Gravitational Force/Earth Rotation Question

[Zarhult]

The force of gravity is what makes things on the Earth rotate with it, instead of flying off. Doesn't this mean, however, that if you were to apply an upward force on something exactly equal in magnitude to the gravitational force on the object (so the net force on it is 0), it would cease to rotate with the Earth? True, it would keep its velocity and initially no change would be noticeable because it takes almost 24 hours for a single rotation of Earth, but if this counteracting force was maintained long enough, wouldn't the object that the force is being applied on begin to fly away from the Earth, since it is not rotating with the planet?

I ask this because, if I am correct, this would make it so that objects like rockets/planes that overcome the force of gravity would cease to rotate with the Earth, seemingly causing some issues. Am I wrong about the cessation of rotating with Earth? Or is this effect compensated for in technology like rockets/planes?

 

[A.T.]

The force of gravity is what makes things on the Earth rotate with it, instead of flying off.

I would rather say, "keeps them rotating". Gravity doesn't affect the tangential velocity to "make" a thing rotate in the first place.

Doesn't this mean, however, that if you were to apply an upward force on something exactly equal in magnitude to the gravitational force on the object (so the net force on it is 0), it would cease to rotate with the Earth?

If the net force is zero, it would move tangentially into space, yes.

Or is this effect compensated for in technology like rockets/planes?

There is nothing to compensate for. Nobody forces you to apply forces that just exactly cancel gravity. Instead you apply the forces that will create the needed trajectory of the vehicle.

 

[Buckleymanor]

No it would not fly away.
The object in question has momentum in the direction of the Earths rotation.Applying an upwards force does not change that.
An object traveling in a certain direction will maintain that direction unless a force is applied to change that direction.
Applying an upwards force will not stop the object following it's rotational path.

 

[Zarhult]

There is nothing to compensate for. Nobody forces you to apply forces that just exactly cancel gravity. Instead you apply the forces that will create the needed trajectory of the vehicle.

Does the force have to be exactly equal? Or would any force that is greater than gravity also have the same effect? I would think that any force overcoming gravity would make an object stop rotating with the planet.

No it would not fly away.
The object in question has momentum in the direction of the Earths rotation.Applying an upwards force does not change that.
An object traveling in a certain direction will maintain that direction unless a force is applied to change that direction.
Applying an upwards force will not stop the object following it's rotational path.

Conservation of momentum is only true without an outside force on the system, though. A force that makes the object overcome the force of gravity would be an outside force, wouldn't it?

 

[russ_watters]

Doesn't this mean, however, that if you were to apply an upward force on something exactly equal in magnitude to the gravitational force on the object (so the net force on it is 0), it would cease to rotate with the Earth?

You mean the way your chair is currently applying such a force to your backside?

I would think that any force overcoming gravity would make an object stop rotating with the planet.

Why? If the force is perpendicular to the direction of the rotation, how can it affect the speed in that direction? F=ma and Newton's laws say that a force is required in the direction of the motion to change the state of motion in that direction.

 

[Orodruin]

You mean the way your chair is currently applying such a force to your backside?

Well, the net force is not zero. There remains a small component which is needed to keep him at the same distsnce from the Earth's center. I believe this is something which the OP is confused about. This is miniscule in comparison to the actual gravitational force though.

 

[Zarhult]

Well, the net force is not zero. There remains a small component which is needed to keep him at the same distsnce from the Earth's center. I believe this is something which the OP is confused about. This is miniscule in comparison to the actual gravitational force though.

Ah! I think I see now. The only force that gives us weight is the component of the force of gravity (almost the entirety of this force) that is left over after the force of gravity overcomes the centrifugal "force," and no upward force on anybody on the Earth can make the force of gravity stop counteracting this centrifugal "force," am I correct? (Since centrifugal force is only an apparent force.)

 

[russ_watters]

Well, the net force is not zero. There remains a small component which is needed to keep him at the same distsnce from the Earth's center. I believe this is something which the OP is confused about. This is miniscule in comparison to the actual gravitational force though.

Oh, I see: true vs apparent weight. Such an object would very slowly appear to accelerate upward while in reality just maintaining the tangential path they started on...the magnitude/direction of that force would be constantly changing, though.

Maybe, but the way I interpreted the question was like the "why isn't the atmosphere (or a helicopter) left behind by Earth's rotation" questions. The OP will need to clarify.

 

[Zarhult]

I'm wrong, centrifugal force does not exist, however the centripetal force needed to keep us rotating with Earth does exist and can be overcome.

Oh, I see: true vs apparent weight. Such an object would very slowly appear to accelerate upward while in reality just maintaining the tangential path they started on...the magnitude/direction of that force would be constantly changing, though.

Maybe, but the way I interpreted the question was like the "why isn't the atmosphere (or a helicopter) left behind by Earth's rotation" questions. The OP will need to clarify.

That's my question, wouldn't anything that overcomes the force of gravity (both weight and the centripetal force component) appear to slowly accelerate upwards from the point of view of someone on Earth? If so, how do rockets compensate for this? I see why it doesn't matter for planes; planes rely on moving through the atmosphere, which rotates with Earth normally.

 

[russ_watters]

That's my question, wouldn't anything that overcomes the force of gravity (both weight and the centripetal force component) appear to slowly accelerate upwards from the point of view of someone on Earth?

So, the first one: Orodruin's interpretation.

If so, how do rockets compensate for this?

I'm still not quite following: Rockets are trying to accelerate up, so that is part of it. Like planes, though, they get steered into exactly the path they are wanting to travel along. I suppose the most direct impact is that rockets are launched to the east so that this effect helps them instead of hurting them (they get a boost from it instead of being slowed down or pulled toward the Earth by it).

 

[Buckleymanor]

Does the force have to be exactly equal? Or would any force that is greater than gravity also have the same effect? I would think that any force overcoming gravity would make an object stop rotating with the planet.



Conservation of momentum is only true without an outside force on the system, though. A force that makes the object overcome the force of gravity would be an outside force, wouldn't it?

Yes a force that makes the object overcome the force of gravity would be an outside force but an upward force alone would not as already stated effect the conservation of momentum.There is a rotational component that would also have to be taken into consideration.
A cannon ball fired exactly verticle overcomes gravity for a while but it does not cease to rotate with the Earth.
Or a person jumping vertically up in the air will come down in the same spot because he also rotates with the Earth he does not fly off.

 

[Zarhult]

So, the first one: Orodruin's interpretation.

I'm still not quite following: Rockets are trying to accelerate up, so that is part of it. Like planes, though, they get steered into exactly the path they are wanting to travel along. I suppose the most direct impact is that rockets are launched to the east so that this effect helps them instead of hurting them (they get a boost from it instead of being slowed down or pulled toward the Earth by it).

I suppose my question is more about this: would a rocket launched vertically upward find itself to no longer be above the same point that it launched from as it kept moving upward?

Also, making something "float" requires that you cancel out its weight, but not its centripetal force of gravity that causes it to rotate with the Earth. Does this mean that if you applied an upward force slightly more than its weight, but not enough to overcome the centripetal force, there would be no apparent upwards acceleration, despite applying more force than the object's weight? (Ignoring apparent upward acceleration due to the Earth rotating away under the object.)

Yes a force that makes the object overcome the force of gravity would be an outside force but an upward force alone would not as already stated effect the conservation of momentum.There is a rotational component that would also have to be taken into consideration.
A cannon ball fired exactly verticle overcomes gravity for a while but it does not cease to rotate with the Earth.
Or a person jumping vertically up in the air will come down in the same spot because he also rotates with the Earth he does not fly off.

Well, a cannon ball does not have a force being applied to it against gravity during its flight, only briefly is a force applied while it is being launched.

I'm more looking for a theoretical explanation of why this doesn't happen, rather than examples that it doesn't.

 

[russ_watters]

I suppose my question is more about this: would a rocket launched vertically upward find itself to no longer be above the same point that it launched from as it kept moving upward?

Yes. That's the essence of the coriolis effect:
http://abyss.uoregon.edu/~js/glossary/coriolis_effect.html

That shows a path parallel to the surface, but it also applies to vertical trajectories.

Also, making something "float" requires that you cancel out its weight, but not its centripetal force of gravity that causes it to rotate with the Earth. Does this mean that if you applied an upward force slightly more than its weight, but not enough to overcome the centripetal force, there would be no apparent upwards acceleration, despite applying more force than the object's weight? (Ignoring apparent upward acceleration due to the Earth rotating away under the object.)

I think you said that backwards or even contradictory: the Earth's rotation lowers the apparent acceleration due to gravity, it doesn't raise it. So a force equal to the acceleration due to gravity alone would be enough to make an object accelerate upwards.

Well, a cannon ball does not have a force being applied to it against gravity during its flight, only briefly is a force applied while it is being launched.

I'm more looking for a theoretical explanation of why this doesn't happen, rather than examples that it doesn't.

Why what doesn't happen?

 

[Zarhult]

Yes. That's the essence of the coriolis effect:
http://abyss.uoregon.edu/~js/glossary/coriolis_effect.html

That shows a path parallel to the surface, but it also applies to vertical trajectories.

I think you said that backwards or even contradictory: the Earth's rotation lowers the apparent acceleration due to gravity, it doesn't raise it. So a force equal to the acceleration due to gravity alone would be enough to make an object accelerate upwards.

Why what doesn't happen?

Ah, so the coriolis effect is caused, in some ways/situations, by having the centripetal force of gravity overcome?

With my example of applying the upward force, I mean that the apparent acceleration of the object is slightly less than its true acceleration (some if its acceleration is what keeps it rotating with the Earth.) Consequently, if you overcome the object's weight (what is left over after the centripetal force is taken care of), it will keep rotating with the Earth, but if you overcome slightly more than its weight (but not enough to entirely overcome centripetal force), then it will still appear as if the net force on it is 0 from your frame of reference? (Ignoring the apparent movement of it caused by the Earth rotating away from under it).

I was asking why objects that overcome both their weight and the centripetal force of gravity don't stop rotating with the Earth in that quote, but from what I've gathered in this conversation, they do, correct?

 

[Orodruin]

Ah, so the coriolis effect is caused, in some ways/situations, by having the centripetal force of gravity overcome?

No, it is created by radial motion in a rotating coordinate system.

 

[Buckleymanor]

I suppose my question is more about this: would a rocket launched vertically upward find itself to no longer be above the same point that it launched from as it kept moving upward?

Also, making something "float" requires that you cancel out its weight, but not its centripetal force of gravity that causes it to rotate with the Earth. Does this mean that if you applied an upward force slightly more than its weight, but not enough to overcome the centripetal force, there would be no apparent upwards acceleration, despite applying more force than the object's weight? (Ignoring apparent upward acceleration due to the Earth rotating away under the object.)



Well, a cannon ball does not have a force being applied to it against gravity during its flight, only briefly is a force applied while it is being launched.

I'm more looking for a theoretical explanation of why this doesn't happen, rather than examples that it doesn't.

A canon ball does not have a force applied only briefly.What I imagine to be the problem with your take on what is happening is that you fail to take into consideration that there are forces being constantly applied to a stationary object other than gravity.The cannon ball sits on the ground and it looks stationary but it is not depending on where it is placed it is rotating with turn of the planet.The planet is also orbiting the sun within the solar system and that in turn is rotating within the galaxy.These in turn are all applying forces constantly on our ever moving ball.
So when you come along and add an upwards force you don't cancel out the other forces acting upon the ball you just add another directional force.
How the ball behaves then depends on the direction and the amount of force applied to the ball plus the amount of effect the other forces have on the ball.

 

[Zarhult]

A canon ball does not have a force applied only briefly.What I imagine to be the problem with your take on what is happening is that you fail to take into consideration that there are forces being constantly applied to a stationary object other than gravity.The cannon ball sits on the ground and it looks stationary but it is not depending on where it is placed it is rotating with turn of the planet.The planet is also orbiting the sun within the solar system and that in turn is rotating within the galaxy.These in turn are all applying forces constantly on our ever moving ball.
So when you come along and add an upwards force you don't cancel out the other forces acting upon the ball you just add another directional force.
How the ball behaves then depends on the direction and the amount of force applied to the ball plus the amount of effect the other forces have on the ball.

Well yes, there are always forces from other sources in play, but when you add a force exactly opposite to the force of Earth's gravity, then the only forces acting on it will be the forces making it orbit the sun, the galactic center, etc., without the force of gravity from the Earth that keeps it in rotation with the Earth.

 

[Buckleymanor]

Well yes, there are always forces from other sources in play, but when you add a force exactly opposite to the force of Earth's gravity, then the only forces acting on it will be the forces making it orbit the sun, the galactic center, etc., without the force of gravity from the Earth that keeps it in rotation with the Earth.

It's slightly different from your OP where an upwards force was mentioned.Suppose a force was applied horizontally you could send the object into a geo- stationary orbit if more force was added the object could remain stationary relative to where it took off.
You would have to launch it in the direction opposite to the Earths rotation and it probably would fall back to Earth and not go into orbit.
The object would not fly away though unless some more extra force was given to it.

 

[jbriggs444]

It's slightly different from your OP where an upwards force was mentioned.Suppose a force was applied horizontally you could send the object into a geo- stationary orbit if more force was added the object could remain stationary relative to where it took off.
You would have to launch it in the direction opposite to the Earths rotation and it probably would fall back to Earth and not go into orbit.
The object would not fly away though unless some more extra force was given to it.

Let us not complicate matters. It is unhelpful to talk about the motion of solar systems, stars, galaxies and such when the question involves only a vertical force on a rotating earth. It is unhelpful to talk about what might or might not happen under some pattern of horizontal forces when the scenario in question involves a vertical force. It is unhelpful to talk about cannon balls and impulsive forces when the scenario involves a continuous force. It is unhelpful to conjure up a bunch of hypothetical real forces when the essence of the problem involves an inertial force -- to whit, the Coriolis force. It is unhelpful to keep going after Orodruin's terse, correct and complete response in #15.

 

[Buckleymanor]

Unhelpful to who I am not so sure most posters will will fully understand post 15 that is one of the reasons they post.
Someone got out of bed on the wrong side this morning.

 

[MarkJW]

No, it is created by radial motion in a rotating coordinate system.

Might it be more accurate to say it is a mathematical consequence of having radial motion in a rotating coordinate system? This is why it is often referred to as a "fictitious force" in the Newtonian system.

 

[Orodruin]

Might it be more accurate to say it is a mathematical consequence of having radial motion in a rotating coordinate system? This is why it is often referred to as a "fictitious force" in the Newtonian system.

No, it is a very appreciable and real effect in a rotating coordinate system. The maths tell you how it arises in relation to an inertial system, but if you set up an appropriate experiment in a rotating system, you will certainly be able to measure it.

 

[A.T.]

Might it be more accurate to say it is a mathematical consequence of having radial motion in a rotating coordinate system?

Coriolis acceleration occurs for tangential motion as well, not only radial motion.

 

[LagOutLoud]

OP, as a point of clarification, If you were to create a force exactly opposite that of Earth's gravitational pull that would not "cancel out" gravity. This is not a math equation. Earth's gravity is still pulling at the body in question. There is just a new force providing a new vector of acceleration. The resulting vector is the Sum of the two vectors.
I think the biggest issue here is your visualization of how that opposite force is created. We can examine both the theoretical proposition and how it works in practice.
Theoretically, if you were to imagine the situation where you created a force exactly opposite of gravity and started floating upward, you would not fly off tangentially. If you were to draw a tangential line from a circle and pick a point to compare from your original "Take off point" and draw the vector of the forces of both gravity and your new force you would see the problem. Gravity is always pulling at you directly from the center straight down perpendicular to the surface. Your original force if it did not rotate with the surface now does not point opposite of gravity, meaning gravity again begins to pull you back down and your new vector is again toward Earth and in the direction of the original force. What would really have to happen to be constantly be opposite of the force of gravity, would be for it to rotate constantly to remain perpendicular to the surface. In this situation, Your rotational momentum is conserved as no other outside forces are acting on you otherwise and you were rotating to begin with and any change in rotation or even you beginning to float higher in the atmosphere would only come from you accelerating in that direction by an additional outside force.
Practically, When you create a real force like that to hover, with a jet engine or helicopter. You are displacing a lot of air downward and creating high pressure beneath it. But what it pushes, and what it is pushing against is all a part of the rotating system. If you have a jet engine pushing down, it is still pushing against the surface of the rotating Earth. and you have momentum keeping you spinning and simply creating life opposite that of the Earth doesn't change that you will still spin. and you will not fly off tangentially because you are constantly being pulled at by gravity perpendicular to the surface, so your gravity opposite force must likewise rotate to be perpendicular with the Earth and your rotational momentum remains unchanged.

Hope this helped out.