[Shadow6363]

I feel like I was just nerd sniped, but this drove me crazy until I thought about it for a bit.

If we treat Earth's orbit as a perfect circle, then the number of milliseconds in a year would be its circumference. To get to pi then, we just need to divide that by its diameter or 2*its radius. In addition, we have the circumference in ms so we want to convert that into a distance or the radius into ms so we need the speed the Earth is rotating around the sun.

The average radius of the Earth to the Sun is 149,600,000 km so the diameter is 299,200,000 km. Earth's average orbital speed is 30 km/s or 0.03 km/ms. Combining these two numbers to get ms, (299,200,000 km / 0.03 km/ms) = 9,973,333,333.333 ms, which is very nearly 10 billion.

[Armisael16]

This isn't a reason or an explanation, just a statement of the arithmetic.

The siblings comments to yours are right - it's nearly random chance (give or take conservation of momentum during accretion of the solar disk into planets).

[leetcrew]

sure, but this is still just a consequence of the definition of "second" and a coincidental relationship between orbital period and day length. you can readily see that no such relationship holds for any of the other planets in our system.

unless i am grossly misunderstanding something, this is just an interesting tautology, similar to why torque and power curves for ICEs always cross at the same rpm.

[xelxebar]

Oh cool. My thought process went pretty much the same way. Essentially we're just using time as units and dividing circumference by diameter.

The nice denominator is what makes this interesting at all though, so the question sort of boils down to why Earth's orbital radius is such a round number of milliseconds.

[jonsen]

... the diameter is 299,200,000 km ...

The distance light travels in a kilosecond.