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For example, if the Sun suddenly disappeared, would we physically feel it 8 minutes later (not counting light/temperature), since propagates moves at the speed of light.

And if so, would the effect be noticeably different depending on size/distance?

Every answer I've seen so far is mostly about light and/or temperature, or our orbit. I am talking specifically about what the average person would feel in their body (like a drop or lurch or jolt).

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  • $\begingroup$ Does this answer your question? Sudden Effects of Sun Disappearing $\endgroup$
    – DarkDust
    Commented Nov 16, 2023 at 16:54
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    $\begingroup$ @DarkDust Not really. It does touch on the most important parts of the sun dissapearing, but not if our bodies would be able to "feel" the gravity well effectively vanishing. $\endgroup$ Commented Nov 17, 2023 at 8:38

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Firstly, the sun can't just "disappear". Even if it were converted by magic into "pure energy", that energy can't go anywhere faster than the speed of light, and Energy has gravitation equal to mass (by E=mc²)

However, the Earth and all its denizens are in free-fall around the sun. We are on a "space station" and so we are weightless with respect to the sun. Imagine the Earth vanished and the Space Station floated off in a straight line. The astronauts would not notice any change in their weighlessness.

There are small tidal forces. The sun can cause a tidal acceleration of $5\times 10^{-7}\ ms^{-2}$, more than a million times smaller than your weight on Earth. But these are not noticeable.

So you wouldn't directly notice if these forces suddenly ceased.

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    $\begingroup$ No, because people on the Earth's surface are not in free fall about the Earth. But the Earth (and everyone on it) are in free-fall about the sun. $\endgroup$
    – James K
    Commented Nov 16, 2023 at 21:53
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    $\begingroup$ If the sun would disappear, tidal forces will be not the first thing we notice. $\endgroup$ Commented Nov 17, 2023 at 4:44
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    $\begingroup$ "the sun can't just "disappear"" - Citation required $\endgroup$
    – Valorum
    Commented Nov 17, 2023 at 5:16
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    $\begingroup$ @BradV: "like an elevator instantly dropping from under you". Not instantly! Earth is compressed by it's gravity somewhat (iron densities 7.8, but Earths center is ~12 despite being ~6000K). If gravity "turns off" Earth will decompress. Initially the ground will accelerate upward exactly at 1g due to decompression. It will take maybe seconds to notice anything, and minutes before gravity is substantially reduced. $\endgroup$ Commented Nov 17, 2023 at 5:46
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    $\begingroup$ If, with a magic wand, the Sun would disappear almost instantaneously -- say, within one nanosecond -- there would be a gravitational ripple propagating at light speed with a steep gradient. A ns equivalent is 33cm. One moment there is the Sun's gravitation, the next moment there isn't; your feet are pulled, your head isn't. The difference creates tidal forces much larger than the ones caused by the inhomogeneous field, though still tiny. The Sun accelerates our feet at about 6mm/s^2, creating a tidal force of a few hundredth N which will be unnoticeable. $\endgroup$ Commented Nov 17, 2023 at 17:26
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No, the human body couldn't practically feel the sudden disappearance of a gravitational force

Humans are able to feel because different accelerations applied to different parts of the body cause it to deform. For example you can feel the jerk as a car comes to a complete stop (non-zero acceleration to zero acceleration), because a force that was being applied only to your bottom is suddenly no longer applied, which changes the overall flex of your spine (among other deformations).

On the other hand, gravitational fields between a very large body and a very small body are practically uniform across the small body. So no matter how the field changes, the same acceleration is being applied to every part of the smaller body at any point in time. Therefore a human body wouldn't deform if the sun disapeared, so the human would not feel the change.

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  • $\begingroup$ I'm afraid that's not how you feel jerk. Sure you can feel forces on your body too, but what you really sense is an inner-ear function, and it's inertial so it reports jerk relative to your current direction of motion. That's why those flight/driving simulators on big hydraulics never feel right - because the inertial component isn't there. And because it's dynamic, not static, the justification that you could remove all forces and have everything remain static is incorrect. Try removing the force on a swingball by cutting the string mid-swing and see if it changes the ball's travel. :) $\endgroup$
    – Graham
    Commented Nov 19, 2023 at 10:29
  • $\begingroup$ @Graham The inner ear can only feel acceleration because its structure deforms. Typically, the inner ear isn't being directly accelerated, it's being accelerated by its connection with the rest of the body; thus it deforms due to inertia. If the whole inner ear structure is accelerated uniformly, the acceleration will not be felt. As for why flight simulators feel different than real flight, it's because they don't reproduce all the same forces on the body as real flight. It's impossible to reproduce the same forces without reproducing the same flight path. $\endgroup$
    – Vaelus
    Commented Nov 19, 2023 at 18:00
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While I think James K's answer is correct, it may help to add to the explanation.

Consider the traditional Newtonian definition of gravity:

$$ F = G \frac{m_1 m_2}{r^2} $$

The two $m$ terms refer to the mass of two objects for which you want to know the attractive force. The $r$ term is more important to your question - it refers to the distance between the two objects. It's important to realise that it's a squared term, and on the bottom of the equation, meaning that the attractive force decays by the inverse square of the distance between the two objects. All this means is that objects need to be very close to have a significant attractive forces - what we experience as gravity.

Finally - Here's what it looks like if substitute in some numbers:

$G$ = 6.67430E-11 $\frac{\mathrm{N \cdot m}^2}{\mathrm{kg}^2}$ Gravitational Constant
$m_{\mathrm{you}}$ = 80 kg Approx mass of observer
$m_{\mathrm{Earth}}$ = 5.972E+24 kg Approx mass of Earth
$m_{\mathrm{Sun}}$ = 1.989E+30 kg Approx mass of the Sun
$r_{\mathrm{Sun}}$ = 149.6E+6 km Approx distance to the centre of the Sun
$r_{\mathrm{Earth}}$ = 6371 km Approx distance to the centre of Earth
$F_1 = \frac{G \cdot ( m_{\mathrm{you}} \cdot m_{\mathrm{Earth}} ) }{r_{\mathrm Earth}^2}$ = 785.598 N Force between you and Earth
$F_2 = \frac{G \cdot ( m_{\mathrm{you}} \cdot m_{\mathrm{Sun}} ) }{r_{\mathrm{Sun}}^2}$ = 0.475 N Force between you and the Sun
$ \frac{F_1}{F_2} $ = 1655.515 Factor difference between forces

You'll notice that the force between you and the Sun is the equivalent of the force exerted by 50 grams of mass on Earth - so not much.

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    $\begingroup$ But we are in a rotating frame of reference, so to find the force we feel you would need to subtract the "centrifugal force", which is 0.475 N $\endgroup$
    – James K
    Commented Nov 17, 2023 at 6:25
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From 1,156,810 kilometers that is very near but still outside the Sun.

The formula to calculate the tidal force F exerted by the Sun on an object like a human is given by:

F = 2 * G * M * r^2 / D^3

where G is the gravitational constant, M is the mass of the Sun, r is the the difference in distance between the two points on the object (assuming the height of the human, 2 m) and D is the distance between the astronaut and the Sun.

Further, we assume the human is able to sense a sudden change of the force equal to 1 power gram (nobody knows for sure but it you would feel a coin of this mass dropped on your palm).

This gives the distance of 1,156,810 km from the centre of the Sun that may be somewhat survivable with science fictional technologies. The Sun has the radius (not diameter) of 695,500 km.

Assuming a spaceflight (free fall), the astronaut would not feel the disappearance of the main gravity force.

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The text in the question body is a little at odds with the question itself, so I'm going to ignore anything specifically about the sun vanishing (since that involves a whole lot of extra baggage, and has been answered, and actually has a very small effect anyway).

Could we feel a sudden change in gravitation? Yes, but only indirectly. As far as our bodies are concerned, there's no such thing as gravity, but there is such a thing as weight (which is just gravity acting on a mass... like our body), involving things like prioperception and our inner ear.

We're quite good at detecting (large) changes in that. For experimental verification, use an elevator.

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  • $\begingroup$ The case of an elevator is different than an orbiting body, because the elevator pushes on your feet only. If the elevator pushed on all parts of your body uniformly, including the structures in your inner ear, you would not feel it accelerating you. $\endgroup$
    – Vaelus
    Commented Nov 18, 2023 at 17:21
  • $\begingroup$ @Vaelus Not true - you've forgotten that inertia also exists, because this is not simply static forces in equilibrium. The jerk you experience from an elevator or car has nothing whatsoever to do with where the force is applied, and everything to do with the fact that there is a change of acceleration relative to the current direction of travel. $\endgroup$
    – Graham
    Commented Nov 19, 2023 at 10:20
  • $\begingroup$ @Graham I think that is true. If the acceleration affected your body uniformly, there would be no changes for you to feel. What we feel in an elevator is different forces acting through our body due to the force being applied or lessened at our feet. That's the same reason we 'feel' the gravity of the earth when we're standing on it. $\endgroup$ Commented Nov 21, 2023 at 17:41

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