Questions about understanding circular motion & the forces involved

[A.T.]

How can the observer in the free-falling frame apply Newton's law of universal gravitation

By plugging numbers into the formula:
https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation#Modern_form
As you see the force is independent of reference frame (observer).

 

[Andrew Mason]

By plugging numbers into the formula:
https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation#Modern_form
As you see the force is independent of reference frame (observer).

Your means of determining the mass of the gravitating object is to use M = r^2g/G where r is the distance to the centre of mass of M and g is your acceleration toward the common centre of mass. But our premise is that the frame of reference of the spacecraft is treated as an inertial frame for applying the laws of physics, so it is not accelerating.

I think that all we can say is that inertial forces do not arise in a frame of reference that is undergoing gravitational free fall in a locally uniform gravitational field and that this is not the case with any other force. Why it is an exception is something that Einstein explores in the General Theory of Relativity. jbriggs asks the right question: "If you have a frame that is experimentally indistinguishable from inertial, why are you calling it non-inertial?"

AM

 

[Andrew Mason]

By plugging numbers into the formula:
https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation#Modern_form
As you see the force is independent of reference frame (observer).

The force is independent of which inertial frame in which it is measured.

AM

 

[A.T.]

The force is independent of which inertial frame in which it is measured.

Newtonian gravity is independent of reference frame, regardless whether inertial or not.

But our premise is that the frame of reference of the spacecraft is treated as an inertial frame

That's the GR interpretation, not your premise under Newtonian gravity. Read you own post #26.

 

[Andrew Mason]

Newtonian gravity is independent of reference frame, regardless whether inertial or not.

That would mean that acceleration measured in a noninertal frame will be the same as measured in an inertial frame...?

That's the GR interpretation, not your premise under Newtonian gravity. Read you own post #26.

??The whole point is to apply the laws of physics in a noninrtial frame. If the body is undergoing constant acceleration due to gravity, one can apply Newton's laws without having to posit some non-Newtonian force.

AM

 

[jbriggs444]

That would mean that acceleration measured in a noninertal frame will be the same as measured in an inertial frame...?

The acceleration measured in a non-inertial frame is different from the acceleration measured in an inertial frame. If one accepts Newton's second law, the net force in a non-inertial frame is different from the net force in an inertial frame. The delta is an inertial force associated with the choice of a non-inertial frame.

If you consider a freely falling frame to be non-inertial then Newtonian gravity is not that inertial force.

??The whole point is to apply the laws of physics in a noninrtial frame. If the body is undergoing constant acceleration due to gravity, one can apply Newton's laws without having to posit some non-Newtonian force.

But that is not the situation that you are positing in post #26. You are positing an object that is NOT undergoing constant acceleration due to gravity. Rather, you are positing an object that is stationary in a "non-inertial frame" [your words] in spite of gravity. This demands some non-Newtonian force to keep it in place.

 

[Andrew Mason]

The acceleration measured in a non-inertial frame is different from the acceleration measured in an inertial frame. If one accepts Newton's second law, the net force in a non-inertial frame is different from the net force in an inertial frame. The delta is an inertial force associated with the choice of a non-inertial frame.

If you consider a freely falling frame to be non-inertial then Newtonian gravity is not that inertial force.

I agree.. One does not need to assume any non-Newtonian forces in order to make Newton's laws of motion work.

But that is not the situation that you are positing in post #26. You are positing an object that is NOT undergoing constant acceleration due to gravity. Rather, you are positing an object that is stationary in a "non-inertial frame" [your words] in spite of gravity. This demands some non-Newtonian force to keep it in place.

In post 26 I refer to a free-falling or orbiting spacecraft . Perhaps you mean some other post. If a body is stationary in the non-inertial frame of that spacecraft there is no need to posit any non-Newtonian force to keep it in place. That is all I am saying.

AM

 

[A.T.]

That would mean that acceleration measured in a noninertal frame will be the same as measured in an inertial frame...?

No, it doesn't mean that.

 

[nrqed]

The only difficulty here is: how do you determine that there is a force of gravity? There is no experiment that you can do to measure the gravitational force.

AM

If we are working in the context of Newtonian gravity (not GR), then you determine that there is a force of gravity by looking outside the craft and observing the planet below. Then you deduce that you should be falling toward it but you are not, and therefore you have to postulate (in your frame a reference) an imaginary force keeping you from falling.

 

[Andrew Mason]

If we are working in the context of Newtonian gravity (not GR), then you determine that there is a force of gravity by looking outside the craft and observing the planet below. Then you deduce that you should be falling toward it but you are not, and therefore you have to postulate (in your frame a reference) an imaginary force keeping you from falling.

The difference between a spacecraft i) being hurled around in a centrifuge on the one hand and ii) being in gravitational orbit is that the observer can detect and measure the force (that the inertial observer views as centripetal) in i) but cannot measure that force in ii). In the case of i) he can measure tensions - i.e. the force required to keep an object stationary. In the second case, no force is required to keep an object stationary. We could suppose, for example that the gravitating mass is an invisible black hole or dark matter - ie. the observer would not be able to tell that he is subjected to a gravitational force. No inertial forces would have to be postulated in order to make Newton's laws of motion work in that frame of reference.

AM

 

[nrqed]

The difference between a spacecraft i) being hurled around in a centrifuge on the one hand and ii) being in gravitational orbit is that the observer can detect and measure the force (that the inertial observer views as centripetal) in i) but cannot measure that force in ii). In the case of i) he can measure tensions - i.e. the force required to keep an object stationary. In the second case, no force is required to keep an object stationary. We could suppose, for example that the gravitating mass is an invisible black hole or dark matter - ie. the observer would not be able to tell that he is subjected to a gravitational force. No inertial forces would have to be postulated in order to make Newton's laws of motion work in that frame of reference.

AM

Well, if I would put Newton in the ISS, he would know that there is a face of gravity because of the presence of the planet, do you agree??
The situation is not different from being in a centrifuge. If I have a plumb line in a centrifuge, I know there is a tension force pulling one way and therefore I may invent the concept of centrifugal force to explain what happens. If I am in the space station, I know there is a force of gravity pulling one way and therefore I may invent a force to explain why objects seem to be floating around in my frame. You are saying that because I don't see anything physical acting on an object, because it is gravity which seems to act a distance (in Newtonian gravity), I can ignore it. I would think that Newton would have disagreed.

 

[A.T.]

We could suppose, for example that the gravitating mass is an invisible black hole or dark matter - ie. the observer would not be able to tell that he is subjected to a gravitational force. No inertial forces would have to be postulated in order to make Newton's laws of motion work in that frame of reference.

Newtonian inertial frames extend to infinity, and aren't limited by what some person can see. Newton's laws of motion do not hold throughout that frame, so it's not inertial.

 

[Andrew Mason]

Well, if I would put Newton in the ISS, he would know that there is a face of gravity because of the presence of the planet, do you agree??

Yes. But then he knows that he is accelerating and that defeats the premise (that he thinks of his non-inertial frame as inertial). You might as well use the example of a person in an accelerating car and say that he knows that the trees and buildings that are fixed to the Earth are passing by at an accelerated rate and must conclude that he is accelerating. The point is that he is not supposed to know what is actually happening. He is supposed to make Newton's laws of motion work in his frame of reference while being oblivious to the fact that his frame is non-inertial. To do that he has to invent an inertial force.

AM

 

[A.T.]

The point is that...

Do you actually have a point, that goes beyond what the Equivalence Principle states? Because I don't think that anybody here argues against the EP, just against your confused description.

 

[nrqed]

Yes. But then he knows that he is accelerating and that defeats the premise (that he thinks of his non-inertial frame as inertial). You might as well use the example of a person in an accelerating car and say that he knows that the trees and buildings that are fixed to the Earth are passing by at an accelerated rate and must conclude that he is accelerating.

AM

I think you are missing the point about non inertial frames. How would you convince someone that he is accelerating? You say that you can just point out to the trees moving by with a relative acceleration and that shows that one is accelerating. But that is not the point! The person in the car could say "actually, I think it is the trees of that are accelerated past me, while I am at rest (or moving at constant velocity). Maybe I am in a huge hangar and my car is immobile while you are rolling past me a huge carpet with trees past me! *That* is the point: how does one disprove that? And the answer is that if one tries to apply Newton's laws, the only way to make it work is to introduce fictitious forces to make F =ma work in the frame of the car, and *this* is what shows that the car is accelerating, *not* that trees are accelerating by!

Now, in the case of the space shuttle, the situation is the same: one knows that there is a planet nearby (in order to make any statement about forces, one must be given information about the system in which one is. If you close the eyes of someone and give them no information whatsoever about their surroundings, there is no way to discuss anything regarding frames in classical physics). Now, given that there is a planet nearby, the person knows that he/she is attracted to it. So the only way to stay in orbit is to either introduce a fictitious force in the non inertial frame to make Newton's laws work or to realize that since the frame is non inertial, Newton's laws are not valid in that frame.

 

[Andrew Mason]

I think you are missing the point about non inertial frames. How would you convince someone that he is accelerating? You say that you can just point out to the trees moving by with a relative acceleration and that shows that one is accelerating. But that is not the point! The person in the car could say "actually, I think it is the trees of that are accelerated past me, while I am at rest (or moving at constant velocity). Maybe I am in a huge hangar and my car is immobile while you are rolling past me a huge carpet with trees past me! *That* is the point: how does one disprove that? And the answer is that if one tries to apply Newton's laws, the only way to make it work is to introduce fictitious forces to make F =ma work in the frame of the car, and *this* is what shows that the car is accelerating, *not* that trees are accelerating by!

That is exactly what I have been saying. It is the experiments performed in the non-inertial frame that cause the non-inertial observer the posit fictitious forces. The point is that if the acceleration is provided by gravity, all experiments show that Newton's laws work without fictitious forces. That really should not be controversial. That is all I am saying.

AM

 

[nrqed]

That is exactly what I have been saying. It is the experiments performed in the non-inertial frame that cause the non-inertial observer the posit fictitious forces. The point is that if the acceleration is provided by gravity, all experiments show that Newton's laws work without fictitious forces. That really should not be controversial. That is all I am saying.

AM

And all I am saying is that if one looks out the window of the ISS and sees a huge planet there, and one knows about Newtonian gravity, and one notices that all the objects in the station are floating, one has to introduce a fictitious force to cancel the force of gravity (if one wants to apply Newton's laws using the station as the frame of reference). I don't see anything controversial in any of that.

 

[Andrew Mason]

Ok. So what experiment can he do to measure this mysterious force?

AM

 

[nrqed]

Ok. So what experiment can he do to measure this mysterious force?

AM

One cannot directly. But that does not mean it is not there. Do you think that Newton in the ISS would have conclu

Ok. So what experiment can he do to measure this mysterious force?

AM

One cannot directly. But that does not mean it is not there. Do you think that Newton in the ISS would have concluded that the force of gravity due to this huge planet suddenly disappeared because he is floating inside the station? This is what my first year novice students believe (the astronauts float because they are in space and therefore there is no gravity there!).

It sounds to me that you want to argue for the EP. As A.T. said, we all agree about that. I thought the question was about discussing fictitious forces in Newtonian physics.

 

[Andrew Mason]

The distinction that you are making seems to be that in the case of gravitational free fall the fictitious force is produced by an intellectual argument, whereas in the other cases it can actually be measured.

AM.

 

[A.T.]

The distinction that you are making seems to be that in the case of gravitational free fall the fictitious force is produced by an intellectual argument, whereas in the other cases it can actually be measured.

It's produced by the general rules of how inertial forces and inertial frames are defined in the Newtonian context. It's not different from other inertial forces.

 

[Andrew Mason]

It's produced by the general rules of how inertial forces and inertial frames are defined in the Newtonian context. It's not different from other inertial forces.

And I disagree with that view. Fictitious forces can be directly measured in the non-inertial frame. The posited "anti-gravity" fictitious force cannot.

AM

 

[jbriggs444]

And I disagree with that view. Fictitious forces can be directly measured in the non-inertial frame. The posited "anti-gravity" fictitious force cannot.

Sure it can. Measure gravity, measure acceleration, deduce ficticious force. Easy. Easy enough for Newton.

 

[Andrew Mason]

Sure it can. Measure gravity, measure acceleration, deduce ficticious force. Easy. Easy enough for Newton.

It is the measurement of gravity in the non-inertial frame that is the problem. Gravity is measured by the acceleration it provides to a unit mass. In the non-inertial frame, there is no acceleration.

AM

 

[jbriggs444]

It is the measurement of gravity in the non-inertial frame that is the problem. Gravity is measured by the acceleration it provides to a unit mass. In the non-inertial frame, there is no acceleration.

Newton's universal law of gravitation can be deduced from within an accelerated reference frame. The result is a net inertial force of the form:
$$F=Km+\frac{GMm}{r^2}$$
It is not difficult to distinguish between the constant term and the term which depends on gravity.

Though why you would chose to use a non-inertial frame which results in freely falling objects being unaccelerated in only one place is a mystery.

 

[A.T.]

Fictitious forces can be directly measured in the non-inertial frame.

Forces in general cannot be directly observed. We observe effects like acceleration or deformation, and postulate forces to match them. Assuming Newton's gravitation, you need to postulate inertial forces in the free falling frame, to make the net force match the observed acceleration.

 

[A.T.]

In the non-inertial frame, there is no acceleration.

Nonsense. The reference extends to infinity, and isn't limited to a small area with only free falling masses. There are plenty of accelerating objects in that frame.

 

[nrqed]

It is the measurement of gravity in the non-inertial frame that is the problem. Gravity is measured by the acceleration it provides to a unit mass. In the non-inertial frame, there is no acceleration.

AM

But if you look out of a window of the ISS and you see the Earth moving around you, surely the Earth is accelerating as observed in that frame. The non inertial frame of the ISS does not stop at its outer hull.

 

[nrqed]

And I disagree with that view. Fictitious forces can be directly measured in the non-inertial frame. The posited "anti-gravity" fictitious force cannot.

AM

The distinction that you are making seems to be that in the case of gravitational free fall the fictitious force is produced by an intellectual argument, whereas in the other cases it can actually be measured.

AM.

I don't see the problem with using an intellectual argument. We know that all masses produce an attractive gravitational force. We see a planet very nearby. We therefore know that there is a non negligible attractive pull toward the planet. But we are free floating and feel no acceleration. Therefore a (fictitious) force must cancel the gravitational pull.

You seem to say that it is only when we can use a plumb line or a spring scale to measure a force that it must be taken into account. What about the e/m experiment? You have an electron floating in an electric field. The net force is zero, you cannot use a spring scale to measure the gravitational force on the electron, nor the electric force . You use an intellectual argument to argue that the electric force cancel the force of gravity to determine the e/m ratio. That is not controversial!

 

[Andrew Mason]

Newton's universal law of gravitation can be deduced from within an accelerated reference frame. The result is a net inertial force of the form:
$$F=Km+\frac{GMm}{r^2}$$

Ok. So you are falling toward an object - a body of unknown mass. How do you determine M? And how do you determine the distribution of mass within the body? The only way to determine that is by measuring your acceleration. But in the non-inertial frame you are in, there is no acceleration.

Though why you would chose to use a non-inertial frame which results in freely falling objects being unaccelerated in only one place is a mystery.

? The free-falling body is always unaccelerated in its non-inertial frame of reference (ie. a frame of reference the body - a frame in which the origin is undergoing non-inertial motion) regardless of the acceleration or rate of change of acceleration that an inertial observer measures. (We are assuming that tidal forces within the body are negligible).

AM

 

[jbriggs444]

Ok. So you are falling toward an object - a body of unknown mass. How do you determine M? And how do you determine the distribution of mass within the body. The only way to determine that is by measuring your acceleration. But in the non-inertial frame you are in, there is no acceleration.

Newton did it. Why can't you?

The free-falling body is always unaccelerated in its non-inertial frame of reference (ie. a frame of reference in which the origin is undergoing non-inertial motion) regardless of the acceleration or rate of change of acceleration that an inertial observer measures. (We are assuming that tidal forces within the body are negligible).

NO NO NO. We are NOT assuming that tidal forces are negligible. We are NOT confined to a small local region. Your post #26 makes no such restriction.

Edit: Are you, perhaps, under the mistaken impression that frames of reference are physical and restrict the set of observations we can make?

 

[A.T.]

The free-falling body is always unaccelerated in its non-inertial frame of reference

But other bodies are accelerated in that frame, and you have to introduce inertial forces to reconcile those accelerations with Newtons 2nd Law.

 

[nrqed]

And I disagree with that view. Fictitious forces can be directly measured in the non-inertial frame. The posited "anti-gravity" fictitious force cannot.

AM

Just to be clear: if you were teaching college physics (not GR but Newtonian physics), would you tell your students that in the ISS there is no force of gravity acting and the proof is that people observe themselves to be free floating? So inside a free falling elevator at the surface of the Earth (ignoring friction, Coriolis force, etc), you would say the same thing: for the people inside there is no force of gravity since they are free floating.?That's what you would tell them? But now, if one analyzes the ISS from the point of view of the ground, would you say that there is a force of gravity on it or not? (I am guessing yes). So you would say that the force of gravity on a given object may be present or not depending on the frame of reference we use to analyze the system? Is that what your point of view?

 

[Andrew Mason]

Just to be clear: if you were teaching college physics (not GR but Newtonian physics), would you tell your students that in the ISS there is no force of gravity acting and the proof is that people observe themselves to be free floating? So inside a free falling elevator at the surface of the Earth (ignoring friction, Coriolis force, etc), you would say the same thing: for the people inside there is no force of gravity since they are free floating.?

I expect the student would have an understanding of Newton's law of motion and gravity from high school so I don't think you are going to get away with telling them that gravity disappears 100 miles above the earth. But it is precisely because there are no inertial pseudo forces required to make Newton's laws of motion work in a free-falling frame of reference that the principle of equivalence was postulated. It is based on Newtonian physics.

If you introduce tidal forces, of course, it is another matter. Then you have to introduce some pseudo force causing the tensions or you go to GR for the better explanation. The fundamental difference between gravity and all other forces is the fact that the force of gravity is proportional to inertial mass (as far was we can tell). As such, inertial forces are not required to treat a free-falling frame (locally) as an inertial frame. I guess I will just leave it at that.

AM

 

[Andrew Mason]

JSo you would say that the force of gravity on a given object may be present or not depending on the frame of reference we use to analyze the system? Is that what your point of view?

Why would you ask such a question?

Would you ask: does the car stop accelerating because the person inside is trying to apply Newton's laws as if he were an inertial observer?

It is not a matter of whether the non-interial observer has the means of figuring out that is frame of reference is accelerating. He assumes it is not and invents fictitious inertial forces to make Newton's laws work as if his non-inertial frame were inertial.

Before wasting your time with these kinds of questions, I suggest you re-read the entire thread and, in particular, my posts 6, 10, 13, 15, 18 and 22 where I think I have made it clear what I have to say on the subject. My purpose was not to provide a treatise on pseudo forces but to simply point out an important difference between gravity and other forces for the OP. I think we can all agree that there is an important difference.

AM