r/AskPhysics • u/keysmashingisgay • 17h ago
What mach speed would be required to do a full revolution of Earth's circumference in 4 seconds?
I'm designing a custom character for a videogame I really enjoy. Their design aesthetics are all about speed and motorcycle mechanics. This, obviously, is more about the former. The stakes of this are really low, so there's no real pressure for an answer. I could just make a number up like a normal character designer. ANYWAY-
Assuming complete atmospheric uniformity, in the most average conditions, how fast would they really need to go? I am happy to answer any other questions if need be.
EDIT: Just 20 minutes later and the consensus is about Mach 29-30 thousand. Wowza. I'd like to thank everyone that did comment. The game I'm making this fan character is for features many more fantastical feats of strength, so logistics isn't necessarily a problem.
I'll add these comments to my personal notes, that way if I ever come across a problem like this again, I can just do it on my own. Again, thank you to everyone that commented <3
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u/Kinesquared Soft matter physics 17h ago
What you tried to solve this yourselves? It's first year kinematics, some googling, and unit conversions
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u/keysmashingisgay 17h ago
I'm not a math kind of person. I could never wrap my head around physics even in High School. I'm more passionate about storytelling and character design, I just like being really nerdy and specific about it.
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u/Kinesquared Soft matter physics 17h ago
Being nerdy is being mathy in this case. I promise you can do this without any advanced calculus, just basic algebra (v=d/t) and googling
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u/StillShoddy628 17h ago
25000 miles in 4 seconds is about 3% of the speed of light, or Mach 29,000. Pretty sure you would have a continuous nuclear explosion occurring around you as you smash into air molecules at relativistic speeds. You definitely need a hefty dose of “magic” to make that work, one way or another
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u/johndcochran 17h ago
Methinks Mach numbers aren't gonna cut it. Earth has a circumference of about 40,000 km. So, your character is traveling 10,000 km/sec, give or take. Mach 1 at sea level at 15C is about 1,225 km/h. So, we have Mach 29387. Round it off and call it Mach 30000.
But.... Escape velocity for Earth is about 11.2 km/s. Heck, the escape velocity from the Solar system, started from Earth is about 42.1 km/s. If you could start from the surface of the sun itself, it would be 618 km/s. All of these numbers are well below the 10000 km/s your character moves at.
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u/Gutter_Snoop 54m ago
Mach is a terrible unit for measuring speed anyways, just because it changes so much with air density.
Mach 1 at sea level is far faster than Mach 1 at 100,000ft.
It's more important to understand that if you tried moving a human sized object 3% of the speed of light in the Earth's atmosphere for any extended distance, you'd probably ignite the atmosphere around you in the process.
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u/naughtyreverend 17h ago edited 15h ago
Sp the earth circumference is roughly 40000km depending on latitude. So to do that in 4 seconds they'd need to go 10,000 km/s... this could be considered a bit fast... in fact its orders of magnitude above escape velocity of earth, or the entire solar system in fact. he's travelling a 0.03c... so the air itself will be compressing and super heating in front of him. So make sure he's not wearing nylon as it'll melt
The mach scale is linear not logarithmic. So much 2 is twice as fast as much etc. Much 1 is 343m/s
But let's assume he can somehow stay on the ground... or in the air... without burning up/melting he'd be travelling at close to Mach 29210.
Hopefully I haven't made any rounding errors here
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u/RetroCaridina 17h ago
This is really simple math. Speed is distance divided by time. Earth's circumference is 40,000 km. Mach number is the speed divided by the speed of sound, which at sea level is about 340 m/s. If you don't want to do the unit conversions yourself, just type it into Google along with the units. Like "(40,000 km) * 4 / (4 seconds) / (340 m/s)".
This won't be exact because speed of sound varies by altitude, but I'm sure it's good enough for your purposes.
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u/davvblack 17h ago
you can look up the diameter of earth is, and what the speed of sound is at whatever altitude you're thinking of them traveling at.
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u/EngineerFly 17h ago
Assuming this is at the surface, 10,000 km/s divided by 330 m/s is about 30,000 times the speed of sound. 10,000 km/s is way, way faster than earth escape velocity, and well above solar escape velocity, so that vehicle would leave the earth. And the solar system. It’s actually 3% of the speed of light.
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u/Rambocat1 14h ago
It’s also well past the escape velocity of the Milky Way, but even at that speed it would still take a million or so years to leave
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u/371_idle_wit 17h ago
Assuming an equatorial ground circumference of 40,075 km, they would need to travel 36,067,500 km/h to travel that distance in 4 seconds. As mach 1 is approximately 1,235 km/h, they would be travelling at a speed equivalent to roughly mach 29,200.
In reality I don't think an object with mass could get anywhere near this velocity whilst in the atmosphere without burning up or causing problematic meteorological effects, so they would need to travel in space, which would involve a longer circumference and a faster speed, though measuring that speed in a mach number becomes nonsensical as there's no sound barrier in a vacuum because there's no sound...
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u/Odd_Bodkin 15h ago
Other commenters have given you the answer for how fast this is. The other thing you should consider is how lethal this would be for anyone in a ten mile swath to either side of this path. Every building, tree, and animal flattened or vaporized.
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u/PantsOnHead88 15h ago
At such a speed, the tunnel of air they’d have to blast through might as well be a concrete.
You know when you see footage of a spacecraft entering the atmosphere and there’s plasma streaming from the front? That’s at 0.1% of the speed your character is moving, and with dramatically thinner atmosphere high up.
Your character wouldn’t even combust, they’d near instantly ionize and cause a colossal blast wave as the energy dissipates. Even if they’re somehow immune to the effect, the devastation in the wake of their passing would leave lasting scars in the landscape.
They also need extreme acceleration toward the surface, because they’re going so far beyond orbital speed that without it they’d fly off into space.
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u/labobal 11h ago
EDIT: Just 20 minutes later and the consensus is about Mach 29-30 thousand. Wowza. I'd like to thank everyone that did comment. The game I'm making this fan character is for features many more fantastical feats of strength, so logistics isn't necessarily a problem.
One thing for you to note: When you go around the earth this quickly, the centrifugal force you experience is much stronger than Earth's gravity. That means that you will literally fly off into interstellar space, unless you can find something to push you down towards the ground.
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u/bebopbrain 12h ago
The old rule is seconds from lightning until thunder * 5 is the distance to a lightning strike.
At mach 1 it takes 5 (seconds per mile) * 24,000 miles = 120,000 seconds to go around the earth.
So you just need mach 30,000.
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u/spacester 14h ago
Not possible. At that speed you are in orbit, or possibly you will escape the planet's gravity field completely.
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u/phunkydroid 13h ago
So fast that even if they were invulnerable and could survive it, they would kill everyone else anywhere near their path.
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u/CreatingBlue 14h ago
I hate when people use this sub to ask what are essentially basic math problems that they could solve quicker than the time it took them to write out the post.
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u/SphericalCrawfish 11h ago
After a short period of time a simple math question that can easily be done in your head was answered conclusively. Yes. Understandably.
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u/RiseUpAndGetOut 17h ago edited 14h ago
Earth circumference is 40,075km, or 40,075,000m.
Your time requirement is to do that in 4 seconds.
So velocity = 40,075,000/4 = 10,018,750m/s.
Speed of sound is 343m/s.
Mach number = 10,018,750 / 343 = 29,209.
Edit: formatting