[SOLVED] Hypothetical question about gravity

[otacon14112]

I know planets orbit their star in an elliptical orbit, but for the sake of simplicity, suppose they orbit in a circle. The centripetal force of gravity keeps the planet from flying off into space. Now suppose you had a button that could instantly "turn off" gravity when you pushed it.

I'm not really sure how to word my question, so I guess I'll break it up into two questions:
1. If you pushed the button to turn off gravity, would the effect be instantaneous, causing the planet to go flying off into space at whatever velocity it was traveling at the moment gravity was turned off?
2. Can this be used to determine if gravity has a speed? For example, if it was possible to create a perfect, ideal scenario in which it was possible to measure the exact amount of time that had passed between the exact point in time you pushed the button (for example, assume there was no bouncing of the switch as the button approached its furthest inward position at the exact moment gravity was turned off) that caused gravity to instantly turn off (this point in time is t₀), and the exact point in time that the planet stopped traveling in a circle, and began to continue to travel at the velocity it had when gravity was turned off (this point in time is t₁), would t₁ - t₀ = 0, or would it be greater than 0, suggesting that gravity has a speed?

[MrEen]

1. Yes. (I'm not an expert on the subject, but I do drive by a Holiday Inn Express on the way to work.)
2. Gravity has an influence, but I don't think speed would be a good way to describe it. For example, the acceleration of an object in free fall on earth would be 9.8 meters per second, per second (and that measurement applies at sea level on Earth in a vacuum.) Here's a nice link with some math on the subject: https://www.grc.nasa.gov/www/k-12/airplane/mofall.html

[lsemmens]

WOW what are you on? I WANT some!!!!

Newton has answered this in his laws of momentum. If gravity were turned off the planets would keep travelling in a straight line at a tangent to the the original arc of momentum at the point gravity ceased. Until they hit another object which would then affect their trajectory according to the mass of the object they hit.

No, gravity does not have a "speed" it only has an attraction, depending upon the size of the attraction. Earth's gravity which we call G has a rate of attraction at 9.8m/second/second. In other words for every second an object is "falling" towards the Earth it accelerates at 9.8 m/s.

[otacon14112]

WOW what are you on? I WANT some!!!!

Newton has answered this in his laws of momentum. If gravity were turned off the planets would keep travelling in a straight line at a tangent to the the original arc of momentum at the point gravity ceased. Until they hit another object which would then affect their trajectory according to the mass of the object they hit.

No, gravity does not have a "speed" it only has an attraction, depending upon the size of the attraction. Earth's gravity which we call G has a rate of attraction at 9.8m/second/second. In other words for every second an object is "falling" towards the Earth it accelerates at 9.8 m/s.

I'm confused by your surprise.

Right, but ignoring the potential energy of a ball hanging in air (since gravity still pulls on it as it's suspended by a string), it starts falling the exact moment the string breaks. For example, even though at 0.0000000001 seconds after the string breaking, the acceleration is is negligible enough to say that it hasn't even moved, even though it has moved a very small distance. This isn't the same situation as I'm proposing, though. I'm asking if the point in time that the attraction ceases to exist between the two (ignoring the very slight attraction of distant objects elsewhere in space) would be the same point in time that gravity is "shut off"? Or would this point in time be later?

[otacon14112]

I found the answer to my question. Gravity does have a speed. I didn't know about gravitons. Depending on the situation, they have the same speed as light.

https://www.quora.com/Why-is-the-speed- ... d-of-light
https://www.researchgate.net/publicatio ... e_Features

[Fred Barclay]

Semi-competent physicist here...
I primarily deal with radiation physics (similar concepts as nuclear physics but different focus) so I'm no cosmologist, but I'll give this a shot.

Gravity has a "speed" yes, but that's really how fast gravity waves or particles (hypothesized "gravitons") propagate through space. I know almost nothing about gravitons. However, https://www.forbes.com/sites/startswith ... 3f4fee604b looks like a great resource for understanding gravity waves!

MrEen and Isemmens are pretty close when talking about "g" (aka "small g"). Gravitational acceleration on Earth's surface is around 9.81 m/s^2, although it varies with elevation and distance from the equator, among other things.
More universally, Newton's Law of Universal Gravitation gives us the force of gravitation attraction between any two objects 1 and 2:
F = (G* M * m)/r^2 where r is the distance between the two objects, M and m are their respective masses, and G (aka "big G") is the "gravitational constant".
If you also use Newton's Second Law: F = m*a where m is any mass and a is its acceleration, you can call this particular acceleration "g" and then set the two forces equal to each other.

F = F
(G * M * m)/r^2 = mg
(G * M)/r^2 = g

For Earth, use our mass (~5.97x10^24 kg) and radius (~6.378x10^6 m) and you get g = 9.8 m/s^2 at Earth's surface. For any other body -- the Sun, another planet, the Moon, any star, and so on -- your "g" will be different because they have different masses and different radii.

Why am I mentioning this? Because you're both right. Gravity does propagate at a particular speed, but that doesn't affect how quickly things "fall". That's determined by Newton's Law of Universal Gravitation. As orbiting bodies are really in constant free-fall towards their sun, this also affects their behavior if gravity is switched off.

If gravity were turned off the planets would keep traveling in a straight line at a tangent to the the original arc of momentum at the point gravity ceased.

That's pretty much it.If gravity were to suddenly quit affecting them, they'd fly off in exactly a straight line from how their velocity vector was pointing at that exact instance at the exact same velocity magnitude.

For example, even though at 0.0000000001 seconds after the string breaking, the acceleration is is negligible enough to say that it hasn't even moved, even though it has moved a very small distance

Not exactly. Acceleration isn't negligible even for a super-short time period "dt"; it's always constant. In this case, on Earth, a = 9.81 m/s^2. Now the displacement would be negligible enough for sure! (Displacement would be the double integral of acceleration with respect to time; equivalently, acceleration is the second derivative of displacement with respect to time).

I'm asking if the point in time that the attraction ceases to exist between the two (ignoring the very slight attraction of distant objects elsewhere in space) would be the same point in time that gravity is "shut off"? Or would this point in time be later?

This is where things get freaky. Yes, no, maybe so, depending on your frame of reference. First off, the time interval between gravity going MIA and you seeing the planet flying off depends on light speed alone. You can't see any result before light has had time to reach you. No matter the real speed at which gravity propagates, you're limited by how quickly you can observe its effects.

As I understand it, though, the big issue with this thought experiment is that gravity is just the curvature of space-time. If gravity ceases to exist, then space-time as we know it would be fundamentally altered. Maybe our concept of elapsed time would be very different in that scenario.

I hope that's right??
Cheers!
Fred

[trytip]

In other words for every second an object is "falling" towards the Earth it accelerates at 9.8 m/s.

you forget to mention that at terminal velocity an object which is "falling" towards the Earth will not accelerate past about 200 km/h (120 mph) and that further minimization of drag by streamlining the object's body allows for speeds in the vicinity of 480 km/h (300 mph)

[catweazel]

In other words for every second an object is "falling" towards the Earth it accelerates at 9.8 m/s.

[Edit: Everyone forgot] to mention that...

... gravity isn't a force, it's a field.

[otacon14112]

First off, the time interval between gravity going MIA and you seeing the planet flying off depends on light speed alone. You can't see any result before light has had time to reach you. No matter the real speed at which gravity propagates, you're limited by how quickly you can observe its effects.

I was talking about the difference in time between when gravity was turned off, and the exact moment when the planet stopped orbiting the star and began continuing on its velocity (adding a tangent line reference is redundant, since velocity is a vector). There is no need to wait until light reached the observer, since there is no observer involved (there doesn't need to be a scientist hypothetically watching from an observatory in this scenario for us to know the unfolding event); this is a hypothetical situation in which you would instantly know, as if you were outside the universe watching the simulation (or whatever you want to call this hypothetical scenario).

I don't see how acceleration is relevant here, since it should theoretically cease to matter as soon as the planet experiences zero gravity, since it would no longer be falling at a constant speed (and continuously changing direction) toward the star. At that exact time, I would think that it would immediately stop falling toward the star, and instantly begin to continue on its current velocity.

I thank everyone for their input, but what does the acceleration rate near Earth (9.8 m/s/s) have to do with this situation? That unnecessarily adds more complexity to this scenario.

[catweazel]

...and instantly begin to continue on its current velocity.

Velocity, in its most simplest form, is the speed of something in a given direction. Furthermore, for all intents and purposes, the speed of gravity is the speed of light. In the old Newtonian days, back in the mists of time, up to Einstein, your question would have a radically different answer than the answer given today.

[otacon14112]

...and instantly begin to continue on its current velocity.

Velocity, in its most simplest form, is the speed of something in a given direction.

Yeah; that's why I used the word "velocity" to refer to the behavior of the planet beginning with the exact moment it would experience a loss of the centripetal force. And it's also why adding a tangent line reference to my velocity references is redundant.

[catweazel]

...and instantly begin to continue on its current velocity.

Velocity, in its most simplest form, is the speed of something in a given direction.

Yeah; that's why I used the word "velocity" to refer to the behavior of the planet beginning with the exact moment it would experience a loss of the centripetal force. And it's also why adding a tangent line reference to my velocity references is redundant.

Regarding your .sig: "Otacon: You remember pre-ripped jeans? Manufacturers thought that just because people loved old, broken-in jeans, they would want to buy new jeans that looked old..."

My youngest daughter once came home in a brand new pair of ripped jeans. In front of the entire family at dinner, I tossed her a 50c piece. When she asked what it was for, I said, "Buy the rest of your jeans."

[otacon14112]

Velocity, in its most simplest form, is the speed of something in a given direction.

Yeah; that's why I used the word "velocity" to refer to the behavior of the planet beginning with the exact moment it would experience a loss of the centripetal force. And it's also why adding a tangent line reference to my velocity references is redundant.

Regarding your .sig: "Otacon: You remember pre-ripped jeans? Manufacturers thought that just because people loved old, broken-in jeans, they would want to buy new jeans that looked old..."

My youngest daughter once came home in a brand new pair of ripped jeans. In front of the entire family at dinner, I tossed her a 50c piece. When she asked what it was for, I said, "Buy the rest of your jeans."

Ha, nice! I don't know if you've ever played Metal Gear Solid, but Otacon is a scientist who provides information via encrypted burst radio transmissions to Snake when he's on special stealth missions. He tries to take the place of a former advisor to Snake who used to provide inspirational quotes and wisdom, but he usually ends up sounding awkward instead . That quote is one of the best examples of when his attempts to inspire and enlighten Snake goes awry, and ends up being awkward instead lol.

I don't understand why people want pre-ripped jeans. I really would like to know their reasoning for wasting their money on them. I came of age in the '90s, back when it was in style wear ripped jeans and flannel, but the jeans were ripped because they got worn out, not because they were purchased that way.

[Pippin]

Also see:
https://www.youtube.com/watch?v=YkWiBxWieQU

[trytip]

... but what does the acceleration rate near Earth (9.8 m/s/s) have to do with this situation? That unnecessarily adds more complexity to this scenario.

well i'm no physicist and far from it but i do like the topic. i especially like the idea used in Star Trek IV where they use Sol's (the sun) gravity to slingshot around and gain momentum in order to go back in time and also use the same formula (modified in reverse i guess) to return to the future. i like the idea but it's as improbable as planting toasters and expecting a crop of refrigerators

gravity only exists in this universe because of celestial objects. there is no gravity without mass and gravity exhumes a different field depending on size of mass. if you're on the moon and you jump you come back slower, but if you're on jupiter and you jump, gravity would've already flattened you to a pancake before you even tried jumping.

don't know what terminal velocity is on mars or jupiter but i'm sure it's much greater than here on earth. gravity is relative. i hear albert einstein says time is also relative, but i believe different. i believe time is the one true phenomenon in the universe that is absolute constant and does not need a source. gravity and light are only bi-products therefore we can use them to our advantage but we can not and will never manipulate time.

gravity does not manipulate time

[jmorris84]

I was just listening to a podcast by Michio Kaku the other day where these very questions came up. I believe it centered around what would happen if the sun just vanished and how long it would take for the Earth to be flung into space off of its orbital path.

If I remember correctly, he said no one really knows because an experiment has really never been done to find out but it is believed to be about 8 minutes. He also mentioned that gravity's speed is the same as the speed of light.

[BG405]

This is interesting. I've always thought that gravitational fields mutually interact, therefore the effect of our star instantaneously vanishing would have an immediate effect on the orbit, even though we wouldn't see the light vanish for ~8 minutes.

As for the gravity at the top of Jupiter's atmosphere, you would probably find it hard to stand up but it wouldn't actually crush you .. unlike the surface of a White Dwarf, or a Magnetar (sp?) etc. & Mars AFAIK has about a third of Earth's pull at its surface.

A subject I've certainly given some thought; a lot to learn, evidently!

[catweazel]

i hear albert einstein says time is also relative, but i believe different. i believe time is the one true phenomenon in the universe that is absolute constant and does not need a source. gravity and light are only bi-products therefore we can use them to our advantage but we can not and will never manipulate time.

gravity does not manipulate time

There goes more than a hundred years of quantum mechanics.

[Pippin]

Yeah, and Einstein?
https://www.youtube.com/watch?v=6zWy6_Mog70

[lsemmens]

I did not forget terminal velocity, I consciously omitted it as it is a factor of atmospheric interaction, and not really anything to do with gravity.

Of course we all know that Gravity is a myth.......the earth SUCKS!!!!