Newtonian Reverie

 

Historical fiction by your teacher.

 

This may be a bit anachronistic [look it up], but it may, perhaps, help you understand how he was thinking… sort of…


 

One sunny Autumn day in the mid 1660s Isaac is chewing on a piece of grass, listening to a babbling brook, and thinking about the moon.  Out of the corner of his eye he sees an apple fall… or the apple falls on his head… I can’t remember.  Apple falls.

He muses on apples falling… he assumes a concept of inertia and some sort of uniform acceleration as proposed by Galileo and runs with it.  La, la, la.

 

Recap: He observes an apple falling.  He figures it falls with uniform acceleration and that things in motion stay in motion unless acted upon by some sort of force. La, la, la.

 

Then his mind wanders back to the moon.  Galileo also shows that the moon appears to be a big, dingy, and blemished spherical apple of sorts and it looks like things are attracted to it.  Galileo also shows that Jupiter is attractive, at least to the Medician moons.  Stuff attracts stuff.  … [back to the moon] …. Why doesn’t the moon fall to the earth like the apple?  Bang…or thud.  Perhaps the moon is falling like the apple?  ...what was I supposed to pick up at the grocery for uncle Stew?... oh yeah, apples… Perhaps the moon is falling.  I’m not scared, I’m a super hero…. [Newton imagines supporting the moon like Atlas.]  If it is falling it never seems to get anywhere since the orbit is essentially circular.  When the apple falls its velocity increases… it accelerates.  The moon, on the other hand, doesn’t really accelerate… or maybe it does… its motion is circular and the apple’s motion is linear, straight down.  Are these two situations apples and oranges… get it?... When I hold an apple, it sort of feels like there is a force pushing down on it, but I resist this force with my hand and arm and the apple remains stationary.  When I let go of the apple I assume that this force will continue to act on the apple and either pushes or pulls it downwards continually.  This explains why it keeps falling faster and faster since this invisible force is continually pushing or pulling it all the time, constantly. It’s not like Descartes claims, where it is as if the apple just hooks up to a conveyer belt of some fixed velocity and by degree settles in for the ride eventually approaching some final velocity as it merges with the motion of the vortex.  This would imply that the apple would not have a constant acceleration since Dv would approach 0 as the object becomes one with the vortex whirlpool.  I don’t doubt that in reality the change in velocity of the apple would eventually hit 0 if it fell far enough, but this would be due to the contrary force of some sort of friction or air resistance which clearly is some function of velocity  -The faster I move my hand through the air the more I feel air resistance.  If there were no air, I bet the acceleration would be quite uniform. Anyway… if I let go of an apple, the force I feel accelerates it uniformly until it hits something.  There is clearly a force.  I feel it.  It pushes me down onto the ground.  It makes things fall.  I see it acting everywhere.  Things fall.

 

New idea- When I’m on a merry-go-round I also feel a force.  This force seems to be rather constant so long as the angular velocity of the merry-go-round is constant.  This force is resisted by my hanging onto the merry-go-round.  This force feels radial rather than tangential even though I know that if the merry-go-round were to suddenly stop that I would fly off tangentially if I lost my grip.  My motion doesn’t appear to accelerate in any way, and yet I am in motion and I feel a force.  I wonder if this centripetal (or centrifugal depending on POV) force is similar to the force felt by that apple. 

 

New idea: When I put a rock on a string and swing it around like a Babylonian cooking eggs, I feel a force pulling the string out of my hand.  Again there isn’t any linear acceleration, but there is this force that feels a lot like the force I feel on the apple when I hold it.  Weight is like a force. Centripetal motion seems to produce some sort of force, some sort of weight.  When the apple surrenders to this force it falls with uniform acceleration, its Dv=Constant.  What would the rock on a string do?  It feels a force.  Is that force somehow related to uniform acceleration too?  If I cut the string to my rock it would fly off on a tangent.  This is easily demonstrated.  Therefore it’s velocity is tangential.  If I could switch off this gravitas concept I suspect the moon would also fly away from the earth on a tangent.  The tangential velocity always tries to take the rock or the moon to a larger and larger radius. Perhaps these counter balance each other?  --A force acting down and a velocity propelling it away.  But how can you compare a force (whatever that is) to a velocity, which is just an abstract idea?  Also, if the moon is like the apple, is it feeling a pull downward or is it always in freefall, not noticing any force at all?  The rock feels the pull from the string.  What pulls at the moon? 

 

New idea: If I throw an apple up, it falls back down. At the moment when it stops moving at the top of its parabolic trajectory, it falls just like it would fall if it fell from a tree.  I'm a superhero again.  Let's say it takes an apple (or anything for that matter) 2 seconds to fall  from some given altitude, a few feet, and then hit the ground.  What if I could throw an apple so hard horizontally, that in those two seconds the apple went all the way around the world?  Does that make any sense?  The initial trajectory of this superfast apple would be roughly tangential to the earth's surface.  As it flew out tangentially, it would also be tugged in towards the earth by gravity.  It would move a little bit away, and then be tugged back in... all at the same time, continuously... out and way and in towards the center.  The tangential motion would, by itself, increase its altitude from the earth... no doubt I'd have to do some trig with the sine function to figure out how much.  But as the altitude increased just from tangential velocity, the apple would be simultaneously tugged back by gravity.  If you could throw the apple at just the right initial velocity (and there were no more air or mountains to get in the way) you could make it orbit the earth.  You could throw it so that it would circle the earth and hit you in the head... at such a velocity that you'd surely explode upon impact... but of course this airless world I'm suggesting might make you fall to the ground, gasping for air, thereby saving your life as the apple whizzes by at an extraordinary speed.

 

Recap: The apple falling is like the moon.  Maybe the moon is perpetually falling but it is perpetually being countered by the tangential component of its velocity. 


The apple and the moon.  How are they related?  What do they experience?  Are they analogies for each other?  How could you negate the feeling of gravity?