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I occasionally come across this argument that there is no gravity on anything in space (orbit). Their reasoning is that the gravitational force is canceled out

I occasionally come across this argument that there is no gravity on anything in space (orbit). Their reasoning is that the gravitational force is canceled out by centrifugal force. You could say that the forces cancel out, if you consider pseudo-forces like centrifugal force or Coriolis force as real forces. However, that view sometimes lead to very misleading notions like 'there is no gravity in space'. It also makes explanation of other phenomena like tidal forces needlessly complicated. For this reason alone, I discourage people from analyzing in non-inertial frames. Inertial frames make life simpler and clearer by removing caveats on Newton's second law. You no longer need to invent imaginary forces.

stouset 5y ago
I apologize for my ignorance, but how does one consider gravity a "force" from within an inertial reference frame? As I understand it, from the perspective of an observer floating in space inside the gravity well of a nearby object, that observer experiences no net forces. They experience acceleration from the perspective of an outside observer, but not from their own reference frame. A classic example is a person inside a falling elevator. From their own perspective, they're floating with no external forces acting upon them (until, of course, the elevator crashes into the ground). Only when the elevator is held stationary (from the POV of an external reference frame) does the occupant feel an acceleration force upward pushing back against the gravitational well they're standing in.
- sreevisakh 5y ago
  Your problem of falling elevator is probably the simplest and best example of problem with non-inertial frames. By definition, an inertial frame is a reference frame where Newton's laws of motion can be applied without caveats. For that to be true, the reference frame must be non-accelerating and non-rotating. By that definition, the reference frame attached to the elevator is a non-inertial frame - because it is accelerating towards ground. In your words, the 'perspective of the outside observer' is the actual inertial frame. Now let's see why there is no gravity from the elevator's frame of reference. Remember that by Newton's law of gravitation, gravitational force is GMm/r^2. If you plug in the values, you won't get a zero. This means that the person inside the elevator is definitely facing gravitational 'force'. (I'm assuming classical mechanics where gravity is a force. Relativity considers it as another pseudo force. But that view won't affect our current discussion) Consider the non-inertial frame inside the elevator first. In order for the person to be experiencing no force, all forces on him must be balanced and cancelling out. We know of only gravitational force that is acting downwards. So to cancel it out, we need to invent an equal and opposite force on the person. That force is called 'rectilinear acceleration force' and its value is given by ma (upwards), where m is the mass of the person and a is the elevator's downwards acceleration. So the net force on the person is mg-ma. Since elevator is in free fall, a=g and so the force on the person is zero. You can see the mess here. You have to invent a new force that doesn't exist and have to be careful about its direction too. If the frame is rotating, then more pseudo forces have to be invented - the Coriolis force, Centrifugal force and Euler's force. All these 4 forces don't exist in reality, and are there purely to account for non-inertial frames. Now let's see how the forces play out when considered from the inertial frame of the external observer. Let's consider if the lift is stationary first. Obviously the person inside the elevator is feeling gravitational force that is equal to his weight. In reality, he is not actually sensing gravity acting on him - he is instead sensing the 'reaction force'. The reaction force is the force that the floor of the elevator is applying on him to counteract his weight. In other words, the reaction force from the floor actually cancels his weight - so he remains stationary instead of accelerating towards the ground. Now, unlike pseudo forces, reaction forces are real forces. In this case, it's provided by the electromagnetic repulsion between the molecules on the floor and in the person. This reaction forces don't just act on the person's foot. It acts throughout his body. For example, his internal organs don't fly off under gravity because the reaction force provided by the connective tissues hold them in place, counteracting gravity. Finally what happens when the elevator is falling? The elevator is in free fall, so its acceleration is g towards ground. The person is also falling with the same acceleration g. This means that there is no reaction force acting on him to counteract the gravity. In other words, the person is no longer supported by the floor - that support was the reaction force. Remember that I said that the reaction force was the force that the person was sensing as gravity. Now that reaction force has disappeared. So the person in effect feels that he is weightless, even though gravity is still acting on him. This is the advantage of inertial frames. All Newton's laws can be applied in terms of real and concrete forces with well known causes. You don't need to invent anything new and then justify their existence.
- ridiculous_fish 5y ago
  An inertial frame is a frame which respects Newton's first law: an object moves with constant velocity iff it experiences zero net force. We can say the sun is at rest. Here the satellite accelerates towards the sun; we say that is due to a force called gravity. This is nice and simple. We can instead say the satellite is at rest. In this frame there is no net force on the satellite. But now the sun accelerates, as do the distant stars; why? And how to explain second-order gravitational effects like tides? It's awkward to work in and leads to bad intuition. To extend it to your freefall elevator example: everything inside the elevator obeys Newton's First Law so we are justified in treating it as inertial. Extend the frame to the surface of the earth and we have a problem: we either have to explain what force causes the earth to accelerate towards the elevator, or admit we have a non-inertial frame. Simplest to just say the earth is at rest and the elevator is accelerating due to gravity. However centrifugal force is not all bad, it has a really cool interpretation which yields a powerful insight. Consider a satellite in an elliptical orbit. As it reduces its radial distance to the sun, it must pump energy into its tangential velocity, to conserve angular momentum. So its tangential kinetic energy is a function of its position. Hey, that sounds like a potential! You can just add this "tangential kinetic potential" to the gravitational potential, yielding a bathtub shaped "effective potential." Now we're in 1D, since we're identifying angular effects with gravity. When the radial distance is large, the satellite will accelerate towards the sun (radial velocity decreasing), as it falls down the gravitational potential well. Eventually it begins to climb the "tangential kinetic potential" hill, and starts accelerating away from the sun (radial velocity increasing). In this 1D world, the sun is attractive at long range and repulsive at short range; the turning points are the apahelion and perihelion of the orbit. What's so cool about this is that we've reduced a 2D kinematics problem to a 1D problem (radial distance varying over time) by absorbing the tangential kinetic energy into the gravitational potential energy. This connects planetary orbits to more familiar problems like the 1D harmonic oscillator. The cost of doing so was the appearance of this "tangential kinetic potential;" the derivative of a potential is a force and that's centrifugal force.
KolenCh 5y ago
Non-inertial frame isn’t the problem, proper language is.

stouset 5y ago

I apologize for my ignorance, but how does one consider gravity a "force" from within an inertial reference frame? As I understand it, from the perspective of an observer floating in space inside the gravity well of a nearby object, that observer experiences no net forces. They experience acceleration from the perspective of an outside observer, but not from their own reference frame. A classic example is a person inside a falling elevator. From their own perspective, they're floating with no external forces acting upon them (until, of course, the elevator crashes into the ground). Only when the elevator is held stationary (from the POV of an external reference frame) does the occupant feel an acceleration force upward pushing back against the gravitational well they're standing in.

sreevisakh 5y ago
Your problem of falling elevator is probably the simplest and best example of problem with non-inertial frames. By definition, an inertial frame is a reference frame where Newton's laws of motion can be applied without caveats. For that to be true, the reference frame must be non-accelerating and non-rotating. By that definition, the reference frame attached to the elevator is a non-inertial frame - because it is accelerating towards ground. In your words, the 'perspective of the outside observer' is the actual inertial frame. Now let's see why there is no gravity from the elevator's frame of reference. Remember that by Newton's law of gravitation, gravitational force is GMm/r^2. If you plug in the values, you won't get a zero. This means that the person inside the elevator is definitely facing gravitational 'force'. (I'm assuming classical mechanics where gravity is a force. Relativity considers it as another pseudo force. But that view won't affect our current discussion) Consider the non-inertial frame inside the elevator first. In order for the person to be experiencing no force, all forces on him must be balanced and cancelling out. We know of only gravitational force that is acting downwards. So to cancel it out, we need to invent an equal and opposite force on the person. That force is called 'rectilinear acceleration force' and its value is given by ma (upwards), where m is the mass of the person and a is the elevator's downwards acceleration. So the net force on the person is mg-ma. Since elevator is in free fall, a=g and so the force on the person is zero. You can see the mess here. You have to invent a new force that doesn't exist and have to be careful about its direction too. If the frame is rotating, then more pseudo forces have to be invented - the Coriolis force, Centrifugal force and Euler's force. All these 4 forces don't exist in reality, and are there purely to account for non-inertial frames. Now let's see how the forces play out when considered from the inertial frame of the external observer. Let's consider if the lift is stationary first. Obviously the person inside the elevator is feeling gravitational force that is equal to his weight. In reality, he is not actually sensing gravity acting on him - he is instead sensing the 'reaction force'. The reaction force is the force that the floor of the elevator is applying on him to counteract his weight. In other words, the reaction force from the floor actually cancels his weight - so he remains stationary instead of accelerating towards the ground. Now, unlike pseudo forces, reaction forces are real forces. In this case, it's provided by the electromagnetic repulsion between the molecules on the floor and in the person. This reaction forces don't just act on the person's foot. It acts throughout his body. For example, his internal organs don't fly off under gravity because the reaction force provided by the connective tissues hold them in place, counteracting gravity. Finally what happens when the elevator is falling? The elevator is in free fall, so its acceleration is g towards ground. The person is also falling with the same acceleration g. This means that there is no reaction force acting on him to counteract the gravity. In other words, the person is no longer supported by the floor - that support was the reaction force. Remember that I said that the reaction force was the force that the person was sensing as gravity. Now that reaction force has disappeared. So the person in effect feels that he is weightless, even though gravity is still acting on him. This is the advantage of inertial frames. All Newton's laws can be applied in terms of real and concrete forces with well known causes. You don't need to invent anything new and then justify their existence.
ridiculous_fish 5y ago
An inertial frame is a frame which respects Newton's first law: an object moves with constant velocity iff it experiences zero net force. We can say the sun is at rest. Here the satellite accelerates towards the sun; we say that is due to a force called gravity. This is nice and simple. We can instead say the satellite is at rest. In this frame there is no net force on the satellite. But now the sun accelerates, as do the distant stars; why? And how to explain second-order gravitational effects like tides? It's awkward to work in and leads to bad intuition. To extend it to your freefall elevator example: everything inside the elevator obeys Newton's First Law so we are justified in treating it as inertial. Extend the frame to the surface of the earth and we have a problem: we either have to explain what force causes the earth to accelerate towards the elevator, or admit we have a non-inertial frame. Simplest to just say the earth is at rest and the elevator is accelerating due to gravity. However centrifugal force is not all bad, it has a really cool interpretation which yields a powerful insight. Consider a satellite in an elliptical orbit. As it reduces its radial distance to the sun, it must pump energy into its tangential velocity, to conserve angular momentum. So its tangential kinetic energy is a function of its position. Hey, that sounds like a potential! You can just add this "tangential kinetic potential" to the gravitational potential, yielding a bathtub shaped "effective potential." Now we're in 1D, since we're identifying angular effects with gravity. When the radial distance is large, the satellite will accelerate towards the sun (radial velocity decreasing), as it falls down the gravitational potential well. Eventually it begins to climb the "tangential kinetic potential" hill, and starts accelerating away from the sun (radial velocity increasing). In this 1D world, the sun is attractive at long range and repulsive at short range; the turning points are the apahelion and perihelion of the orbit. What's so cool about this is that we've reduced a 2D kinematics problem to a 1D problem (radial distance varying over time) by absorbing the tangential kinetic energy into the gravitational potential energy. This connects planetary orbits to more familiar problems like the 1D harmonic oscillator. The cost of doing so was the appearance of this "tangential kinetic potential;" the derivative of a potential is a force and that's centrifugal force.

KolenCh 5y ago

Non-inertial frame isn’t the problem, proper language is.