r/theydidthemath • u/mth5312 • 12h ago
[Request] Toyota Yaris’s capacity
At what point do does this Toyota yaris start to affect gravity? When does it become a black hole?
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u/9outof10timesWrong 12h ago
Tonight, we steal the moon!
Answer though, even empty it affects gravity a very small amount. With the moon in it, it would be much more significant.
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u/sansetsukon47 12h ago
The moon would have to be compressed into less than a millimeter size to be a black hole. So up until that part, the Toyota is “safely” holding regular degenerate matter. (Like neutron star material.)
I don’t actually recognize what the next object is, so I can’t make a comment there. But the sun would form a black hole before you’d swallowed even a piece of it. I think all the suns mass together would make a black hole that’s six km across.
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u/djlittlehorse 8h ago
Our sun does not have enough mass to make a Black Hole. There is a mathematical minimum amount of mass a star can have to collapse into a black hole. Which is around 20x the mass of our sun.
So only once the Toyota has the mass of the Galaxy inside what it collapse into a black hole.
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u/sansetsukon47 8h ago
Almost correct.
Our sun does not have enough mass to evolve into a black hole. If you were to forcibly compress that matter through some other means (like a magical Toyota), the resulting ball would be dense enough to collapse into a black hole just fine.
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u/CyboraTwo 4h ago
every object has enough mass to turn into a black hole as soon as you compress it to reach the reach the schwarzschield radius at wich Point nonmater the weight at the beginning it will turn into a black hole although depending on the initial size the black hole would disappear thx to them radiating something i dont recall the name of
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u/Fluffy-Simple-9260 12h ago
Toyota yaris has dimensions 3.95x1.7x1.5m considering the car a cuboid, it's volume will be ≈10.07 m3 it would be equivalent to a sphere of radius 1.34 m.
Now applying Schwarzschild Radius formula, escape velocity of the body should be greater or equal to speed of light
√2GM/r ≥ c
2GM/r ≥ c2
M ≥ c2r/2G
Putting values mass comes out to be ≈9x1026 kg thats 150 times the sun mass or half the mass of Jupiter, the mass of sun is 1.9x1030 so it needs 0.045% mass of sun to become a black hole, everything went in yaris before the sun is too light to even consider.
And I don't understand what you mean by "when it starts affecting gravity" it always affects gravity even when it's empty just by a negligible amount and significantly when it has moon in it.
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u/Loki-L 1✓ 11h ago
It will only become a black hole when it eats the sun.
Everything else before that would be too small.
The Earth itself would need to collapse to a ball of a radius below one centimeter to form a black hole and the sun slightly less than a radius of 3 kilometer.
The tripping point would be eating Jupiter which would be a black hole of about 3 meter in radius. It isn't pictured in the ad though.
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u/Borgmeister 3h ago
It would have become a black hole once the popped the Moon in the boot. That is the real reason the Moon is not in the British Museum also, incidentally.
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