Centrifugal force and Newton 3rd law

[asi123]

Ok, I have a general question about centrifugal force.

Lets say I have an object who moves in a circular path, we know the object is accelerating because the velocity is constantly changing direction, the acceleration is towards the center.

Now, where does the centrifugal force comes to play?
Is it equal to f = m*w^2*R = m*v^2/r ?
Does it comes from Newton 3rd low to the centripetal force?

10x in advance.

 

[cabraham]

There is no such thing as centrifugal force. My university physics professor taught me that in the 1970's. The force equations you quoted are for centripetal force, which are correct. BR.

Claude

 

[GTrax]

I was taught that the term centrifugal force was the reaction to a centripetal force encountered in applying it.

For example, your moving mass was forced to take a circular path because of a constant centripetal force directed toward the circle centre. Now if this force was delivered via a string by which it was tethered to a central point, the anchor then experiences a force apparently directed outward away from the centre. ie. exactly equal and opposite to the centripetal, it being the reaction.

Centripetal is the true mathematical abstract force concept. It is the force that did the work to effect the acceleration (in this case as a constant changing of direction), and has to be directed inwards. Centrifugal refers to what is experienced in getting that force applied - a consequence.

This whole thing gets close to what we mean by "force". You know what it is when you feel it, but darn that it can only be conceived and defined in terms of its effects. It is "that which" can do work, "that which" causes acceleration to a mass, "that which" drags you to the ground. Its always "that which". The math definition is very fine, but I accept that the pulls and tugs on us can cloud how many names we need for it.

 

[rcgldr]

Using the "classic" definition, centrifugal force, is the inertial reaction force to the centripetal force that is accelerating an object inwards.

Some time ago, physicists decided to change the meaning of "centrifugal" to mean an apparent force when observered from the rotating objects frame of reference. So the old one got a prefix, "reacitve centrifugal force", and "centrifugal force" was changed to the "modern" version.

"Classic" - http://en.wikipedia.org/wiki/Reactive_centrifugal_force

"Modern" - http://en.wikipedia.org/wiki/Centrifugal_force

 

[jostpuur]

Ok, I have a general question about centrifugal force.

Lets say I have an object who moves in a circular path, we know the object is accelerating because the velocity is constantly changing direction, the acceleration is towards the center.

Now, where does the centrifugal force comes to play?

If you are not using rotating frame of reference, then there will not be any centrifugal force. That means, if your coordinate set is stationary, and the object moves in a circle in this frame, there is no centrifugal force.

If you choose to use a rotating coordinate set, so that the object is stationary in the coordinate set, and the coordinate set itself is rotating, then there will be a centrifugal force, which points outwards from the center. In this case the formula

Is it equal to f = m*w^2*R = m*v^2/r ?

gives the magnitude of the centrifugal force correctly.

Does it comes from Newton 3rd low to the centripetal force?

It could be your are on right track, although I cannot be fully sure what you are meaning. If we assume that the Newton's laws to hold without pseudo forces in inertial frames, and then demand that Newton's laws must hold somehow also in non-inertial frames, we can have the demand satisfied by solving what kind of pseudo forces we must add there so that the F=ma would be satisfied. In this case the centrifugal force is put into cancel the centripetal force.

 

[GTrax]

I guess we all could have visited the Wiki first, but my thanks Jeff R. for the links. I never knew there was a deliberate effort to resolve the names.

Some time ago, physicists decided to change the meaning of "centrifugal" to mean an apparent force when observered from the rotating objects frame of reference. So the old one got a prefix, "reacitve centrifugal force", and "centrifugal force" was changed to the "modern" version.

I think one cannot hold that the concept, complete with origin name was simply a fiction! The name, with its Latin origin, is historically quite old. Along with pilots, and drivers and trapeze artists, we can all appreciate how such force was experienced, described, and named. Understanding what it is, we should not be zealots about banishing it from out vocabulary - even if Mr. Newton et al were referring to its effect on moving masses one stage removed from the physical reality of applying it!

 

[cmos]

I'm not sure if I like the "reactive" article completely. First let me clarify something for the OP:

If you have a particle moving in uniform circular motion, then there is a centripetal force which is that equation you have listed. By Newton's second law, this is the only force acting on the particle; there is no centrifugal force.

The definition of the centrifugal force as an apparent force that tends to throw one outward while in a rotating frame of reference. This is why it is sometimes called a fictious force - because it appears only to the observer in the non-inertial frame (i.e. the rotating frame of reference).

The best example is you in a car that is moving at constant tangential velocity in a circle. From your frame of reference, there must be something that pushes you against the side of your car - you call this the centrifugal force. But how about myself, who is miraculously floating overhead and stationary?

From my frame of reference, at a single instant, you are moving in a straight line in the direction of the tangential velocity while the car is moving in a curved path. An instant latter, the side of the car comes crashing into you causing you to change your path. So from my frame of reference, no force whatsoever pushed you into the side of your car - you and your car just so happened to have colliding paths.

Regarding the "reactive" centrifugal force:
This will be manifested as a consequence of Newton's third law in reference to you and the side of your car coinciding. I must say though, I've never heard this term before and don't necessarily know if I like it yet...

 

[tiny-tim]

non-inertial observer

Hi asi123!

On an object moving in a circular path, there is no centrifugal force as viewed by an inertial observer.

Centrifugal force on such an object only exists for non-inertial observers.

The Principle of Equivalence (the basis of Einstein's General Theory of Relativity) says that anyone can be a valid observer, but that the equations of motion may have to be adjusted to introduce imaginary (non-physical) forces.

In particular, a non-inertial observer may invent imaginary forces so that Newton's first law is true.

For example, a rotating observer invents an imaginary centrifugal force to explain why objects appear to move round him.

 

[rcgldr]

On an object moving in a circular path, there is no centrifugal force as viewed by an inertial observer.

What if the inertial observer is a person holding a string while twirling an object around? I'm sure that person is going to feel the outwards tension force that is the result of the equal and opposite reactive centrifugal force of the object. The object "feels" the centripetal force from the string causing it to accelerate inwards. The string "feels" the reactive centrifugal force from the object at one end, and the centripetal force from the inertial observer at the other end, and experiences these opposing forces as tension.

 

[tiny-tim]

The object "feels" the centripetal force from the string causing it to accelerate inwards. The string "feels" the reactive centrifugal force from the object at one end, and the centripetal force from the inertial observer at the other end, and experiences these opposing forces as tension.

Hi Jeff!

Yes, that's why I emphasised "on an object moving in a circular path".

An inertial observer recognises no centrifugal force on the object, but usually does recognise a centrifugal force from the object, on whatever is keeping it in the circle.

 

[swraman]

A centrifugal force does not exist. The reason people think it does is because, say you are in a car that is turning right. You get pushed outward. They think this means that there is a force pushing you outward.

That is completely wrong, it is actually the opposite that is true. A force is pulling you inwards. Think of a car accelerating in a straight line. You get pushed back in your seat; does this mean that there is a force pushing you backwards? Of course not, it is just the force of the car pushing you forwards (or to the center during a turn) and your bodies resistance to the change in motion.

 

[cmos]

A centrifugal force does not exist. The reason people think it does is because, say you are in a car that is turning right. You get pushed outward. They think this means that there is a force pushing you outward.

That is completely wrong, it is actually the opposite that is true. A force is pulling you inwards. Think of a car accelerating in a straight line. You get pushed back in your seat; does this mean that there is a force pushing you backwards? Of course not, it is just the force of the car pushing you forwards (or to the center during a turn) and your bodies resistance to the change in motion.

Your post sounds overly forceful (no pun intended) and more or less repeats several of the posts above. With that said, I would like to somewhat disagree with you.

The centrifugal force is usual called a fictious/inertial/psudo/quasi force. The reason is simply because it is not an actual force in the Newtonian/formal sense. So really, it does exist, just remember to add fictious/inertial/psudo/quasi/etc before the word force.

Regarding the accelerating car in a straight line, you being "pushed back" is just another example of a fictious force. Saying these effects do not occur can get you into some serious trouble. Not accounting for the centrifugal force can cause an intercontinental ballistic missile to hit your ally rather than your enemy.

 

[Doc Al]

A centrifugal force does not exist.

Realize that two different meanings of "centrifugal force" are being discussed in this thread.

• Using the "old-fashioned" meaning where centrifugal force refers to the 3rd-law pair ("reaction") of the centripetal force, then centrifugal force is quite "real" (it has an agent).

• Using the "modern" meaning of centrifugal force as a psuedoforce, then centrifugal force only exists as an artifact of viewing things in a non-inertial frame. It's not a "real" force in that it has no agent.

As tiny-tim points out, the two "centrifugal forces" act on different bodies. Most standard physics textbooks use the "modern" definition.

 

[swraman]

Realize that two different meanings of "centrifugal force" are being discussed in this thread.

• Using the "old-fashioned" meaning where centrifugal force refers to the 3rd-law pair ("reaction") of the centripetal force, then centrifugal force is quite "real" (it has an agent).

• Using the "modern" meaning of centrifugal force as a psuedoforce, then centrifugal force only exists as an artifact of viewing things in a non-inertial frame. It's not a "real" force in that it has no agent.

As tiny-tim points out, the two "centrifugal forces" act on different bodies. Most standard physics textbooks use the "modern" definition.

guess I was never taught the old fashioned method. :(

 

[rcgldr]

A centrifugal force does not exist. The reason people think it does is because, say you are in a car that is turning right. You get pushed outward. They think this means that there is a force pushing you outward.

What you feel is getting "pushed" inwards, doesn't matter if it's in a turn or linear acceleration. However, if there's someone sliding into you from the "inside" part of the seat, the "centrifugal force" from that person sliding into you is going to "feel" real.

If an ice-skater were to spin around while holding weights, the skater could "feel" the centrifugal force. The force is only "ficticious" in that it doesn't result in acceleration of an object, but is the reaction force to acceleration.

 

[GTrax]

If an ice-skater were to spin around while holding weights, the skater could "feel" the centrifugal force. The force is only "ficticious" in that it doesn't result in acceleration of an object, but is the reaction force to acceleration.

This is a better example! The only force constraining the skater's weights to move circular is applied to the weights by the skater's arms. Its the centripetal, and is the only force required to explain the weights motion.

The reaction force is felt, as if the weights were being tugged outward. The human experience of forces is so conditioned that there is intuitive surprise in many that when the mass is released, the trajectory is a tangent!

There is nothing wrong in language and culture about inventing an expression for this. Its not required for the calculation of the motion, but is necessary and relevant to express the experience of this reaction, whether it be "sliding across a seat" or "skaters spinning". To thump the tub as in "this force does not exist" is maybe to misunderstand its concept and purpose in language.

 

[pmb_phy]

There is no such thing as centrifugal force. My university physics professor taught me that in the 1970's. The force equations you quoted are for centripetal force, which are correct. BR.

Claude

That is incorrect. Something like that exists as soon as you define it. What your professor was referring to was the notion that the centrifugal force is what is known as an inertial force. Such forces can be transformed away be moving to an inertial frame of referene.

Pete

 

[tiny-tim]

feeling the centrifugal force

Our perceptions are designed to work in an inertial (non-rotating) frame.

In a non-inertial frame, we therefore perceive things which are not really there.

However, we really do perceive them!

In that sense, although we see hear or feel things which are not there, we genuinely see hear or feel them.

An observer holding onto a string which is whirling him in a circle feels a force along his arm toward the centre of the circle.

However, he is "programmed" to work in an inertial frame.

And he knows that he is not moving toward the centre.

So he also feels a force in the opposite direction, balancing the force along his arm.

In that sense, he genuinely feels a centrifugal force.

 

[cabraham]

That is incorrect. Something like that exists as soon as you define it. What your professor was referring to was the notion that the centrifugal force is what is known as an inertial force. Such forces can be transformed away be moving to an inertial frame of referene.

Pete

Well Pete, no offense, but you weren't in the class room with me that day (or were you?), so how do you know what my professor was referring to? The science community for as long as I can remember has been consistent with my professor.

I fully understand what you and others are referring to with the concept of "inertial force". The "forces" I'm referring to are those acting on a body in circular motion. My mechanical engineering dynamics profs, civil engr statics profs, and physics profs insisted that we draw free body diagrams detailing each and every force acting on the body in question. In these free body diagrams, "centrifugal force" does not show up anywhere. The velocity of the object is tangential, and the acceleration is centripetal, or inward. There is no outward force/acceleration, aka "centrifugal". If the object's linear speed is increasing as well, then another component of acceleration exists in the tangential direction.

I understand what others have state about "inertial force". If I twirl an onject attached to a rope, I feel an outward force on my hand from the rope. That is merely tension. If I pull on a rope attached to an object, the object accelerates in the direction of my force. But I "feel" a "force" in the opposite direction due to tension. Call this "inertial" or whatever, but I do not accelerate in the direction of said force. Likewise with centrifugal "force". I feel it in the rope, but it does not accelerate me.

The free body diagrams never include centrifugal force. If F=ma holds, then centrifugal would result in acceleration outward. It doesn't.

I stand by what I wrote initially. As far as "something like that exists as soon as you define it" goes, I am at a loss. Does the mere fact that I define something, give it actual existence? I think that is quite a stretch. Peace and best regards.

Claude

 

[cmos]

The free body diagrams never include centrifugal force. If F=ma holds, then centrifugal would result in acceleration outward. It doesn't.

This is only true for the inertial observer. Consider, as I have used above, the example of a passenger (the non-inertial observer) in a car in uniform circular motion. To highlight the argument, let the car have no windows so the passanger is closed off from the rest of the world.

In the case of the inertial observer,
\Sigma F=-\frac{mv^2}{r}
where the negative sign indicates acceleration towards the origin (uniform circular motion).

However, the non-inertial observer, where his only reference frame is the car, will say that
\Sigma F=0.
The reasoning here is that the centrifugal force is balanced by the normal force of the car pushing back into the passenger. So from the reference frame of the passenger, the free-body diagram will include the centrifugal force.

This is precisely how one may simulate gravity on a spaceship...

 

[tiny-tim]

gravitational vs centrifugal

As far as "something like that exists as soon as you define it" goes, I am at a loss. Does the mere fact that I define something, give it actual existence?

Hi Claude!

But what about gravitational force?

Haven't we defined that into existence?

"Space tells matter how to move" … a stone accelerates toward the ground because it follow a geodesic in space-time.

But we invent the fiction of a gravitational force.

When a motorcyclist goes in a circle, there is an angle that he leans at so as not to roll over sideways.

Using the motorcyclist's own coordinates, two "fictitious" forces are defined: gravitational and centrifugal.

That angle is determined by equating the torques of those two fictitious forces!

So why should we regard the centrifugal force as any less existent than the gravitational force?

 

[jostpuur]

cabraham, your posts seem to be attempts to cause confusion. Do you understand what I wrote in the post #5, and tiny-tim in the post #8. Those are the standard explanations on the idea behind pseudo forces, as explained by the university level books of mechanics. If you are disagreeing with those posts, then you are disagreeing with the mainstream view. However, it doesn't look like you are disagreeing with them. It looks like you are not reading these posts and are merely assuming that people in this thread are doing silly mistakes that they are not doing in reality.

 

[cmos]

But what about gravitational force?

tiny-tim, I hate to being to get off topic, but I disagree with how you present your argument. The gravitational force is by all means a real force, given (or rather approximated) by Newton's law of gravitation, definitely experienced by both the inertial and non-inertial observers. The centrifugal force on the other hand is not a "real" force as it is experienced only by the non-inertial observer.

Whether we want to view gravity as a fundamental interaction (i.e. a force) or as a curvature of 4-dimensional spacetime is simply a matter of taste (or rather a matter of which model is more convenient for your specific problem). Similarly to how it is more convenient at times to use a wave approach as opposed to a matrix approach...

 

[tiny-tim]

… it's all relative …

The gravitational force is by all means a real force, given (or rather approximated) by Newton's law of gravitation, definitely experienced by both the inertial and non-inertial observers. The centrifugal force on the other hand is not a "real" force as it is experienced only by the non-inertial observer.

Hi cmos!

But gravitational force is not experienced by inertial observers … an observer in a lift which is freely falling will find no gravitational force.

We often choose to call a stationary-on-the-Earth's-surface observer inertial … but he isn't.

He's only "stationary" because of the reaction from the Earth.

But we define him as inertial 'cos it's convenient , and then we have to define a gravitational force to fit the inertial laws of motion into a non-inertial frame!

 

[cabraham]

Hi asi123!

On an object moving in a circular path, there is no centrifugal force as viewed by an inertial observer.

Centrifugal force on such an object only exists for non-inertial observers.

The Principle of Equivalence (the basis of Einstein's General Theory of Relativity) says that anyone can be a valid observer, but that the equations of motion may have to be adjusted to introduce imaginary (non-physical) forces.

In particular, a non-inertial observer may invent imaginary forces so that Newton's first law is true.

For example, a rotating observer invents an imaginary centrifugal force to explain why objects appear to move round him.

cabraham, your posts seem to be attempts to cause confusion. Do you understand what I wrote in the post #5, and tiny-tim in the post #8. Those are the standard explanations on the idea behind pseudo forces, as explained by the university level books of mechanics. If you are disagreeing with those posts, then you are disagreeing with the mainstream view. However, it doesn't look like you are disagreeing with them. It looks like you are not reading these posts and are merely assuming that people in this thread are doing silly mistakes that they are not doing in reality.

My posts do not attempt confusion or anything. Science, especially centrifugal force, or "cf" herein, is already confusing. I have indeed read the other posts. The ones you site use "pseudo" and "fictitious" to describe cf. That is all I'm getting at. We "feel" cf when we are the subject in a rotating reference frame. It doesn't act on us in an F=ma manner is what I was pointing out.

I'm familiar with Einstein's equivalence principle. Regarding the car with no windows moving in uniform circular motion, some choose to look at it your way. That is, the car interior side panel exerts a centripetal force on me, and I exert a centrifugal force on it in return. The 2 forces balance and no acceleration is incurred. Thus cf is considered as an actual entity to some. I agree with the above about an observer inventing imaginary forces, cf being one of them. If that is what is the mainstream view, I have no problem with it. I agree fully that cf is an imaginary entity. So it looks like there is nothing to argue about!

But, I feel that looking beyond the car and passenger is more enlightening. A car in ucm (uniform circular motion) requires force to maintain said motion, ie friction. Such force acts towards the center, ie centripetal. Likewise the acceleration is centripetal, not centrifugal. The free body diagrams is how I was programmed to think, and I'm not aware of free body diagrams no longer being "mainstream". Have free body diagrams been abandoned, or deemed less important since the 1970's when I was an EE undergrad? I'm just wondering. Anyway, the "force" acting in the rotaing frame, ie a passenger feeling cf, is actually the reaction to friction. The car's wheels need friction to maintain ucm. If a car in ucm all of a sudden ran into wet ice, it would cease ucm, and move tangentially to the original circle. Thus, the imaginary "cf" felt by me pressing against the interior side panel is a reaction to friction. If you prefer the cf concept, then call it cf.

CF is treated as an actual entity to an observer in the rotating frame of reference. I don't have problems with that at all. This is analogous to holes and electrons in semiconductor physics. We define holes as having charge, mass, and mobility, as well as velocity. But does a hole actually exist? Is it a real entity? Lately the view is that holes are an actual entity, but for many years they were not considered as such.

All I meant originally is that cf is not a true entity in the fullest sense. Centripetal force OTOH is an actual entity. If "centrifugal force" implies "reactionary force to friction", then so be it. BR.

Claude

 

[cmos]

But gravitational force is not experienced by inertial observers … an observer in a lift which is freely falling will find no gravitational force.

tiny-tim,

The example of the enclosed lift in free-fall is the textbook example of the best inertial frame we have on Earth. But this is because the enclosed observer will be able to conduct experiments free of the effect of the Earth's gravitational field. Now suppose that the experiment the observer is performing is on a peanut, also enclosed with him in the lift. Does the peanut not exert a gravitational force on the observer and vice-versa? This force may be very small, but it is still there.

Even without the peanut, the isolated observer will still create his own gravitational field by the mere fact that he is there. Gravity is one of the fundamental forces; it is by no means "fictious" in respect to that of the fictious centrifugal force.

EDIT: Just to add a quick note: The enclosed observer is still subject to the effects of the Earth's gravity. It is just that he does not realize it since he is closed off from the world - i.e. he does not realize that he is falling.

 

[D H]

Gravity is one of the fundamental forces; it is by no means "fictious" in respect to that of the fictious centrifugal force.

In General Relativity, the gravitational force is an inertial force, (or pseudo force, or fictitious force; they're synonyms). All inertial forces have one thing in common: They are proportional to the mass on which the force is acting. That gravitation is proportional to mass led Einstein to question whether gravitation is a real force, and that in turn led to the development of General Relativity.

 

[tiny-tim]

reactions … two's company … three's a crowd!

Hi Claude!

CF is treated as an actual entity to an observer in the rotating frame of reference. I don't have problems with that at all. This is analogous to holes and electrons in semiconductor physics. We define holes as having charge, mass, and mobility, as well as velocity. But does a hole actually exist? Is it a real entity? Lately the view is that holes are an actual entity, but for many years they were not considered as such.

All I meant originally is that cf is not a true entity in the fullest sense. Centripetal force OTOH is an actual entity. If "centrifugal force" implies "reactionary force to friction", then so be it. BR.

Yes, I like that analysis …

the only thing I would disagree with is:

Anyway, the "force" acting in the rotaing frame, ie a passenger feeling cf, is actually the reaction to friction.
The car's wheels need friction to maintain ucm. If a car in ucm all of a sudden ran into wet ice, it would cease ucm, and move tangentially to the original circle.
Thus, the imaginary "cf" felt by me pressing against the interior side panel is a reaction to friction. If you prefer the cf concept, then call it cf.

First, technically, the cf isn't a reaction: reactions come in pairs, and they act on different bodies.

The friction you refer to, and the cf, both act on the same body (the car).

And the reaction to the friction force from the road on the car is the friction force on the road from the car.

Where reaction is concerned, two's company, and three's a crowd! ​

Second, you are only looking at a rotating observer observing objects rotating with him.

For those, the centrifugal force is indeed always equal and opposite to a centripetal force (from good ol' Newton's first law ).

But in the general case, a rotating observer regards a centrifugal force as acting on any object.

To take your example: if a car in ucm all of a sudden ran into wet ice, it would indeed cease ucm, but the driver would then have a choice of frames.

If the driver insists on the car itself "being" his frame, then his frame becomes inertial, and the cf disappears because the frame is inertial.

But if the driver insists on keeping the same uniformly rotating frame as before (perhaps the car is in two halves, and only one half is on the ice, and "separates"), then he regards the car as drifting away from the centre of the turn, which he ascribes to the presence of a centrifugal force and the absence of a friction force.

So the cf is not a reaction to friction, or to any other centripetal force … it is an inertial force … as described by D H …

All inertial forces have one thing in common: They are proportional to the mass on which the force is acting.

… and it acts on all objects, whether under centripetal forces or not.

 

[per.sundqvist]

The force applies on you due to friction, if not you slipper away! The general case of fictious force is described in wikipedia here:http://en.wikipedia.org/wiki/Rotating_reference_frame"

 

[cabraham]

Hi Claude!


Yes, I like that analysis …

the only thing I would disagree with is:


First, technically, the cf isn't a reaction: reactions come in pairs, and they act on different bodies.

The friction you refer to, and the cf, both act on the same body (the car).

And the reaction to the friction force from the road on the car is the friction force on the road from the car.

Where reaction is concerned, two's company, and three's a crowd! ​

Second, you are only looking at a rotating observer observing objects rotating with him.

For those, the centrifugal force is indeed always equal and opposite to a centripetal force (from good ol' Newton's first law ).

But in the general case, a rotating observer regards a centrifugal force as acting on any object.

To take your example: if a car in ucm all of a sudden ran into wet ice, it would indeed cease ucm, but the driver would then have a choice of frames.

If the driver insists on the car itself "being" his frame, then his frame becomes inertial, and the cf disappears because the frame is inertial.

But if the driver insists on keeping the same uniformly rotating frame as before (perhaps the car is in two halves, and only one half is on the ice, and "separates"), then he regards the car as drifting away from the centre of the turn, which he ascribes to the presence of a centrifugal force and the absence of a friction force.

So the cf is not a reaction to friction, or to any other centripetal force … it is an inertial force … as described by D H …


… and it acts on all objects, whether under centripetal forces or not.

Hi Tiny Tom,

First I was chastized for viewing things only in an inertial reference frame. So I then viewed things in a rotating refreence frame, and now I'm guilty of only considering objects rotating with the frame. Whether I explain in inertial or rotating frames I'm excluding something!

Every attempt to counter my view results in contradictions among the people arguing with me. Then we go off on the tangent "is gravity force REAL?"!

Can we simplify to a two body system? The moon revolves around the earth. It has a velocity tangential to its path. I know already that orbits are slightly elliptic, but the eccentricity is generally less than 0.02 so that ucm is approx. valid. The moon's force/acceleration keeping it from departing its Earth orbit is purely *centripetal*. The moon also attracts the earth. The Earth encounters a force towards the moon and like its counterpart is due to gravity. Thus gravity accounts for the centripetal force/accel and the moon's velocity is always tangential to the path.

In the moon's ref frame, it feels a force of gravity towards the Earth and is there a counter force?

By the way, gravity is REAL. Some time ago, not far from my home, a despondent jilted lover took a leap from a local bridge. The personnel who had to tend to the situation and his survivors are quite convinced that the gravitational force and acceleration acting on him was indeed real. Peace.

 

[D H]

First I was chastized for viewing things only in an inertial reference frame. So I then viewed things in a rotating refreence frame, and now I'm guilty of only considering objects rotating with the frame. Whether I explain in inertial or rotating frames I'm excluding something!

In Newtonian mechanics, the acceleration of a fixed-mass object as viewed from the perspective an inertial reference is given by Newton's second law,
m\,\mathbf a = \mathbf{F}_{\text{ext}}
Things get just a bit hairier when things are viewed from the perspective of rotating, accelerating reference frame:
m\,\mathbf a = \mathbf{F}_{\text{ext}}<br /> \;-\; m\, \mathbf{\omega}\times(\mathbf{\omega} \times \mathbf{r})<br /> \;-\; 2 m\, \mathbf{\omega}\times \mathbf{v}<br /> \;-\; m\,\frac{d\mathbf{\omega}}{dt} \times \mathbf{r}<br />
In general, yech. Yet at times it does make more sense to use a rotating frame. We live on a rotating frame, for example. The circular restricted three body problem is also easier to solve in a rotating frame.

Every attempt to counter my view results in contradictions among the people arguing with me. Then we go off on the tangent "is gravity force REAL?"!

That was not a tangent. The gravitational force is no more "REAL" than is the centrifugal force.

By the way, gravity is REAL. Some time ago, not far from my home, a despondent jilted lover took a leap from a local bridge. The personnel who had to tend to the situation and his survivors are quite convinced that the gravitational force and acceleration acting on him was indeed real. Peace.

It was the normal force that kept the lover from sinking into the Earth at the end of the fall, not the gravitational force, that killed the despondent lover.

 

[cmos]

Every attempt to counter my view results in contradictions among the people arguing with me. Then we go off on the tangent "is gravity force REAL?"!

It would seem to me that tiny-tim, DH, and myself are more or less backing each other up with the slight deviation in our views on gravity. Perhaps I will think of this more and make a new post somewhere in the forum; my apologies for helping to start the tangent.

Can we simplify to a two body system? The moon revolves around the earth. It has a velocity tangential to its path. I know already that orbits are slightly elliptic, but the eccentricity is generally less than 0.02 so that ucm is approx. valid. The moon's force/acceleration keeping it from departing its Earth orbit is purely *centripetal*. The moon also attracts the earth. The Earth encounters a force towards the moon and like its counterpart is due to gravity. Thus gravity accounts for the centripetal force/accel and the moon's velocity is always tangential to the path.

In the moon's ref frame, it feels a force of gravity towards the Earth and is there a counter force?

Regarding the last sentence, the Newton's third law force pair is the gravitational attraction of the moon acting on the Earth and the gravitational attraction of the Earth acting on the moon. Is this what you are trying to get at?

Keeping with the two body system, let's simplify the problem to a geosynchronous satellite, i.e. a satellite that stays over the same piece of ground at all times (satellite's orbital period is equal to the Earth's rotational period).

If we analyze this system from an inertial reference frame, then yes, as you said, the centripetal acceleration will be equal to the gravitational field of the Earth. That is, the only force present is the gravitational force.

However, if we analyze this system from the non-inertial reference frame which we take to be on the satellite, what do we see? We see that the satellite does not move and we see that the Earth does not move. So from this frame of reference we see that the gravitational force due to the Earth is exactly balanced by the centrifugal force.

 

[cabraham]

It would seem to me that tiny-tim, DH, and myself are more or less backing each other up with the slight deviation in our views on gravity. Perhaps I will think of this more and make a new post somewhere in the forum; my apologies for helping to start the tangent.



Regarding the last sentence, the Newton's third law force pair is the gravitational attraction of the moon acting on the Earth and the gravitational attraction of the Earth acting on the moon. Is this what you are trying to get at?

Keeping with the two body system, let's simplify the problem to a geosynchronous satellite, i.e. a satellite that stays over the same piece of ground at all times (satellite's orbital period is equal to the Earth's rotational period).

If we analyze this system from an inertial reference frame, then yes, as you said, the centripetal acceleration will be equal to the gravitational field of the Earth. That is, the only force present is the gravitational force.

However, if we analyze this system from the non-inertial reference frame which we take to be on the satellite, what do we see? We see that the satellite does not move and we see that the Earth does not move. So from this frame of reference we see that the gravitational force due to the Earth is exactly balanced by the centrifugal force.

The centripetal force is that of gravity. But there is no source for centrifugal. Where does it come from? A free body diagram of the satellite includes only centripetal. In the inertial frame of the satellite there is an attractive force of gravity. There is no centrifugal. In the satellite ref frame, it is still and the Earth moves towards it due to gravity. In order to do so an attractive force is needed. This is the force due to gravity. No counter force is present. The action-reaction or force-pair at work here is not centripetal-centrifugal, but Earth attracts satellite and satellite attracts earth. But, you seem to indicate that because the satellite is attracted to Earth due to gravity, yet it does not accelerate to earth, that there must be an equal and opposite counter force. Using this logic, since the Earth does not accelerate towards the satellite, there must be a counter force directing the Earth away from said satellite. Where does this come from.

Many feel compelled to balance every force with a counter force. Hence centripetal must have its balancing counterpart in the form of centrifugal. But in classical mechanics, I was taught (were my profs mistaken or did I misinterpret them?) that when the forces summed on a body did not balance, then the "ma" vector closes the force polygon. For a satellite in space, the force is gravity directed inwards, or centripetally, and its own velocity tends to follow a tangent. The sum of these 2 tend to maintain ucm. No balancing force is present or needed. A rotating frame has Coriolis force cs. an inertial frame which doesn't. Those who insist on looking at the rotational reference frame viewpoint have ignored Coriolis. Projectiles fired on Earth ae influenced by Coriolis force. You can't treat a geosat (geosynchronous satellite) as an inertial frame. The geosat and the Earth attrct each other due to gravity, yet do not accelerate towards each other, so there MUST BE another force counterbalancing the centripetal. Oh well.

I'll re-examine the equivalence principle, but from memory I don't think a geosynchronous satellite's inertial frame of reference is equivalent to 2 stationary objects. If I'm wrong I'll accept correction, but rotating frames are not the same as translating frames.

As far as the despondent lovers leap is concerned "it wasn't gravity that killed him, it was normal force", my answer is "get real!"

 

[cmos]

cabraham,

You're on the right track; you have valid arguments but you are not following them all the way. As you stated (or rather Newton) F=ma. So for the geosync. satellite-Earth system, when viewed in an inertial reference frame,
F=ma=G\frac{Mm}{r^2} .
If it helps to visualize, think of this reference frame as a point hovering over the orbital plane of the two-body system.

But if you view the events from on the satellite (this being a non-inertial reference frame), then you see that you do not move and you see that the Earth does not move. Therefore the acceleration, thus net force, is equal to zero:
F=ma=0=G\frac{Mm}{r^2}-|F_{centrifugal}|
where the centrifugal force as equal in magnitude to the gravitational force.

I want to note that philosophers, prior to Newton, held the second view that the centrifugal force must balance the centripetal force to keep the planets in the heavens. Their view wasn't necessarily wrong, it just took the view of a non-inertial observer.

Newton's laws require an inertial system and by invoking that, we get the first view that there is no balancing of forces for the above system and that the net force does not equal zero.

In solving problems, it is sometimes convenient to resort to the "old view" and work the problem in a non-inertial frame. Being more enlightened than the old philosophers, we invoke the use of "fictious" forces realizing that they are only manifested because we are using a non-inertial frame.

 

[cmos]

A rotating frame has Coriolis force cs. an inertial frame which doesn't. Those who insist on looking at the rotational reference frame viewpoint have ignored Coriolis. Projectiles fired on Earth ae influenced by Coriolis force.

The Coriolis force requires that something be moving with respect to a rotating frame of reference. I have been careful in my examples to make sure that the Coriolis force can be neglected.

Excuses me if I may, but if you have no problem with invoking the Coriolis force, then why so much scrutiny to the centrifugal force? Both are fictious forces that are manifested in a rotating frame.

 

[D H]

The centripetal force is that of gravity.

A free-falling object is following a geodesic in space-time. You get a fictitious centripetal force when you use a non-inertial frame.

But there is no source for centrifugal. Where does it come from? A free body diagram of the satellite includes only centripetal. In the inertial frame of the satellite there is an attractive force of gravity.

You are using Newtonian mechanics and you are assuming that it is perfectly true. It is not. General relativity is a better (more accurate) model, and gravity is not a force in general relativity. It arises from the use of a non-inertial frame.

Look at it this way. Suppose you are designing a spacecraft or an airplane that uses accelerometers as a part of its inertial navigation system. The flight software will have to augment the accelerometer readings with estimates of the gravitational force to have any chance of making the propagated state reflect reality for the simple reason that accelerometers measures all real forces acting on a body except for gravity. This, of course is the Newtonian mechanics view of accelerometers. From a general relativistic viewpoint, the viewpoint is simple: Accelerometers measures all real forces acting on a body, period.

As far as the despondent lovers leap is concerned "it wasn't gravity that killed him, it was normal force", my answer is "get real!"

People jump out of planes on a regular basis. The free-fall period is, from what I have been told, very exhilarating. The act of free-fall itself doesn't kill. Hitting the ground sure does.

 

[cabraham]

A free-falling object is following a geodesic in space-time. You get a fictitious centripetal force when you use a non-inertial frame.

You are using Newtonian mechanics and you are assuming that it is perfectly true. It is not. General relativity is a better (more accurate) model, and gravity is not a force in general relativity. It arises from the use of a non-inertial frame.

Look at it this way. Suppose you are designing a spacecraft or an airplane that uses accelerometers as a part of its inertial navigation system. The flight software will have to augment the accelerometer readings with estimates of the gravitational force to have any chance of making the propagated state reflect reality for the simple reason that accelerometers measures all real forces acting on a body except for gravity. This, of course is the Newtonian mechanics view of accelerometers. From a general relativistic viewpoint, the viewpoint is simple: Accelerometers measures all real forces acting on a body, period.


People jump out of planes on a regular basis. The free-fall period is, from what I have been told, very exhilarating. The act of free-fall itself doesn't kill. Hitting the ground sure does.

I don't believe what I'm reading. I am an EE, not a pure physicist, and I make no claims as to being a physics expert. But, those who are debating me don't seem to be experts either. I can't believe what I'm reading. Now you are arguing that centripetal force is fictitious. Also presented is that Coriolis is fictitious. Previously it was stated that gravity is fictitious. My dear contrarian friends, is there any force in the universe that is "real", other than your cherished beloved centrifugal force. That's real, all others are fictitious.

"Free fall doesn't kill, hitting the ground does" is so ludicrous it doesn't deserve a response. But I'll give one. How hard you hit the ground depends on how long the "fictitious gravity force" was acting on you. You don't need an advanced physics degree to know that.

In an attempt to "prove" that cf is "real", my opponents have collectively reduced gravity, centripetal, and Coriolis forces to the status of "fictitious". Amazing!

Nothing personal, but now is the time to get on my horse and ride off into the sunset. Best wishes to all. ---sound of horse hoofs ----

Claude

 

[D H]

Nobody but you has said the centripetal force is an inertial force. So please stop with the straw man arguments.

If you are going to college, go ask a physics professor. If you're not going to school, you should have enough money as an EE to buy a book or two on general relativity aimed at the layman.

Regarding things the centrifugal force, the coriolis force, gravity, and other inertial forces: They result solely because of the reference frame of the observer. In the sense that a real force is what an accelerometer reads, none of these forces are real.

 

[tiny-tim]

real and fictitious centripetal force

Now you are arguing that centripetal force is fictitious.

A free-falling object is following a geodesic in space-time. You get a fictitious centripetal force when you use a non-inertial frame.

Hi cabraham!

No … D H was saying that this particular centripetal force … gravitation … is fictitious … because it is absent in genuine inertial coordinates.

Centripetal force due to friction, or to a string, or to reaction from a track, is undeniably real … it is present in any coordinate system.

 

[cmos]

I think DH and tiny-tim have said enough in response to cabraham. It just amazes me that you claim to be an engineer but still misinterpret what we are saying to the point that you start making up what we say. Are you even reading our responses thoroughly?

We have all taken the time to give very good examples, sometimes with the pertinent mathematics. Go back a read through our posts and then you may speak knowledgeably. Either that or realize that engineering technologist is not the same as an engineer...

 

[cabraham]

I think DH and tiny-tim have said enough in response to cabraham. It just amazes me that you claim to be an engineer but still misinterpret what we are saying to the point that you start making up what we say. Are you even reading our responses thoroughly?

We have all taken the time to give very good examples, sometimes with the pertinent mathematics. Go back a read through our posts and then you may speak knowledgeably. Either that or realize that engineering technologist is not the same as an engineer...

Engineering TECHNOLOGIST! Who are you? I'm a full EE and a Ph. D. candidate. What I posted was based on the teachings of Ph.D. physics professors while an undergrad studying **full EE**, NOT EET. What are you, just for the record? Where do you even get off talking in such an uppity manner? Are you a Ph.D. physicist? If not, then you are arguing with profs who are more qualified than you. What are your credentials? You think that I am a mere EET, but you don't state what you are "cmos". Please enlighten us.

 

[D H]

On the Coriolis effect: This is a very good example of how the name fictitious force is a bit misleading. The Coriolis effect is a real phenomenon. All one has to do is look at a hurricane or cyclone: Coriolis effect. So, how to explain this very real phenomenon?

Anyone who tries to do planetary atmospheric modeling from a general relativistic perspective is insane, or will go insane while trying to solve the problem. Atmospheric modeling assumes Newtonian mechanics, which means treating gravity is treated as a real force.

Another way to go insane is to model the Earth's atmosphere from the perspective of an inertial reference frame. No meteorologist or climatologist in their right mind would think of modeling a large rotating ball of gas that co-rotates with a large plastic object (the Earth) from the perspective of an inertial frame. It makes a whole lot more sense to model things from the perspective of an accelerating and rotating reference frame.
This means various pseudo forces will need to be modeled to make Newton's second law appear to apply. Since the Earth's rotation rate is nearly constant, these are pseudo forces are

• Earth acceleration due to other bodies in the solar system. The typical approach is to compute the difference between the gravitational acceleration at some point toward these other bodies and the gravitational acceleration of the Earth toward these other bodies. The difference between these accelerations are called third-body gravity effects. Third body effects are roughly proportional to the inverse of the cubes of the distances to the other bodies. These effects appear in the form of ocean and solid body tides.
• Centrifugal force. For objects located at some position \mathbf r with respect to the center of the Earth, the centrifugal force is \mathbf{\omega} \times (\mathbf r \times \mathbf{\omega}) (see post #31). This effect is typically combined with the gravitation acceleration caused by the Earth to form the acceleration due to gravity. Geodesists distinguish the terms gravitation and gravity to mean the acceleration that results from Newton's law of gravitation and the combined effects of Earth gravitation and centrifugal acceleration due to the Earth's rotation. Acceleration due to gravity is largest at the poles and smallest at the equator. The difference is small.
• Coriolis force. For objects moving with a velocity \mathbf v with respect to the rotating Earth, the Coriolis force is 2 \mathbf v \times \mathbf{\omega} (see post #31). The Coriolis effect in the atmosphere arises directly from the Coriolis force when the Earth's atmosphere is modeled from the perspective of an Earth-fixed frame.

Suppose instead you want to model the flight of a shell fired from a large gun. This can be done from the perspective of an inertial reference frame, and no Coriolis force is needed to model the flight of the shell. The Coriolis force only needs to be introduced if one wants to model the flight of the shell from the perspective of an observer fixed with respect to the Earth.

 

[D H]

I don't believe what I'm reading. I am an EE, not a pure physicist, and I make no claims as to being a physics expert. But, those who are debating me don't seem to be experts either. I can't believe what I'm reading.

Either that or realize that engineering technologist is not the same as an engineer...

Engineering TECHNOLOGIST! Who are you? I'm a full EE and a Ph. D. candidate.

You two need a time out. Stop the name calling right now.

FYI Cabraham, tiny tim is a PhD physics candidate. I am a physicist who has worked in the field of aerospace engineering for 30+ years.

 

[cabraham]

You two need a time out. Stop the name calling right now.

FYI Cabraham, tiny tim is a PhD physics candidate. I am a physicist who has worked in the field of aerospace engineering for 30+ years.

Tiny Tim isn't the one who called me a technologist, cmos was. I have not engaged in any name calling. I was the target of such and simply reacted. I have not, to this point downgraded anybody's knowledge, experience, or academic credentials. When mine were challenged, I gave my background, and only asked that the other party do the same. That is not name calling.

BTW, I worked in aerospace engr for a decade, then in commercial engr where I still practice, totalling 30 yrs. But my specialty is EE, not physics. Having 30 yrs. experience in EE and returning to grad school for PhD after 26 yrs since the MSEE program does not make me a physics expert. My position is based on PhD physics prof teachings, not my own opinions. Regarding physics, esp. modern (relativity, quantum mech) I only had one course at the undergrad level from the physics dept as a senior EE elective. We covered SR, QM, and kinetic theory of matter. Only one couse, so I do not claim to be an expert. If you'd rather that I not post in this forum, just say so.

 

[D H]

We are here to answer questions. Ask away!

The post by cmos was out-of-line. Then again, your post where you questioned our expertise was a bit inflamatory as well. Bottom line: ask away, keep it civil.

A couple web references on the Coriolis effect:

Wikipedia, http://en.wikipedia.org/wiki/Coriolis_effect.

"In physics, the Coriolis effect is an apparent deflection of moving objects when they are viewed from a rotating frame of reference. ... The Coriolis force is an example of a fictitious force (or pseudo force), because it does not appear when the motion is expressed in an inertial frame of reference, in which the motion of an object is explained by the real impressed forces, together with inertia."​

Wikipedia is not the most reliable of sources. The University of Illinois hosts the weather world 2010 project. From
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml" ,

"Coriolis Force
an artifact of the Earth's rotation
Once air has been set in motion by the pressure gradient force, it undergoes an apparent deflection from its path, as seen by an observer on the earth. This apparent deflection is called the "Coriolis force" and is a result of the Earth's rotation."​

 

[cmos]

I do sincerely apologize. My previous posts was meant to exemplify a fact: it is very infuriating to be publicly misrepresented; this being in reference to post #37. With the example made, I do again apologize. I think we can all agree that we should get back to the physics?

Is it possible we are dwelling down an argument of semantics? The term fictious force does not mean that the so-called force has no effect. It simply means that when viewed from an inertial frame, the force disappears. Only when viewed from a (specific) non-inertial frame does the force prevail. Hence we refer to it as a fictious or psudo-force.

I refer you to my post #34. In the non-inertial frame, the fictious centrifugal force prevails and balances the gravitational force. When viewed inertially, the centrifugal force disappears and all that remains is the gravitational force. Note that this is a classical argument, i.e. we consider the gravitational force as "real" since we do not want to bring Einstein into play (as noted by DH).

Similarly, in reference to DH's post #45, when viewed on Earth, the Coriolis force is a dominant mechanism in the dynamics of weather. In this case the Earth is a non-inertial frame. We may however take our view point from some point in space at which point we can consider our frame to be inertial and we will see no sign of the Coriolis force. Instead, this will be accounted for by our observations of the Earth's movement.

 

[D H]

Some levity

Looks like the time-out period worked. Thanks, guys.

Before we go back to physics, some levity thanks to http://xkcd.com" :

Edit:
Hey! What's the deal with [noparse][/noparse] tags? Why does the image link show up as a link rather than an image?

 

[cabraham]

I do sincerely apologize. My previous posts was meant to exemplify a fact: it is very infuriating to be publicly misrepresented; this being in reference to post #37. With the example made, I do again apologize. I think we can all agree that we should get back to the physics?

Is it possible we are dwelling down an argument of semantics? The term fictious force does not mean that the so-called force has no effect. It simply means that when viewed from an inertial frame, the force disappears. Only when viewed from a (specific) non-inertial frame does the force prevail. Hence we refer to it as a fictious or psudo-force.

I refer you to my post #34. In the non-inertial frame, the fictious centrifugal force prevails and balances the gravitational force. When viewed inertially, the centrifugal force disappears and all that remains is the gravitational force. Note that this is a classical argument, i.e. we consider the gravitational force as "real" since we do not want to bring Einstein into play (as noted by DH).

Similarly, in reference to DH's post #45, when viewed on Earth, the Coriolis force is a dominant mechanism in the dynamics of weather. In this case the Earth is a non-inertial frame. We may however take our view point from some point in space at which point we can consider our frame to be inertial and we will see no sign of the Coriolis force. Instead, this will be accounted for by our observations of the Earth's movement.

Apology accepted.

Regarding the moon orbiting earth, no one has even touched that one. Where, oh where, my learned friends, is centrifugal force? I'm from Missouri (figuratively) so you must show me. The centripetal is due to gravity. It is directed towards the center. From either the moon or Earth frame of ref, centripetal shows up in both free body diagrams. Where is centrifugal? Sorry to be so insistent, but please show me.

Regarding the geosat example, an observer stationary on the geosat sees the Earth and the geosat as two non-moving bodies. Since gravity tends to attract the 2 towards each other, there must be a counter force to neutralize said force, since the 2 don't attract. Such is labeled "centrifugal". But I don't think that you can draw such a conclusion. The centripetal is an artifact of gravity, a known phenoenon. Where does cf originate from? If the geosat and the Earth were both stationary, the gravity force is still there. But "cf" isn't. Where did it come from and where did it go.

If I'm on a geosat, looking towards the earth, and observe no relative motion between the 2, I would NOT conclude that the gravity is canceled by a counter force, preventing attraction, but rather that one body is orbiting the other. The geosat IS FALLING. Its inertia tends to carry it out in space along a tangent line to its orbit. It also "falls" towards earth. The reason that the geosat does not fall to the Earth is due to its own velocity, tangential to the orbit, accelerated towards the center of the orbit due to gravity. The centripetal/gravity is always there regardless of whether the geosat is still or orbiting the earth.

At best, I would regard cf as a "fictitious", "virtual", or "pseudo-" force. When examining forces and accelerations of bodies in ucm, centripetal is always there. Centrifugal is just a mental concept. It is not an active phenomena which exerts influence on bodies. It is like the "bubble" in a carpenter's level, akin to a "hole" in semiconductors. A void has no mass, velocity, energy, wavelength, etc. But we can treat such as a real entity. If we tilt the level downwards to the right, the bubble moves upward towards the left. Inside the fluid we can regard the bubble as an actual entity. Outside the tube, should it break and the fluid exit, the concept of bubble is not valid.

If cf is regarded as something perceived which can be regarded as an actual entity under specific conditions, then I don't think there is a problem accepting it as such. It does not however, enjoy the same status as gravity, centripetal, or Coriolis. Peace and best regards to all.

Claude

 

[George Jones]

I have taught first-year physics several times, and, each time I presented Newtonian gravity as a real force.

I have taught second and third-year mechanics (for physics majors) several times, and, each time I presented centrifugal force and Coriolos force as fictitious forces. When working through some problems it is convenient to think (fictiously?) of these forces as real, but when push come to shove, I would have to stick with the fictitious classification.

I have taught very introductory general relativity once (based on the book Exploring Black Holes by Taylor Wheeler), and I presented gravity as a fictitious force. (More on why later; on my out the door.)

In my experience at a number of universities, these choices are fairly standard in physics departments.

 

[D H]

cabraham: I am going to address the issues you raised in your post out of order. I want to deal with the Newtonian mechanics first.

At best, I would regard cf as a "fictitious", "virtual", or "pseudo-" force. ... It does not however, enjoy the same status as gravity, centripetal, or Coriolis.

The Coriolis force is no more real, and no more unreal, than is the centrifugal force. I supplied two references on the Coriolis effect. Read them, please. The Coriolis effect is a "fictitious force". Since you are going to school, you have access to a library. Look at any junior-level classical mechanics physics text. I have Classical Dynamics, J. Marion, 1970 right in front of me. Goldstein is another. Whichever book you look at, it will inevitably have a detailed treatment of motion in a noninertial reference frame. Here is what Marion says:

It is important to realize that the centrifugal and Coriolis forces are not "forces" in the usual sense of the word; they have been introduced in an artificial manner as a result of our arbitrary requirement that we be able to write an equation which resembles Newton's equation and which at the same time is valid in a noninertial reference frame.​

I think we are all agreed that gravity is a real force in Newtonian mechanics. It is not viewed as such in general relativity.

The geosat IS FALLING. Its inertia tends to carry it out in space along a tangent line to its orbit. It also "falls" towards earth. The reason that the geosat does not fall to the Earth is due to its own velocity, tangential to the orbit, accelerated towards the center of the orbit due to gravity. The centripetal/gravity is always there regardless of whether the geosat is still or orbiting the earth.

You are implicitly assuming Newtonian mechanics here. That is not how things are viewed in general relativity. In general relativity, an object in free-fall follows a geodesic in space-time. The four-acceleration of an object following a geodesic is zero. There is no acceleration, so no centripetal force. So, why use such a theory that stupidly says an object in free-fall is not "accelerating"? Simple. It works, and works better than does Newtonian mechanics. One reason general relativity was accepted so quickly is because it explained a phenomenon that had been vexing physicists for quite some time: the precession of Mercury's orbit. General relativity is a more accurate (better) model than is Newtonian mechanics.