Centripetal vs. Centrifugal force, & the Solar System

One of the worst teaching tools physicists use (and they almost all do it) is to tell students,

There’s no such thing as centrifugal force.

What can you do when the top physics education website says, “It is important to note that the centrifugal force does not actually exist. We feel it, because we are in a non-inertial coordinate system.” There’s a very funny comic over at xkcd that goes as follows:

Well, what’s the deal? What really goes on, physically, and what causes a centrifuge to work? Is your physics teacher right, or is there more to the story than “the centrifugal force does not actually exist?”

So, your physics teacher is partially right. When an object moves in a circle, it’s moving, at any instant, tangentially to the circle, and it’s the centripetal force, causing an acceleration towards-the-center, that keeps it moving in the circle.

But that’s not the end of the story, or I wouldn’t be posting this. Do you remember Newton’s third law? It says for every action, there’s an equal and opposite reaction. That is, for every *force*, there’s an equal and opposite force. Take the photo below:

Notice how the man’s face getting pummeled is not only experiencing a force from the fist, but the fist experiences an equal and opposite force! (And if you don’t believe me, go punch a brick wall.) Well, if there’s a centripetal force acting on an object, pulling it towards the center, then there’s a centrifugal force from the object reacting to it, pushing things away from the center. If it’s a ball attached to a string, the string pulls the ball towards the center, and the ball pulls the string away from the center. If it’s a wall pushing a person towards the center, the person pushes back against the wall, pushing it away from the center, like so (that’s why the walls need to be sturdy):

So, that’s an example of a real centrifugal force. But beyond that, how does a centrifuge actually work, with only centripetal forces acting on the stuff being centrifuged?

Centrifuges spin really fast, causing the stuff inside to separate out according to density, with the most dense pushed out the farthest, towards the bottom, and the least dense winding up at the top, closest to the center. Because we don’t know the difference between gravity and any other acceleration or force, centrifuging something is basically like turning the knob on gravity way up — by up to a factor of 15,000, depending on the centrifuge! In zero gravity, things don’t sort themselves by density, but in a high enough field of gravity, they do. Even solids. Like this thing:

The centripetal force of the sides of the centrifuge push back just like the seat of your chair pushes back against you when you’re in a gravitational field. The faster the centrifuge, the harder the sides push back; and the whole thing acts like an enhanced version of gravity. Well, what does this have to do with the Solar System? Sir Arthur Eddington once described all the life on Earth as follows:

We are bits of stellar matter that got cold by accident, bits of a star gone wrong.

While it’s true that all of the elements on Earth that we know and love (except for hydrogen and helium) were formed in stars, the Sun is almost all hydrogen and helium, and the planets are almost exclusively heavier elements! How did that happen? Was it an accident, as Eddington suggests? No; it was centrifugal force pushing the heavier elements (like carbon, oxygen, nitrogen, iron, phosphorus, silicon, etc.) away from the center relative to the light ones!

So the Earth, and for that matter, all other planets, are made out of denser elements than stars are. And the reason is all due to a force that your physics teacher probably told you doesn’t exist!

UPDATE (January 29, 2008): It occurred to me that some of you might like a way to *test* this. It’s well known that solar systems form from dusty disks, known as proto-planetary disks. If what I’ve just articulated is correct, the material closest to the center of the disk should be preferentially less dense than the material farther away. We don’t have a dusty protoplanetary disk around our sun, but we have an analogous, dusty disk around one of our larger planets:

Any volunteers to test it out?

33 thoughts on “Centripetal vs. Centrifugal force, & the Solar System”

  1. I just realized that if your blog title was shortened to an ackronym, it’d be SWAB. Was that an intentional backronym? You astro-types seem to love those….

  2. Yes, yes it was intentional, and also fortuitous. Now I can make awful pirate jokes galore. Where does a pirate keep his Buccaneers? Under his buckin’ hat! (Ha ha ha…)

  3. Your explanation is still misleading regarding “centrifugal” force. While it is true that Newton’s Third Law is in play (the string pulls centripetally on the ball, so the ball pulls back outward equally) this outward force acts on the string and not on the ball. Thus, there is no centrifugal force—a force acting on an object throwing it outward due to its circular motion.

    This really comes down to properly defining the “system of interest”. If the ball is your system, then the only force acting on it is the string, pulling inward. No centrifugal force. If your system is the ball+string, then the only force acting on it is the “pin” holding string in place. Again, outward forces.

    If your system is the string, then, yes, there is an inward force (pin) and an outward force (ball) but all it does is increase the string tension since the two forces balance—there’s nothing pushing the string outward.

    But, even if you want to quibble and call this outward force on the string a centrifugal force, it still does not act on the ball.

    So, when you move to your centrifuge example, it is erroneous to state that there is anything pushing the material in the tubes outward. The only possible centrifugal force would be the force of the fluids+solids on the tube.

    The best description of what’s happening in a centrifuge is that the material is given some initial velocity (and since the distances from the axis are relatively small, we could even pretend that everything in the tube is moving with about the same tangential velocity). Then the amount of force needed to keep them in a circle is proportional to the mass/radius. The more massive (higher density) stuff needs more force, which the fluid around it can not provide—therefore it moves to a larger radius of curvature until it collides with the tube bottom that can provide the necessary force. This is much the same as taking a curve too fast; if your tires-on-the-road can’t give you enough centripetal force, eventually the guardrail will.

    The dense stuff eventually gets so close-packed it pushes the less dense stuff inward; those solids then provide the centripetal force for the less dense solids, etc.

    Once again, from an inertial reference frame, no centripetal force is required. And we can find no object that is physically providing an outward force on the objects.

  4. David,
    Centripetal and centrifugal forces are easily confused, and I know that when I was in High School, College, and Graduate School, I was taught it incorrectly three times.
    Centrifugal force on the stuff in a centrifuge is an effective force. Think about it in terms of buoyancy; just as the less dense stuff floats to the surface in a pool, the less dense stuff floats to the inside in a centrifuge.
    I agree that it’s important to think about what forces are acting on what objects, but everything I’ve written in the above article is both correct and self consistent. In the centrifuge, the material inside is receiving a “Normal force” from all the material beneath it, and the least dense stuff will rise to the top. That’s all.
    Also, remember that you’re assuming that the stuff being centrifuged can be treated as a point. But if I put you in a centrifuge, your feet would feel a much greater force than your head would, since they feel the centrifugal force from everything above them!
    Hope this answers your question, and thanks for your curiosity!

  5. hi… nice to read ur blog …..
    it has very informative info ……abt centrifugal force and …….
    but i have one query when we derive equation for sedimentation velocity we consider frictional , buoyancy force ….but we didnt consider centripetal force ….but centripetal force is always counteract to centrifugal force …..
    can u help me out ..
    my email id is

  6. Tushar,

    You will be okay; the frictional force is always there, and buoyancy forces are, effectively, the combination of gravitational and centripetal/centrifugal forces.

    Did you know that if the Earth rotated five times per hour instead of once per day, the oceans and rocks at the equator would be thrown into space, overcoming the Earth’s gravity? How’s that for centrifugal force??

  7. Sorry, just a little question? I am not too knowledgeable about physics or whatever other field this might be in,but I was wondering, as you stated that things heavier than the Sun were thrown out or pushed out . I can see that happening ,but at the same time I was told that the center core of the Sun was made of Iron, but that could be a wrong theory . How about the Earth. The center of the diagram has the solid center then the liquid center , but wouldn’t the solid be more dense than the liquid. and how about the air being lighter than the water why is that being pushed upward. and Centrifugal and centripetal are the principals of Gravity, right? So it is Centripetal forces keeping us to the ground , is that right ? So how heavy does something have to be to be thrown out?I guess there might be a equation for that . and another question would (in theory) the planets in general be denser than the ones closer to the Sun ?

  8. You’re right on this account, Adrian. When you get close to the center of a bound object, gravity is much stronger than centripetal/centrifugal force, and so the dense thing sinks to the center. When you’re far away, if your velocity exceeds gravity, the opposite is true. In reality, things are distributed in some very complex balance dependent on initial conditions. Also, Saturn’s rings aren’t a solidly rotating disk either, so I’m not sure my analysis applies.

  9. You say:
    “Did you know that if the Earth rotated five times per hour instead of once per day, the oceans and rocks at the equator would be thrown into space, overcoming the Earth’s gravity? How’s that for centrifugal force??”

    That’s just the Earth’s gravity not providing enough centripetal force to stop the fast moving surface travelling off in to space.

    …and it would still be rotating once per day, as that’s what a day is :-p

    Of course, ignoring further pedantry about a day not being a full rotation, but the sun returning to above the same point… err I mean line of longitude.

    It’s a minefield this expressing an opinion thing, isn’t it.

  10. Steve,

    I think that’s strictly a point-of-view question, but there’s no doubt that the forces must balance somewhere; there’s no net force on a golfer from taking a golf swing.

    Not that I know from experience; I am lousy at golf!

  11. I think this blog as a good example of ‘bad science’. We were taught to steer clear of centriful force discussions. (Full stop). There is no string connecting the moon to the earth (last time I checked). There is no magical balancing act between gravitaional attraction and inertia (reluctance to changes in states of motion). There is a world of misguided notions re: orbital mechanics – it’s right in there with zero-point energy ‘anti’ gravity schemes or strategies. The moon is in reality constantly falling towards the earth (or more accurately the earth is accelerating toward the moon and the moon is accelerating toward the earth (consistent with Newtons Law of Universal Gravitation and Newtons 2nd Law) and to really round things out state that this all is centered about a point known as the Barycenter of this two-body system. The moon and the earth are indeed accelerating toward one another as has been the case for the past 4 billion years. Where the moon to lose it’s velocity component (normal to the direction of gravitional attraction) it would no longer miss the earth (in it’s continuous 4 billion year-old fall) and a condition where the two bodies would attempt to occupy the same space at a velocity approximately consistent with that of the escape velocity (17 km/sec).

  12. Terri,
    The point isn’t that you should steer clear of centrifugal force discussions. Why would you not discuss something that’s a real, easily-observed physical phenomenon that students are familiar with?

    The hard part is explaining it properly, which is what I’ve attempted to do here. Orbital mechanics is one of the things I’m kind of a scientific expert on, and so I have a particular interest in it. The Moon and Earth are unique in our solar system; no other inner, rocky planet has its own large moon, and so we’ve got something truly remarkable to study right in our backyard.

  13. Ethan,

    Is the going theory that the earth was thrown from the sun…and the sun’s gravity pulls it from it’s tragectory resulting in an eliptical orbit…neither overcoming the gravity of the sun and spinning away from it unending, or becoming reabsorbed into it due to the centrifugal (gravity-bended inertia?) force that holds it at it’s distance?

    I ask the question for this reason…if the above explains the earths orbit, then by this same interpretation of forces wouldn’t earth’s orbit eventually be increasingly and exponentially forced either to or away from the sun? Whatever precarious ballance might exist between opposing forces to keep us at this ideal proximity to the sun in order to sustain life…could that not be easily tipped merely by the subtle presence of other masses in our solar system whose gravitational pull acts upon the earth in a direction away from or towards the sun’s pull?

  14. Years ago I remember reading an article in Scientific American that gave examples of popular misconceptions among high schoolers in the U.S., examples of their “physical intuition” being wrong.

    One such case being the mistaken notion that an object latched to the rim of a fast-spinning disk, if you released it, would trace an outward spiraling path, instead of flying off in a straight line (the correct answer).

    I believe that such misconceptions are partly to do with the fictitious “centrifugal force”. In my opinion commentors David and Terri are right, and Ethan (though he would give the correct answer to the example question) is wrong to insist on teaching “centrifugal force”, which in people’s minds is connected with “roundness” and “circles”, messing up their physical intuition.

  15. gosh , this time I will be very quick, and say that I love physics for its logic. I just love it.
    thank you for what you are doing
    keep writing
    can you for example write about Albert Einstein?

  16. In awe for the laws governing our world, our universe
    but there is something bugging me
    Quantum physics
    you have described an experiment in which electrons behave differently depending on who is looking at them
    and now… if electrons do that, can the laws of physics, those that we have discovered be also man-made, occurring because our imagination tells them to?
    this is very interesting

    Ethan I would like to read about the Unified Field Theory, write about it, please:)

  17. It must be amazing to know more about the universe, and the laws governing our world, as every time you broaden your perspective, you broaden your level of happiness.

  18. Here’s the best example: Go watch a well-trained male ballet dancer execute (multiple) pirouettes or consectutive tours… case closed. thx!

  19. Consider a body tied at the end of a string moving with uniform speed in a circular path. A body has the tendency to move in a straight line due to inertia. Then why does the body move in circle? The string to which the body is tied keeps it to move in a circle by pulling the body towards the centre of the circle. The string pulls the body perpendicular to its motion. This pulling force continuously changes the direction of motion and remains towards the centre of the circle. This centre seeking force is called the CENTRIPETAL force. It keeps the body to move in a circle. Centripetal force always acts perpendicular to the motion of the body. Hence,
    “Centripetal force is a force that keeps the body to move in a circle.”
    I think that this example help the students to understand it properly!

  20. The notion that centrifugal force pushed the heavier elements away from the sun causing the planets to form is the biggest line of bullshit I ever read.

    The sun has the same composition as the intersteller medium from which it was born. Why the planets don’t match the intersteller medium is the sun turned on and boiled the lighter elements off.

  21. The ball strong example is incomplete to describe a planet around a star, as a planet will have some rotation on its axis, save tidally locked that is.

    Standing on this planet, we are in a centrifuge, in a centrifuge, in a centrifuge. Planetary rotation, rotation around the sun, rotation around the galaxy.

    Gravity is just a descriptor for the centrifugal force created by the spinning of the planetary body as it revolves around the star.

    The mass of the object in motion also creates an opposing force to what is holding it in place.

    Perceptual mind games to try and seem more intelligent don’t change all the forces at play.

    Well written article, I wish more people pointed out the inaccuracies in science “facts”.

  22. “Why the planets don’t match the intersteller medium is the sun turned on and boiled the lighter elements off.”

    That only explains the planets closer in than Jupiter: photon pressure and temperatures aren’t enough to do that to things further out than about the asteroid belt.

    I think maybe you need to dial back the ” the biggest line of bullshit I ever read” hyperbole until you’ve checked your own “reasoning”.

  23. “That’s just the Earth’s gravity not providing enough centripetal force to stop the fast moving surface travelling off in to space.”

    Yes, Chris, apart from it should be “gravitational force”.

    The question you quoted was “did you know?” and you failed to answer it, but instead rephrased it.

    Care to answer the question?

  24. “No; it was centrifugal force pushing the heavier elements (like carbon, oxygen, nitrogen, iron, phosphorus, silicon, etc.) away from the center relative to the light ones!” This is not true. The heavier elements would be thrown outward tangentially due to their momentum. They would not be thrown outwards radially due to a centrifugal force. A rotating mass “Exerts” a centrifugal force, it is not subject to such a force.

  25. Question: if the effect of a centrifuge pushes denser material away from the axis of rotation why is the densest part of the earth nearest its axis?

  26. Terri Philips
    I always say when you are going to point a finger at someone, look at the ones pointing back at you first. You began your post by calling this article bad science but in your comment you made mistakes like saying the earth and moon will collide one day. Nope, they are moving apart at a rate of a few cm per year, and guess what? It’s happening to the earth and sun too, we are very slowly moving away from the sun. It’s because of tidal interactions. Look it up, no kidding! lol

  27. Okay, take parachute man and swing him around by a string attached to the feet. Give him a parachute of greater volume and spin him again. Repeat until the string ceases to get taunt and starts to slacken again.

    The solar system is still hot and the CNO cycle just began. All that material is spinning and gravity as yet to win the day. Imagine its is the volume itself that allows the larger element to travel outward.

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