It is written in my text that in space we feel weightlessness. But I have been wondering what about the weight that arises due to revolution around the Earth. Wouldn't someone be feeling the weight due to centripetal force in space?
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$\begingroup$ we feel weightless in free fall and in space ( assuming you meant to be in revolution about the earth) we are still in free fall ... Yes you are falling but not hitting the earth because it is a curved body and not flat... $\endgroup$– AnkitCommented Jul 24, 2021 at 4:43
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$\begingroup$ What do you mean by "weight that arises due to revolution around the earth"? $\endgroup$– David WhiteCommented Jul 24, 2021 at 4:55
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$\begingroup$ Weight arises due to Normal Force the ground applies on you to counter Earth's gravity. The feeling of your weight comes through your feet (while standing) as it pushes against the ground. $\endgroup$– Tony StarkCommented Jul 24, 2021 at 5:39
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$\begingroup$ You don't have to be revolving around the earth to be in space. $\endgroup$– SteevenCommented Jul 24, 2021 at 6:46
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$\begingroup$ You might want to read answers to this question which explain more. Note that as commonly used, the phrases "weightless" and "zero G" are the same thing (although nothing is actually "zero G" in realiry). space.stackexchange.com/q/54198 $\endgroup$– StilezCommented Jul 25, 2021 at 0:34
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4 Answers
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You body cannot feel a force that applies equally to every atom in your body. Gravity does this (excluding situation where tidal forces are relevant).
On the other hand things like a chair, wall, or floor pushing on you is felt as "weight" because it doesn't apply to every molecule equally. The biological reason for this is what you "feel" is your nerves getting pressed by surrounding tissue.
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$\begingroup$ I get what you are saying, but it does not mean that if we don't feel the force it doesn't exist. In space centrifugal force equally apply on body parts and thus we don't feel it just like gravity but won't there be a net weight due to this force ? $\endgroup$– CyberaxCommented Jul 30, 2021 at 4:48
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$\begingroup$ Centrifugal force is not itself a force - it is a label for a force that keeps an object in circular force. The centrifugal force in space is gravity. You do not feel gravity. The centrifugal force acting on your body in a car is the seat and seat belt - you do feel those because they don't apply force evenly across every molecule of your body. $\endgroup$– Señor OCommented Jul 30, 2021 at 5:08
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$\begingroup$ Thanks for explanation, just one more thing to ask. In my text there is a problem in which one has to find the true weight of an object which weighs 10N at the north pole in a geostationary satellite. It comes out to be 0.23N . So what is this weight in the answer i am getting ? $\endgroup$– CyberaxCommented Jul 30, 2021 at 7:57
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$\begingroup$ @Cyberax earth's gravity is about 50 times weaker at that orbit (~35 km) compared to at the surface, and we most use the word "weight" as force due to gravity (though it can be force in general). If you're in a stronger gravitational field, you "weigh" more, even though you have the same mass. But it still stands you can never feel the force of gravity, only the force of something pushing against you. $\endgroup$– Señor OCommented Jul 30, 2021 at 21:08
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If you were in a satellite orbiting the earth, the centripetal force will be given by $$F=\frac{mv^2}{r}$$ where $m$ is the mass of the satellite, $v$ is its tangential velocity, and $r$ is its distance away from the center of the earth. If you are in a satellite in orbit around the earth, you are essentially in free-fall, and hence "weightless" as you stated.
But the centripetal force is equal to the gravitational force on it due to the earth, so that $$F_g=\frac{GMm}{r^2}=\frac{mv^2}{r}$$ In other words, by being in orbit, gravity provides the centripetal force required to keep the satellite in orbit. This means that the centripetal force is the same as the weight of the satellite.
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In the language of forces and acceleration:
When you feel your weight, standing on the ground, you are experiencing a normal force (from the ground) balancing gravity, and your acceleration is 0.
When you are in orbit, you feel no normal force from the ground, only gravity, and your acceleration is g=v^2/r.
So, somehow, the net force you feel is not the same as the net force that goes into F = ma. Because on the ground you feel a force with no acceleration, and in space you feel no force but have acceleration. How puzzling!
In the language of general relativity:
When you are on the ground, your geodesic with no other forces would be causing you to move towards the center of the Earth, but you are prevented from taking your natural trajectory. You are deviating from your natural trajectory (your geodesic) because of a force (the normal force) and you are accelerating relative to your geodesic.
When you are in orbit or in space or in freefall in a falling elevator or in the Vomit Comet, you are following your geodesic because no other forces are acting on you. You are not accelerating relative to your geodesic, hence you feel weightless. But you are accelerating relative to someone on the ground.
In the GR perspective, your felt force is now corresponding to your acceleration, but your definition of 'moving in a straight line' is now warped or curved (that's the concept of a geodesic).
In both languages, weightlessness actually means you are accelerating relative to a stationary observer on the surface, but you might say they are the ones accelerating relative to you.
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Yes weightlessness really occurs. I think you are confusing centrifugal force and the artificial gravity it can create. When you are orbiting a planet you are in freefall and that is different.
answered Jul 24, 2021 at 5:25