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.