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I watched some video saying that there is still gravity in space station and almost same strong as it on Earth, the reason they feel no gravity is because the centrifugal force of the orbit is same as the gravity.

So I wonder, if a person fall into a black hole, but his head and feet is pulled by the same amount of gravity, so he doesn't get spaghettification, would he even notice he is pulled by the gravity?

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I think black hole isn't a good example. What if you are inside a field where every molecule constantly get pulled by a 100mg force (100 times stronger than Earth's gravity), and you don't resist the force, you follow it to do the 100g acceleration, then can you feel the 100mg force pulling on you?

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    $\begingroup$ Please link to the video. $\endgroup$ – Ben Crowell Jul 8 '19 at 17:01
  • $\begingroup$ His head and feet experience different amounts of gravitational force. For a supermassive black hole the difference is slight. For a stellar black hole the amount is enough to spaghettify him. $\endgroup$ – G. Smith Jul 8 '19 at 17:09
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    $\begingroup$ Regarding the space station... the force on a mass $m$ outside the Earth, due the Earth’s mass $M$, is $GMm/r^2$, where $r$ Is the distance of $m$ from the center of the Earth. The $r$ at the space station is not much larger than the $r$ at the surface. $\endgroup$ – G. Smith Jul 8 '19 at 17:14
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    $\begingroup$ You don't feel gravity when you're standing on the surface of the earth. You feel the normal force (in the bottom of your feet) that is opposing the gravitational attractive force that the earth is putting on you. $\endgroup$ – David White Jul 8 '19 at 17:40
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    $\begingroup$ I think you need to define what you mean by "feel" $\endgroup$ – Aaron Stevens Jul 8 '19 at 18:30
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Although description of the effects of gravity as a force is not appropriate when discussing gravitational effects near very dense objects like the black holes (we use general relativity for that), consider the following argument:

According to Newtonian gravity the force is proportional to $1/r^2$ from the center of the gravitating object. In orbit around earth the astronauts are about $7000*10^3$ meters from the center of earth. If the height of an astronaut is 2 meters then the difference of the gravitational force between her head and her feet is proportional to $$1/(7000*10^3)^2-1/(7000*10^3+2)^2=1.16618*10^{-20}$$ On the other hand, if earth was a very compact object and we could get as close as 1 meter to the center of the earth without reaching the surface of earth, the same difference of forces between head and feet would be proportional to $$1/(1)^2-1/(1+2)^2=0.888889$$ That is 20 orders of magnitude stronger!

Such effect of gravity are extremely weak in most cases since objects the size of 1 meter are extremely light and objects that are very heavy are much much larger than 1 meter.

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If the local gravity is such that the acceleration due to gravity ($g$) is the same at the location of all the molecules in your body, then all the molecules will accelerate at $g$ and if there are no other forces on you then you will feel nothing at all. So yes, you can have super-high gravitational acceleration and feel nothing.

The other answers deal with the case where the acceleration due to gravity is different at different parts of your body. In that case you will experience a squashing or squeezing effect called the tidal effect of gravity.

Now for an added thought. At any place you can always imagine a reference frame moving near that place with a very high acceleration. Relative to that reference frame you have a high acceleration! But you don't notice, because it is like the situation in the first paragraph of my answer.

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The answer here is no. Einstein's equivalence principle states that, so long as you can't feel tidal forces, that free-falling and floating in empty space are indistinguishable. This is because, in both cases, there is a sense in which you are moving in a straight a line as possible, with no forces acting on you. This interpretation is the basis for General Relativity.

And, for what it's worth, a black hole is not a bad example. If the black hole is massive enough (and you ignore the infalling radiation from the rest of the universe), the equivalence principle tells us that an infalling observer should notice nothing special about the horizon (except, of course, that the observer can no longer escape it). Of course, this is simply what classical General Relativity tells us. We know that General Relativity must be modified in order to resolve certain inconsistencies surrounding black holes, so it's anyone's guess what actually happens near the event horizon.

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Yes of course but for very short time. In the scenario you want to discuss the person’s body will be ripped apart but before getting ripped he will be feeling a huge pain due to gravitational pulling. The molecule in his body will be pulled by gravity and person will disintegrate.

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Feeling needs to be defined. Do you feel gravity while standing on earth? Say yes. We are used to this feeling. We are not used to free fall, so, we will feel the free fall. Because that will be a feeling very different from what we are used to, so, we will feel lack of the feeling that we are so used to. Meaning we will feel it.

Will we feel it as acceleration - No! Because all parts of our body move together at same speed all the time.

Will we feel differently while falling free on two very different planets - No. Because on both planets, all parts of our body move together at same speed all the time. Though that speed will be different on the two planets, but same for all parts of the body in both cases.

Proximity of a black hole (spaghettification) would be felt painfully.

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There are two cases:

  1. Free falling towards Earth, you would feel nothing special, like no force was acting on you. You are on a geodesic, and you feel as if no force was acting on you. Why? Let's disregard atmosphere. If you let two objects fall to Earth, they will arrive at the same time. Why? Because in the geodesic equation, the only thing that matters is the acceleration they will feel, their masses do not matter. Now your body is made up of different parts, that have different weight, so they should not move at different speeds towards Earth (disregarding atmosphere), so you will feel as if you were floating.

  2. Free falling into a black hole. Now it is a common misconception that you will feel something when you cross the EH, but in reality, you will not even notice you crossed it. Spaghettification depends on the type of balck hole as you see in the comments.

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  • $\begingroup$ Your number 1 seems to suggest that due to the nature of geodesics, bodies shouldn't be able to experience tidal forces. I know nothing about geodesics, but that doesn't seem correct to me. "If you let two objects fall to Earth, they will arrive at the same time." Only if you release them from the same location; which on a body made of multiple parts, would literally be impossible. $\endgroup$ – JMac Jul 8 '19 at 18:51
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Generally speaking, because it is not an inertial frame of reference, you could at least tell that the field was accelerating you (at least if you could see something as a reference point like a nearby satellite or something). Now as for whether or not you would actually feel anything, that opens an entirely new can of worms. The basic "intuition" (I use quotes because this is going to be somewhat of a blasphemous portrayal of GR) for general relativity is that in 4D space-time, objects want to move on their geodesics, or "path of least resistance." In this case, that would be unobstructed motion through the gravitational field, so you would feel exactly the same as if you were weightless on the space station, or as if you were falling. They are in fact the same basic principle, which is that in a gravitational field if there is nothing to impede your path, you will exist in a state of "free-float" essentially weightlessness until you are prevented from continuing to move along the geodesic (say by a planet). Now does the sensation of weightlessness count as feeling the field? You would not feel a "pulling" force as if you where on Earth or some other planet, that is for certain, however you would probably still be aware of the acceleration.

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