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Poziom:
Temat: Nauka i technologia
Have you ever wondered how the earth stays
in orbit around the sun? I mean, the pull
of gravity is stronger the closer you are
to the sun, so you'd think that if the earth
got bumped slightly towards the sun (like,
if you jumped, or something), then the sun
would pull just a little bit stronger, tugging
the earth yet closer still, at which point
the sun's pull would be stronger yet again,
… and the earth would spiral in to its eventual
doom.
But you and I and swiss cheese are clearly
evidence that the earth doesn't just spiral
in to its doom – so why not? Well, when
the earth does get pushed a little bit towards
the sun, the sun's pull speeds it up a little
bit, too - so even though the nearby sun's
pull is stronger, the earth will be going
fast enough that it overshoots and ends up
farther away from the sun. Of course, the
sun's pull slows it down again in the process…
at which point the earth turns back and starts
the cycle all over again.
The amazing thing is that the two effects
of speeding up plus stronger gravitational
attraction perfectly balance, so that the
earth stays in its orbit the same way a marble
stays at the bottom of a bowl even if it gets
knocked around a little bit.
This balance is very special indeed - it's
highly dependent on the strength of the gravitational
force and the number of dimensions we live
in, and in fact, these stable orbits only
exist in a three dimensional universe.
The details are a bit subtle, but if gravity
were just slightly steeper, as it would be
if we lived in four spatial dimensions, you
could never orbit the sun because you'd get
pulled in without picking up enough speed
to escape and you WOULD spiral in to your
doom. And if we lived in fewer dimensions
so that gravity were a bit tamer, then you
could ALSO never orbit the sun, because as
you approached it, you wouldn't be pulled
enough and would merely pass by with your
path slightly bent.
So we're incredibly lucky to live in a three
dimensional universe where there ARE stable
orbits that allow planets, solar systems,
and galaxies to exist at all! Thank you, stable
orbits, for without you, life as we know it,
and especially cheese, would be impossible.
ps An awesome down-to-earth example of stable
orbits are the hyperbolic funnels that you
often see at museums or in shopping malls:
the physics is almost identical to the stable
orbits of planets, satellites, and moons,
and the only reason the coins in the funnels
(or satellites around the earth) eventually
DO spiral in to their doom is because they
lose energy to friction and thus shift down
from one stable orbit to another, until eventually,
their orbit coincides with the ground. Which
is called crashing.
