How can classical mechanics explain the lack of centrifugal force in orbit?

[LarryS]

If I'm in one of those carnival rides that spin fast I can feel the centrifugal force. This is due to the radial acceleration caused by the centripetal force, the constraining force of the carnival ride mechanism. But if I'm in Earth orbit in a space shuttle, I feel no such centrifugal force. I understand how GR explains the lack of any centrifugal force while one is falling around the Earth. But how does classical (Newtonian) mechanics explain the lack of any centrifugal force while in orbit? As always, thanks in advance.

 

[mgb_phys]

You do feel a centrifugal force in orbit, it's exactly equal and opposite to the force of gravity. That's why you seem to be weightless.

 

[A.T.]

If I'm in one of those carnival rides that spin fast I can feel the centrifugal force. This is due to the radial acceleration caused by the centripetal force, the constraining force of the carnival ride mechanism.

No, you actually feel the centripetal force, because it is not applied uniformly to your body by the ride. The centrifugal force, which exists only in a rotating frame of reference, is an inertial force and accelerates everything equally, so you cannot feel it.

But if I'm in Earth orbit in a space shuttle, I feel no such centrifugal force.

Here both: the centripetal force (gravity) and the centrifugal force (inertial force, only in a rotating frame) are applied uniformly to your body, so you don't feel anything.

 

[LarryS]

Here both: the centripetal force (gravity) and the centrifugal force (inertial force, only in a rotating frame) are applied uniformly to your body, so you don't feel anything.

Is the fact that gravitational mass and intertial mass are equivalent another valid answer?

 

[pgardn]

I am confused here.

If you are in a spaceship in a circular orbit around the Earth the only force is centripetal due to gravity. This force acts on you and the spaceship. On a ride on the surface of the Earth that turns in circles, a wall or seatbelt or something else "pulling or pushing" is acting on you keeping you in that circular path. In other words, the centripetal force applied to your body is mostly due to something else other than gravity. So you feel a pull or a push while on the ride because the ride is holding you in the circular path. In space, the spaceship is not applying any significant force on you. You and the spaceship are just orbiting together due to gravity which is why you feel weightless? yes?

And do the posts above basically say the same thing but use a frame of reference argument?

 

[A.T.]

If you are in a spaceship in a circular orbit around the Earth the only force is centripetal due to gravity.

Same on the ride (if you ignore the vertical gravity), there is only centripetal force accelerating you. But not as uniformly, as gravity does it. Centrifugal force exits in both cases only if you analyze them in the rotating frame of reference.

 

[A.T.]

Is the fact that gravitational mass and intertial mass are equivalent another valid answer?

Yes, that is the Newtonian explanation why gravity accelerates everything equally. From that it follows that you don't "feel" gravitational acceleration. The GR explanation is that gravity is an inertial force, just like the centrifugal force.

 

[pgardn]

Same on the ride (if you ignore the vertical gravity), there is only centripetal force accelerating you. But not as uniformly, as gravity does it.

But the centripetal force accelerating you on the ride is due to some sort of frictional and/or normal force holding you in that circular path. That centripetal force is supplied by the rides walls, seatbelts, etc... So you "feel" like you are being pushed against or held in place while inertia "wants" you to take off in a straight line? The spaceship is not responsible for holding you in a circular path around the Earth so you feel no push or pull... you are just moving in a circular path right with the spaceship but can easily push off the spaceship or move about within it, thus feeling weightless?

 

[mgb_phys]

 

[D H]

The spaceship is not responsible for holding you in a circular path around the Earth so you feel no push or pull... you are just moving in a circular path right with the spaceship but can easily push off the spaceship or move about within it, thus feeling weightless?

As A.T. mentioned, you cannot feel gravity. When (if) you go skydiving, you at first feel truly weightless when you jump out of the plane. You do not feel that you are accelerating at 9.8 m/s² Earthward because you are in freefall. The spaceship, and the astronauts aboard it, are in perpetual freefall.

From a Newtonian point of view, you can't feel gravity because every part of your body is subject to pretty much the same gravitational force. Things would be different if you were in a spaceship orbiting very close to a neutron star. Suppose you are oriented vertically with your feet facing toward the neutron star. The gravitational force on your feet will be greater than the force on your head. You will be pulled apart by gravity, and you most certainly will feel that!

From a general relativistic point of view, an object freefalling in a uniform gravity field is moving inertially. You can't feel gravity because it only looks like a force if you look at the object from the point of view of a non-inertial frame. In general relativity, inertial frames are only local in extent. In the case of an astronaut being pulled apart by a non-uniform gravity field (the neutron star), the astronaut's head and feet are not moving inertially with respect to the astronaut's center of mass.

 

[A.T.]

But the centripetal force accelerating you on the ride is due to some sort of frictional and/or normal force holding you in that circular path. That centripetal force is supplied by the rides walls, seatbelts, etc... So you "feel" like you are being pushed against or held in place while inertia "wants" you to take off in a straight line? The spaceship is not responsible for holding you in a circular path around the Earth so you feel no push or pull... you are just moving in a circular path right with the spaceship but can easily push off the spaceship or move about within it, thus feeling weightless?

Yes, that's what I mean by: the ride is not accelerating you as uniformly, as gravity does it. Therefore you feel the centripetal force on the ride.

 

[sganesh88]

Is the fact that gravitational mass and intertial mass are equivalent another valid answer?

I reiterate this question. Will the state of weightlessness be possible if the inertial mass is not equal to gravitational mass? I feel it is possible because it(feeling of weightlessness) depends on the size of the body under consideration compared to the distance from the center of earth. How will an inequality(hypothetical) affect the scenario?

 

[A.T.]

Will the state of weightlessness be possible if the inertial mass is not equal to gravitational mass?

Possible yes, but not the general case in free fall.

How will an inequality(hypothetical) affect the scenario?

Some parts of your body could have more gravitational mass than others with the same inertial mass, resulting in different accelerations. You would not feel weightless anymore.

 

[pgardn]

Suppose you are oriented vertically with your feet facing toward the neutron star. The gravitational force on your feet will be greater than the force on your head. You will be pulled apart by gravity, and you most certainly will feel that!
From a general relativistic point of view, an object freefalling in a uniform gravity field is moving inertially. You can't feel gravity because it only looks like a force if you look at the object from the point of view of a non-inertial frame. In general relativity, inertial frames are only local in extent. In the case of an astronaut being pulled apart by a non-uniform gravity field (the neutron star), the astronaut's head and feet are not moving inertially with respect to the astronaut's center of mass.

The bolded makes it clear what you are saying. Thanks.

I guess the word feeling is a bit of a problem. One could say they feel gravity on the surface of the Earth because of the normal force exerted on the feet just as one could say they "feel gravity" in a circular spaceship (away from a gravitational field) rotating at a rate to give a centripetal acceleration close to 9.8 m/s^2 even though gravity is not involved.

 

[LarryS]

I guess the word feeling is a bit of a problem. One could say they feel gravity on the surface of the Earth because of the normal force exerted on the feet just as one could say they "feel gravity" in a circular spaceship (away from a gravitational field) rotating at a rate to give a centripetal acceleration close to 9.8 m/s^2 even though gravity is not involved.

"Feel" was probably not the best word to use. I intended "feel" to be a kind of shorthand for "the force that is responsible for any acceleration (Newton's Second Law)". My original question was in the context of Newtonian Mechanics only.

 

[DrZoidberg]

No, you actually feel the centripetal force, because it is not applied uniformly to your body by the ride. The centrifugal force, which exists only in a rotating frame of reference, is an inertial force and accelerates everything equally, so you cannot feel it.

Actually you don't really feel the centripetal force. You just feel the deformation of certain cells in your skin.
But then again, you don't even feel that. You merely feel electrical signals in your brain.

 

[rcgldr]

You can't "feel" gravity, only the forces opposing it. You also can't "feel" the "reaction forces" related to accelerations by gravity, including what could be called centrifugal reaction force. If you're in free fall or orbiting, you feel "weightless". However if you were in space unaffected by gravity, and a rocket engine was exerting radial thrust on the spaceship, then you'd feel the centripetal force at the contact points between you and the rocket, and you'd exert an equal and opposing centrifugal reaction force at those same contact points, the Newton third law pair of forces. However the accleration is only related to the "real" forces, not the "reaction" forces.

In an amusement part ride you feel the centripetal force at the point of contact, and an internal compression force related to the opposing centripetal force at the point of contact and the centrifugal reaction force within your body. If another person were inside of you, sitting on a frictionless surface, then you'd be exerting a centripetal force upon that other person at the point of contact and that person would be exerting a centrifugal reaction force on you. The reaction force in this case is something you can feel, but it's a reaction force to acceleration, one of the pair of equal and opposing Newton third law pair of forces. The same relationships would apply to an amusement park ride with constant linear acceleration.

For gravity, the Newton third law pair is the force exerted by the Earth on you, and the force exerted by you on the earth. In a two body rotating system, both objects exert a force on each other and orbit around some center of mass, each object experiencing a centripetal force, due to gravity, or perhaps tension in a very long string, towards the center of mass of the two body system. If the frame of reference is fixed to one of the objects in a two body rotating system, then you'd have a centripetal force exerted by the "fixed" body, and a centrifugal force exerted by the "moving" body.

 

[A.T.]

You also can't "feel" the "reaction forces" related to accelerations by gravity, including what could be called centrifugal reaction force.

Careful here. Centrifugal reaction force and centrifugal force are not the same thing:

- Centrifugal force is an inertial force that exists only in a rotating frame, and acts on the same object as the centripetal force, which is here Earth's gravity force acting on the orbiting object

- Centrifugal reaction force is the reaction force of the centripetal force according to Newton's 3rd law. It exists in every frame, and acts on a different object than the centripetal force. Here the centrifugal reaction force is the object's gravity force acting on the earth.

 

[rcgldr]

Here the centrifugal reaction force is the object's gravity force acting on the earth.

But that is not really a centrifugal reaction force, since the object's gravitational force is related to distance (g M m / r²), and not centripetal force (m v²/r).

It could be considered a centrifugal force if the Earth was the frame of reference, but then that would be a rotating frame of reference. Otherwise I already covered this, it's a two body system, each exerting a centripetal force on the other, in the direction of the common center of mass of the two body system. It's a bit more clear if gravity is replaced with a string or spring, so that the force is centripetal in nature as opposed to gravitational.

 

[A.T.]

Here the centrifugal reaction force is the object's gravity force acting on the earth.

But that is not really a centrifugal reaction force,

Maybe "centrifugal reaction force" is not the best name. Wikipedia uses "reactive centrifugal force":
http://en.wikipedia.org/wiki/Reactive_centrifugal_force
Which is different from the centrifugal force in a rotating reference frame:
http://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame )

My point is that the centrifugal force in a rotating reference frame is not the reaction force to the centripetal force acting on the same object. Force pairs in Newton's 3rd law act on different objects. In fact the centrifugal force in a rotating reference frame (like all inertial forces) is not subject to Newton's 3rd law. While the centrifugal reaction force (or reactive centrifugal force) is a direct consequence of Newton's 3rd law, and exists in every frame.

It's a bit more clear if gravity is replaced with a string or spring, so that the force is centripetal in nature as opposed to gravitational.

I don't understand what you mean by "centripetal nature" or "gravitational nature" of a force. Forces don't have an unique exclusive nature as you call it. The very same force can be a centripetal and a gravitational force.

But I think I get your point: In case of gravity, where two bodies are orbiting the common mass center, the name "centrifugal reaction force" is not fitting well. Both forces of the action/reaction pair are centripetal forces here. The name fits better to the force on a pole, with a string and a orbiting mass.