Nah, there is no way any astronomer studying orbital mechanics in our solar system is rounding pi to 1. There is virtually no practical calculation you could do on the mechanics of the sun or planets where rounding a known constant by a factor of 3 would yield any useful result whatsoever.
Rounding pi to 1 only makes sense when the uncertainty in the numbers is large, not the magnitude of the numbers, and we know the masses and distances of the objects in our solar system to an amazing level of precision!
Plus, the fact that Jupiter is massive enough to actually exert an influence that large on the sun is pretty fucking cool!
The reason being, that once you go large enough, a multiplier of three is irrelevant, and they only really care about orders of magnitude. You might be tempted to argue that that doesn’t happen inside the solar system, and you’d be right. Mostly.
Except that astronomy doesn’t concern itself with just our system. So yes. Astronomers do frequently round to 1 because it really doesn’t matter that much in the scheme of things. (particularly talking about distances.) it’s even more so for cosmology.
Sure, I totally agree that when you’re dealing many with orders of magnitude, the factor of 3 is dwarved by the other uncertainties.
But we’re talking about our solar system, and specifically the orbital mechanics of our planets and sun, where the quantities and scales only span a couple orders of magnitude in total. A factor of 3 absolutely makes a difference. That’s the difference between the orbit of Mercury and the orbit of Earth.
Then there’s the practical point that, regardless of scale, rounding a known constant by that much makes no sense at all, unless you’re trying to estimate huge numbers in your head. If you’re using even the simplest of calculator, estimating pi as 1 is a deliberate choice to reduce accuracy.
Not when that definition of pi goes to all 300 trillion decimals that we have resolved. (To be fair, I don’t know of any that do… but eh…yeah. And I’m pretty sure it was defined by a masochist if one did.)
That leads to unnecessary time spent calculating even simple equations. That level of precision is almost never actually needed.
With fermi problems, usually that level of precision is moot and potentially a waste of time. (Particularly when the math is requiring some kind network cluster to do.)
Pi has it’s own button on most graphing calculators, and those that don’t usually only requure 2 button presses to get it. Meanwhile, there’s some iteration of ‘pi()’, ‘pi’, etc. in most programming languages
But sometimes, the problems are complex enough that solve time becomes a concern. When they’re complex enough, you start asking “is everything these precise enough to justify that” and when the answer is “no”, then you don’t do that because runtime on networked clusters like AWS costs money.
And when you’re talking about scales that encompass the galaxy…. Well. There’s just not a lot of precision there to begin with.
fermi approximations happen all the time in astronomy. The numbers are frequently so large that the only meaningful quality is how many orders of magnitude it has.
More to the point, using pi makes calculating things much harder. For example, we don’t really need a precise distance for most things; so using “3” makes the calculation unnecessarily spend time in computation.
It’s like the old joke, “what’s the difference between a millionaire and a billionaire?” (“About a billion.”)
In a field of study where it’s not just acceptable, but prudent to round pi to “1” because the numbers are that big….
I gotta say, it’s close enough to say Jupiter orbits Sol. Just saying.
Nah, there is no way any astronomer studying orbital mechanics in our solar system is rounding pi to 1. There is virtually no practical calculation you could do on the mechanics of the sun or planets where rounding a known constant by a factor of 3 would yield any useful result whatsoever.
Rounding pi to 1 only makes sense when the uncertainty in the numbers is large, not the magnitude of the numbers, and we know the masses and distances of the objects in our solar system to an amazing level of precision!
Plus, the fact that Jupiter is massive enough to actually exert an influence that large on the sun is pretty fucking cool!
The reason being, that once you go large enough, a multiplier of three is irrelevant, and they only really care about orders of magnitude. You might be tempted to argue that that doesn’t happen inside the solar system, and you’d be right. Mostly.
Except that astronomy doesn’t concern itself with just our system. So yes. Astronomers do frequently round to 1 because it really doesn’t matter that much in the scheme of things. (particularly talking about distances.) it’s even more so for cosmology.
Sure, I totally agree that when you’re dealing many with orders of magnitude, the factor of 3 is dwarved by the other uncertainties.
But we’re talking about our solar system, and specifically the orbital mechanics of our planets and sun, where the quantities and scales only span a couple orders of magnitude in total. A factor of 3 absolutely makes a difference. That’s the difference between the orbit of Mercury and the orbit of Earth.
Then there’s the practical point that, regardless of scale, rounding a known constant by that much makes no sense at all, unless you’re trying to estimate huge numbers in your head. If you’re using even the simplest of calculator, estimating pi as 1 is a deliberate choice to reduce accuracy.
This. Most calculators and programming languages already have pi defined, there is no reason to round it nowadays
Not when that definition of pi goes to all 300 trillion decimals that we have resolved. (To be fair, I don’t know of any that do… but eh…yeah. And I’m pretty sure it was defined by a masochist if one did.)
That leads to unnecessary time spent calculating even simple equations. That level of precision is almost never actually needed.
With fermi problems, usually that level of precision is moot and potentially a waste of time. (Particularly when the math is requiring some kind network cluster to do.)
Pi has it’s own button on most graphing calculators, and those that don’t usually only requure 2 button presses to get it. Meanwhile, there’s some iteration of ‘pi()’, ‘pi’, etc. in most programming languages
Sure.
But sometimes, the problems are complex enough that solve time becomes a concern. When they’re complex enough, you start asking “is everything these precise enough to justify that” and when the answer is “no”, then you don’t do that because runtime on networked clusters like AWS costs money.
And when you’re talking about scales that encompass the galaxy…. Well. There’s just not a lot of precision there to begin with.
The counterpoint to that is that including a term for pi (or even rounding it to 3.14) would insignificant to add and look way more professional
You’ve got to be a little bit careful, surely, because then one squared is ten in the sense that log pi is about half.
Rounding pi to 1? Not even 3? Source please? Because what?
fermi approximations happen all the time in astronomy. The numbers are frequently so large that the only meaningful quality is how many orders of magnitude it has.
More to the point, using pi makes calculating things much harder. For example, we don’t really need a precise distance for most things; so using “3” makes the calculation unnecessarily spend time in computation.
It’s like the old joke, “what’s the difference between a millionaire and a billionaire?” (“About a billion.”)
Just wait until you see their periodic table of elements.
H, He, Z
this disgruntled me as a biochem grad and we think the periodic table is
H C N O P S Na Mg Cl K Ca Mn Fe Co Cu Zn Se Mo I F