Mount-Everest-was-on-a-globe-and-wa...]

The actual to scale difference in height of the Himalayan mountains vs sea level on a regular sized globe would be less than .001 inches. Completely imperceptible without precision measuring devices. Even producing such a globe accurately would be a feat of precision manufacturing.

Even on a giant (1 meter) globe, we’re talking less than 1mm.

Literally smoother than a billiard ball.

But they are the highest mountains in the world, and absolutely breaktaking if near them.

And space is even bigger, and satellites even smaller.

An accurate steel replica of earth the size of a ball-bearing would be the most precise ball bearing ever.

Great book on this:

https://goodreads.com/book/show/35068671-the-perfectionists

I've heard this a couple times and never believed it. Earth is perceptibly not round. Scott Manley did a quick video showing that in some satellite images the difference equates to more than a couple pixels. Some quick googling shows the earth being about 0.3% not-round, which would match a 1000-pixel image being not-round by a few pixels. But a 0.3% deviation is exponentially greater than is allowed by the standards for ball bearings.

>> the Earth deviates from spherical by only a third of a percent

https://en.wikipedia.org/wiki/Figure_of_the_Earth

>> For instance, the Anti-Friction Bearing Manufacturers Association (AFBMA) has a set of grades for bearing balls. A grade three ball has to be spherical within 3 millionths of an inch and the diameter must be accurate within 30 millionths of an inch. This means that for a grade three quarter-inch ball, the diameter would have to be between 0.24997 and 0.25003 of an inch and the smallest diameter measured on the ball has to be within 3 millionths of the largest diameter.

https://science.howstuffworks.com/transport/engines-equipmen...

I think you're talking about different things. It's true, the Earth is substantially non-spherical. But things like mountains are tiny irregularities on a smooth (not-perfectly-spherical) surface.

A better way to talk about this is something like: given a globe of Earth, say a 50cm diameter one, finished with plate Bristol paper, the texture of the surface would not be as smooth as a perfect model of Earth at that scale.

If I remember correctly, the term is ‘rugosity’. Hah, yup! [https://en.m.wikipedia.org/wiki/Rugosity]

No the dominant deformation on earth is that it is flattened at the poles and bulges at the equator. This is because of axial momentum and makes the earth an oblate spheroid.

If you stand at sea level at a pole you are much closer to the center of the earth than if you stand at sea level at the equator.

Only tangentially related, but GP's source was The Perfectionists—I've had it on my list of "books to read one day" for a while now, but this makes me reconsider.... If the author didn't bother to verify a basic fact like this, what else might be wrong?

To anyone who's read the book with an existing background in precision engineering (i.e. and can independently vouch for its plausibility), is it still worth picking up?

My mis-representation wasn't from the book, and of course, what I meant was "smoothest" rather than "precise".

Ah, I see—thanks for clarifying.

To do the last extra bit of math - that seems like the ball bearings would then be within .01%? Or am I missing a zero?

Smoothness vs perfect roundness are two different things. The earth is very smooth, even if it's not perfectly round.

Doubt it. Earth is not even a sphere.

Looks like you’re right! Earth is within .3% of being a sphere, where ball bearings are within .01%.

[https://en.m.wikipedia.org/wiki/Earth%27s_circumference]

Correct --- I should have said "smoothest".

That is a tricky problem to solve. The scales are so far apart from each other it’s a bit like solving “how do you scale the distance between the sun and the planets in a way that keeps some detail of each while giving a sense of the true amount of nothing between them”.

According to ChatGPT, if the earth was the size of a spherical cow (approx 1.5m in diameter) then the space station would be about 8.5 micrometers which is roughly the size of some bacteria. It would be 46 millimeters away from the cow.

If earth was a spherical cow then a starlink satellite would be 0.31 micrometers, or 310nm which is about the wavelength of violet light. It would be about a large thumbtack away.

The orbital periods for these would be in the order of microseconds.

Please don't trust ChatGPT. It's got the right orders of magnitude, which is lucky, but it's still giving you the wrong numbers.

If the earth were 1.5m in diameter, the space station would be proportionally 12.83µm long[0], orbiting at a distance of 50.66mm (2 inches)[1].

[0]: https://www.wolframalpha.com/input?i=iss+length+%2F+earth+di...

[1]: https://www.wolframalpha.com/input?i=iss+height+%2F+earth+di...

I don't. The human sensorium (whether actually looking at an image, or visualizing something based on some numbers) has limited dynamic range.

Sometimes, it can help a little to convert to something vaguely human-scale, which probably doesn't fit on a screen. The surface area of the planet is ~500 million km^2, there's a large park near me with long, clear sight lines where I go for runs play disc golf that's about 5 square km. If I shrink the ~3x2 meter satellite dimensions by an equivalent factor of about 100M, it's an object with a size of 30x20 micrometers (unless I've screwed up a square-cube ratio somewhere), on the order of a grain of silt, the thickness of a Sharpie ink mark, or something a little smaller than a cross-section of a hair. My intuition approximates those dimensions and probabilities of two of those infinitesimal specs all the way to zero.

On the other hand, tens of thousands of satellites, those barely-palpable specs crossing that region of space once every 90 minutes, for hundreds of years? Then my intuition says it's a certainty!

Facing the multiplication of an impossibility with a certainty, intuition says they cancel out and it's a 50/50 chance, which is just not how it works.

Sometimes you have to just do the math and trust the numbers.

I suppose you could generate an alternate view (maybe someone has?) that doesn't show the individual satellites, but instead only shows little green/yellow/red flashes whenever satellites cross within some radius of one another.

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