Maggie and Me (a philosophical dialogue): On Isaac Newton, part 2

John:  It’s nice to see you again.  Have I told you recently how much I enjoy our conversations?

Maggie:  I enjoy them too.  I like talking about science with you.  You make it easy to understand.

John:  I think science should be accessible to everyone.  Sometimes I think science teachers make it hard just to make themselves look smarter.

Maggie:  That’s probably true.  But some scientists are hard.

John:  That, my friend, is true.  And as we said last time, Isaac Newton is one of the more challenging thinkers to understand.  But we will see what we can do here with his contributions to astronomy.

Maggie:  Where do you want to start?

The Newtonian Paradigm

John:  Let’s start by talking about the concept of a paradigm shift.

Maggie:  I am going to need an explanation.

John:  We will talk about this in more detail later, but a paradigm shift in science occurs when scientific thinking takes a radical turn and starts down a different path.

Maggie:  Can you give me an example?

John: Sure.  Remember Copernicus?

Maggie: Yeah.  His book On the Revolutions of the Celestial Spheres proved that the solar system is heliocentric, not geocentric.  

John:  Nice.  I am glad you remember the correct terms.  Copernicus started a paradigm shift in astronomy, which culminated with Newton, who explained many of the open questions left by Copernicus, Brahe, Kepler, Galileo, and Descartes.

Does this make sense to you?

Maggie:  It makes perfect sense.  Astronomy was never the same after Newton.

John:  And until Einstein came along, scientists applied Newton’s theories to advance astronomy.

Maggie:  I like that: Newton was a paradigm all by himself.  Let’s call the time between Newton and Einstein the Newtonian paradigm.

John:  Done!  And that is a great description.

Maggie:  What’s next?

The Principia and the Laws of Motion

John:  Let’s discuss Newton’s laws of motion.  Do you recall the title of his famous book that he published in 1687?

Maggie:  Sure.  It was the Philosophiae Naturalis Principia Mathematica, called the Principia for short.

John:   In this book, Newton put forth three laws of motion, which describe how bodies move in space.  Do you remember what they are from our last conversation?

Maggie:  I got this:

First Law: Every object will remain at rest or in a state of uniform motion unless an external force acts on it.

Second Law: Force equals mass times acceleration (F=M*A).

Third Law: For every action in nature, there is an equal and opposite reaction.

But I have to admit that I don’t really understand these laws or how they apply to astronomy.

John:  It is not important for our purposes that you perfectly understand these laws. What is important is that you have enough of an understanding to move on to the discussion of gravity.  So let’s see if we can get there.

Maggie:  Works for me.

John:  Let’s build a word-picture.  Visualize a baseball field and kids playing tee ball.

Maggie:  Okay, I’ve got it.

John:  A baseball sits on top of a tee at home plate.  Under the first law, that baseball will sit there (remain at rest) until the batter comes up to the plate and hits it with a bat.  Does that make sense?

Maggie:  Sure.  An object (the ball) remains at rest until an external force (the bat) acts (or strikes) it.  That makes perfect sense to me.

John:  The first law also says that an object in motion will remain perpetually in motion until an external force acts on it.  So once the batter hits the ball, it will remain in motion (go on moving forever) until an external force (like the second baseman) acts on it.

Maggie:  Now I don’t get that.  It doesn’t make sense.

John:  That is because you have never seen it happen.  Newton is talking about a hypothetical universe, a perfect space.  In our universe, the ball stops because there are a lot of external forces like the grass, the dew on the grass, the air we breathe, friction between the ball and the ground, and the second baseman. But what if the batter hit the ball in perfect space.  

Maggie:  I get it.  The ball would go a lot farther because there are less things to stop it, like grass and the second basemen.  Right?

John:  Right.  

Maggie:  And in Newton’s hypothetical, perfect space, there is nothing to stop it, so the ball would go on forever.

John:  You got this! Let’s move on to the second law.

Under this law, an object’s (the ball) change in motion (from rest to moving) is proportional to the force applied.  This means that the ball will move faster or slower depending on how much force is applied when the bat hits the ball.  And force is equal to mass (the size of the bat) times acceleration (the speed of the bat).

Maggie:  Let me think this through.  The speed at which the ball will move off the tee depends on the size of the bat the batter uses and the speed at which the batter swings the bat.  Is that right? 

John:  Correct.  Now under the third law, when the bat strikes the ball, not only is the ball affected, but the bat is also.  It slows down because the ball exerts a counter-force on the bat.

Maggie:  That makes sense.  The bat exerts a force on the ball, but the ball does likewise to the bat in an opposite reaction.  

But how does all this apply to astronomy?

John:  Good question.  These three laws helped Newton come up with his theory of gravity.

Newton’s Theory of Gravity

Maggie:  All right!  This is where we hear about the apple hitting Newton on the head.

John:  It is a funny story. One afternoon, during the quarantine for the plague, Newton went outside to get some fresh air.  He decided to sit under an apple tree and rest for a bit.  While sitting there minding his own business, an apple fell out of the tree and hit him smack on the head.  Rather than getting irritated, this got Newton thinking about the apple and why it fell straight down onto his head.  Why didn’t it fall sideways, he wondered, or at an angle, or on a curve?  These questions eventually led him to discover the law of gravity.

Maggie:  Did this really happen?

John:  Who knows?  But whatever happened, he eventually came up with his fourth law, which changed astronomy forever.  Do you want to tell me about the fourth law?

Maggie:  Sure. 

Fourth Law:  Every object in the universe attracts every other object in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between the two objects.

That is a mouthful to say!

John:  Do you want to see the cool math formula that describes this law?

Maggie:  Sure, yes.


Maggie:  Do I have to understand it?

John:  No, no, no.  I just like to look at it because it’s beautiful.  It’s like the Mona Lisa of math formulas.

Now remember that we have to interpret Newton’s fourth law in light of the previous three laws.

Maggie:  Can you help me understand this better?

John:  That’s my goal. 

Recall that Newton said objects are at rest or in motion until a force acts on them. Let’s apply this to our galaxy, specifically to the sun, the planets, and the many moons.  Why are the planets and the moons moving?

Maggie:  Because they’re not at rest!

John:  All right smarty pants.  Why do they continue in motion, the planets around the sun and the moons around the planets?

Maggie:  Because a force acted upon them or is continually acting upon them.  

Oh, I get it now, this is how the first law applies here.

John:  Right!  An external force is acting on these objects; and that force, according to Newton, is gravity.  It’s the only thing that explains the motion of the planets.

And here is something more: each of these objects—the sun, the planets, and the moons—exerts a force upon all the other objects because each has its own gravitational force.  The sun, because it is the biggest object, exerts the greatest force upon the planets.  That is why the planets rotate around the sun.  But the planets also have gravity, which is why the moons rotate around the various planets.  

Does the make sense to you?

Maggie: I think so. Yes, yes it does.

John: Do you see how this applies the second and third laws?

Maggie:  Yeah, the bigger the planet the greater the force of gravity (second law), and the greater the force of gravity the more speed a planet picks up in reaction (third law), or something like that. That makes sense to me.

But if the sun is exerting the greatest force on the planets, why aren’t they just pulled right into the sun, like the apple was pulled down from the tree onto Newton’s head?

John:  For three reasons. First, the distance between the sun and the planets weakens the gravitational forces.  Remember in the fourth law that the force of gravity depends on the distance between two objects.  Second, the speed at which the planets are traveling lessons the gravitational pull, just like swinging a bucket full of water around your head is hard at first, but gets easier as the bucket picks up speed. Lastly, remember that all objects have gravitational pull (fourth law).  So the other planets, like Jupiter, are also exerting gravitational forces, pulling planets like the earth outward.  

Maggie:  It’s weird to think about, but what we are trying to say is that the balance of gravitational forces between the sun, the planets, and all the moons keeps the solar system from collapsing upon itself or flying apart.

John:  Geez, you are smart, my friend.  Nice way to summarize what we have been saying. And nice way to make a complicated thought pattern easy.

But, as you can imagine, Newton didn’t stop here. Using his four laws, he and other scientists were able to calculate the orbits of the planets and the moons and various comets.  And do you want to hear something really cool?

Maggie:  Absolutely.

John:  These laws and their corresponding mathematical formulas are still used today by scientists and NASA to establish the orbits of satellites.  Newton’s work is still applicable now!

Maggie:  Newton is such a monster scientist.

What’s next?

The Shape of the Earth and Calculus

John:  Just a couple more things.

Like Kepler, Newton was a serious math god.  In order to prove his scientific theories, he had to work out the math, including the math for calculating the orbits of the planets and comets.  He also worked out the math for the sizes of various planets like the earth.  To do this, he had to invent a new type of math.

Maggie:  Ugh.  Calculus, right?

John:  Yep, that’s it. You can blame Newton for all those long, arduous hours spent studying calculus.  Well…  Newton and a guy named Gottfried Leibniz.  And here is something interesting.

It appears that Newton and Leibniz both came up with a version of calculus at about the same time.  But Newton was convinced that Leibniz plagiarized his work.  So the Royal Society undertook an investigation to determine who should actually get the credit for coming up with this new mathematical field.  But Newton was the president of the Society at the time, and as the president he oversaw the investigation.  So he made sure he was given the credit as the originator.  This controversy hung over both men during their lives, and to some extent it still lives today.  

Maggie:  That’s hilarious.

John:  To me too.

Maggie:  What’s our last point?

John:  Using his science and math skills, Newton was the first person to prove that the Earth was not perfectly round: it actually bulges at the equator and flattens out a bit at the poles.  


Maggie:  So to sum this up, Newton changed astronomy by proving the heliocentric view of the galaxy; came up with his four laws, including the law of gravity; used his laws to predict the orbits of the planets, moons, and comets; used his science and math skills to calculate the size of planets, including the Earth; and invented calculus to help him with his science.  And these are just his contributions to astronomy.

John:  Not bad for an over-emotional nerd who grew up under some very tough circumstances, huh?

Maggie:  I love this guy!  It just goes to show that anyone anywhere can overcome her circumstances and do great things.

John:  I agree.  Thanks for working through Newton’s thoughts with me.  It was fun.

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