Centripetal Force - same thing as gravitational force?

[Unteroffizier]

First off, I'd like to note that I am by no means a physics expert. I am merely a high school student and a physics/maths enthusiast, nothing more, so if my thoughts are completely dysfunctional and downright incorrect, which is more than a distinct possibility, please tell me.

I recently took a class on centripetal force. It was a difficult class for me, as I missed a key lesson, but a few days back I had a thought.

The professor had taught us something about inertia and how objects continue in their path until they are acted upon by another force, one such force (perhaps the most significant in classical mechanics) being gravitational force. He told us that without centripetal force, all objects in all gravitational orbits would (after the information of this change reached them, of course) stray from their paths and continue along a straight line with the velocity they possessed in orbit.

This did initially strike me as odd. Does this not imply that gravitational force relies directly on centripetal force, or the other way around? This is where I could be fundamentally wrong, and as an aspiring scientist (despite my utter stupidity), I have no choice but to accept that reality.

I searched through a few books, had a quick look on the Internet, and realized that in general relativity, gravitational fields around massive objects are represented as this odd well-shaped... Well, for the lack of a better word. Does this not mean that objects in a gravitational field are actually moving along a slope? Objects moving along a (curved, may I add) slope certainly do experience centripetal force, from my understanding, and so could one say that objects in a gravitational field are actually only moving along a very large slope of deformed space (I do not possesses the mathematical skills to understand Gen.R., but I have seen the "deformed space" representation a lot)?

I promise to do the maths later on. I know it only involves mostly some trig and linear equations, more or less, so I will attempt to prove this very unlikely thought whenever I can.

I am so very sorry if you cringe at this whole thing. I want to enjoy doing physics, and that is hard to do this early on with little knowledge in mathematics. I despise pseudoscience, and would hate to render my thoughts exactly that. Please correct every wrong assumption I make.

Edit: Looking at it now, I fail to see how exactly I would calculate an object's orbit. I thought about using circular motion (what we call it in my country), but that fails to take into account the force of gravity. Looking at it now, it seems to me that it could be solved using centripetal force equations.

I'm doing the maths, I'm very tired, I can't get myself to think clearly. Still, if this is true, it only reinforces my belief that gravity may indeed be the same as centripetal force.

Nevermind. It seems that proving this idea would require some thorough knowledge of topology. I do not know how to calculate the slope of curved space, so I suppose my efforts will only be wasted.

 

[jbriggs444]

This did initially strike me as odd. Does this not imply that gravitational force relies directly on centripetal force, or the other way around?

Centripetal force is not a special type of force. It is a direction of force. Literally, it means the force on an object toward the center about which it is revolving.

It's not that gravity depends on centripetal force. Gravity is an example of a centripetal force.

 

[Unteroffizier]

I see... Well, that was slightly disappointing. No need to do any mathematics now. Suppose I'll have to place my efforts elsewhere.

Nonetheless, I thank you for clearing this up. I suppose this means that centrifugal force is actually nothing more than inertia at its core, or that inertia is an example of a centrifugal force. Actually, now that I think about it, inertia is the only centrifugal force out there, isn't it?

Thanks again!

 

[jbriggs444]

I suppose this means that centrifugal force is actually nothing more than inertia at its core, or that inertia is an example of a centrifugal force. Actually, now that I think about it, inertia is the only centrifugal force out there, isn't it?

The correct term is not "inertia". Inertia is not a force. A better term is "inertial force" or "fictitious force".

Centrifugal literally means "center fleeing". Some people (myself included) will sometimes use the term "centrifugal" in this literal manner to refer to any force that is away from a center. For instance, one might use the term to refer to the pressure of the air inside a balloon on its rubber skin. Using the word this way is not usually a good move. People are apt to misunderstand.

Or one might use "centrifugal" to refer to the third law reaction force that goes with the centripetal force that holds an object in its circular path. Since the centripetal force is toward the center, it's third law partner will be away from the center. There is a term coined specifically to refer to such forces: "reactive centrifugal force". If you find yourself needing to refer to a centrifugal force of this sort [see how I just used "centrifugal" in the literal sense above], you should call it a "reactive centrifugal force" to avoid confusion.

Almost always, when someone speaks of "centrifugal force", they are speaking specifically of the apparent force that arises when you pretend that a rotating system is at rest and try to explain the outward acceleration of objects that are at rest in the rotating frame of reference. Centrifugal force in this sense of the word is a fictitious force.

An inertial force is a force that is proportional to an objects mass. All fictitious forces are inertial. So centrifugal force (in the usual sense of the word) is always an inertial force. Which may be what you were trying to say above.

Although all fictitious force are inertial, not all inertial forces are fictitious. Gravity is the exception. It is an inertial force that is also a real force...

...at least until you get to the point of learning about general relativity.

 

[Unteroffizier]

I see! So gravity is both a centripetal force and a form of inertial force (though not fictitious)? Quite interesting, yet difficult to imagine. I suppose it is in general relativity that the gravitational force becomes a centripetal force and ceases to be inertial (as you stated). So in classical mechanics, it is inertial, and in GR centripetal? Or is it centripetal in both cases, but not inertial in the latter?

I have learned something about reactive forces, since I'm doing mechanical engineering. Definitely crucial to state when a force is reactive. Has led to much confusion in the classroom when it wasn't clearly said.

This whole idea of fictitious forces is quite fascinating. Indeed, technically speaking, it seems that no force pushes you forward when the bus rapidly stops, and instead it is Newton's first law that affects the objects. The force remains the same as before (while the vehicle was in motion), yet the circumstances change, and a reactive force (drag, gravitational force, hitting your body against a seat, or another person) must be made to stop the object from moving forward forever.

I'd really like to know more about all of this. Could you recommend a good book on Newtonian physics, possibly some book on calculus? Saying that as someone who has never taken a calculus class before, and I also can't integrate.

 

[A.T.]

So gravity is both a centripetal force and a form of inertial force (though not fictitious)?

Centripetal is not a category of forces, just a direction. And inertial force is exactly the same as fictitious force. Whether gravity is one, depends on the model (Newton or General Relativity)

 

[Nidum]

Go back several steps .

Consider a spacecraft which has been moving in a straight line at constant speed in a region remote from any other bodies .

If now the spacecraft enters a region where there is another body such as a planet the gravitational pull of the planet will bend the motion path of the spacecraft into a curve .

Depending on the strength of the gravitational pull one of four things can happen :

The spacecraft travels past the planet and eventually reverts to moving in a straight line but on a different heading to originally .

The spacecraft gets captured and goes into stable orbit around the planet .

The spacecraft gets captured , goes into decaying orbit and ultimately crashes into the planet .

The spacecraft crashes into the planet directly .

Try drawing a set of diagrams showing the forces acting on the spacecraft for each situation .

 

[Unteroffizier]

Precisely. It seems to me, however, that when thinking about gravity as curved space, it makes all the more sense. It helps me visualize gravitational force extremely easily. A marble in the sink, when launched with sufficient strength, will have a curved path but will escape the sink. Or, of course, as you said, it can enter an orbit, or crash directly into the sinkhole. While a marble will always be in a decaying orbit in the sink, it still offers a great representation, in my opinion.

So if I calculated orbits by simply creating a curve (its angle proportional to the strength of the gravitational field) around massive objects, would that yield accurate results?

 

[A.T.]

Precisely. It seems to me, however, that when thinking about gravity as curved space, it makes all the more sense. It helps me visualize gravitational force extremely easily. A marble in the sink, when launched with sufficient strength, will have a curved path but will escape the sink. Or, of course, as you said, it can enter an orbit, or crash directly into the sinkhole. While a marble will always be in a decaying orbit in the sink, it still offers a great representation, in my opinion

No, it doesn't represent the GR mechanism of gravity at all. We discussed here many times why. Use the search function.

 

[Unteroffizier]

I am not much of an active member on the site, to be honest. I just come on to ask a question occasionally, get involved with the STEM community, so I would not know what generally goes on. Forgive me.

Very well, I shall read more on the topic and hopefully understand better.

 

[CWatters]

Velocity has components speed and direction. So if an object moves in a curved path it's direction is changing and that's an acceleration. If an object is accelerating there must be a net force acting on it due to Newton's law. The force required to make an object follow a curved path is called the centripetal force.

Depending on the situation gravity can provide exactly the required centripetal force to make the object move in a circle (mv²/r), or it can provide too much or too little. Typically gravity and some other force combine to provide the required centripetal force to move in a circle. A man standing on the surface of the Earth experiences too much gravity to provide the required centripetal force. If the Earth wasn't solid the radius of his "orbit" would reduce. You can prove this by trying to walk on water. On land gravity and the normal force from the ground provides exactly the required centripetal force so you move in a circle and don't "fall in" or "float off" into space.