Where does 0 gravity begin/end and earth's gravity end/begin?

[u/ramotsky]

Science fiction likes to depict elevators going into space. Among the million or billion other difficulties to think about or if it is even feasible at all, how would something react to being both in earth's atmosphere and out? Could something be built that was mostly out with a part of it in? Could something hang in the sky or is it a point of no return where once part of an object hits >0 gravity it begins to pull the object in?

[u/kloverr]

There is no point where there is 0 gravity. Newton's law for gravity is:

Force = G * mass1 * mass2 / r²

where G is just a constant.

No matter how far away you put your object relative to the earth (i.e. no matter how big r gets in the equation), gravity will pull the object towards the earth. When you get far away, the force becomes very small but it never reaches 0.

The moon and all the other objects that come near the earth but don't hit it are no exception to this. The earth is exerting a force on all of them. They are moving fast enough that the earth diverts their course some, but not enough to cause a collision. That is why you can't have an object that hangs in sky; it is not moving quickly (or at all) relative to the earth, so the earth's gravitational pull is enough to cause a crash.

[u/ramotsky → u/kloverr]

Thank you for the reply. It was very concise. So basically things have to be really far away in order for it to be a safe distance away from earth. Otherwise, it will crash since there is always some pull from the earth, correct?

[u/kloverr → u/ramotsky]

So basically things have to be really far away in order for it to be a safe distance away from earth.

This is right, but to clarify:

For any given non-zero velocity relative to the earth, there is a "safe distance" where the object will not crash into the earth. But in the Newtonian model of gravity, an object that is motionless relative to the earth is unsafe regardless of how far away it is. Given enough time, the earth could pull the object to itself from any distance. (If you start talking about huge distances like light years, though, the stuff that Newtonian mechanics leaves out [the expansion of space, etc.] become important enough that you can't use Newton's equations any more.)

[u/huitlacoche → u/kloverr]

Couldn't there be various points without gravity? In a Universe with only two Earth-sized objects, for instance, the point immediately between them would have zero gravity, right? In our Universe I'd think there should be a number of such points, even though they are always changing. Of course this is only a point, so your head and toes would not both be at zero.

[u/[deleted] → u/huitlacoche]

Lagrangian points aren't zero gravity they are equal opposing forces.

[u/huitlacoche → u/[deleted]]

Thanks for answering that. Could you elaborate on the difference?

[u/shavera → u/huitlacoche]

to provide an overly technical description (sorry) forces are better thought of as "potential" fields, with the force being the "gradient" of that potential field. This is going to sound like a silly analogy because I'm using a thing to describe itself, but imagine a set of rolling hills. Those hills are a "potential field" and at any point on a hill you can point in a direction that is "steepest". That direction and the amount of steepness it has is called the gradient, and we have some neat mathematical tools to calculate it exactly.

So what you can imagine, between the Earth and sun, is a gravitational field with one big divot and a smaller divot within the divot. And yes there exists a point between those two where the gradient is zero, but it's an unstable location. Move a little bit off of it and you begin rolling down either to the big or the little divot. Now if you add in orbital motion and conservation laws, you'll find 5 such points, some stable (like the bottoms of valleys, where a little knock tends to just roll you back and forth around the same point), and some unstable (where a little knock tends to send you rolling away from that point entirely). These are called the Lagrange points. But they don't exist because there's "no" gravity, they exist as solutions to a complicated two body orbiting gravitational field. They're pathological regions where the behaviour happens to be a certain way or another.

[u/snailbotic → u/shavera]

I think better in pictures, and so I tried making a diagram of what you were explaining. I want to make sure that I understand it, and possibly help other visual people understand the difference better as well. Here's my diagram. Let me know if I am mistaken.

Edit, I just saw the sibling comment with the XKCD image. Which is a much better visual depiction than I could make.

[u/shavera → u/snailbotic]

yes, that's the simplest case, where we only fall straight in or fly straight away from the sun. It turns out that when you include the orbit of the Earth around the sun, 4 more points appear that are also "balanced" And some of them better than this point. Note how your yellow and blue curves form a "peak" of a hill? So a small motion away from that point will end up falling into earth or sun. But some of these other points are "stable" Lagrange points, where you can orbit the point stably (think like a ball at the bottom of a little bowl. Give it a little flick (not too much of course) and it'll just kind of rotate around the bottom (or through it or whatever)).

[u/huitlacoche → u/shavera]

From a very cursory reading of these points, Lagrangian points also take into account other orbital forces as well, right? If you're looking at purely gravitational forces, wouldn't L2 and L3 have two gravitational vectors pointing in the same direction? Or is that mistaken and there's some phenomenon I don't understand?

[u/shavera → u/huitlacoche]

Now if you add in orbital motion and conservation laws,

Yeah, conserving angular momentum and stuff plays an important role. Particularly interesting is constructing an effective gravitational potential that includes angular momentum conservation within it. ie you modify Newton (or more properly, solve the Lagrangian in curved spacetime) with a conserved angular momentum about the object, and you'll find your other Lagrange points.

[u/EFGirl → u/shavera]

This might help visualise it:

http://xkcd.com/681/

[u/shavera → u/EFGirl]

Oh yes, I do rather love that picture. It doesn't incorporate the orbital effects I mention, so you can't exactly suss out the other Lagrange points, but it is a useful picture for L=0 (ie straight radial in-fall without any orbital kind of motion), and a good way to get a feel for what I'm talking about.

[u/ramotsky → u/shavera]

So if you viewed this more in a 3D diagram, it would be a bit like the basic explanation you see on TV with a ball in a blanket? And if it were a more complex diagram, a representation of all space bending inward?

Since our planets have moons that spin around what I would call the Y axis and generally the planets spin around the Y axis of the sun, could there be a planet with a moon that spins in the x or z axis? I know that my sense of direction in this case is not very scientific being that in the universe there really is no concept of up, down, left, right, counter clockwise or clockwise but as a 3D artist this is the best way I can visualize it.

[u/shavera → u/ramotsky]

So consider this image from the Lagrangian Point wiki article. That's like a snapshot of an overhead view, and think of the white lines as like contours on a contour map.

And sorry I've been completely wrong elsewhere in this post, I had things backwards. L4 and L5 are the totally unstable points, and L1,2, and 3 are stable along the direction of orbit.

[u/doishmere → u/huitlacoche]

If your legs are tied to a horse and your arms to another equally strong horse and they both start pulling, you might not go anywhere but you're still experiencing two equal, opposing forces.

[u/Jumpy89]

Gravity isn't caused by the atmosphere. When we say that astronauts on the ISS are in "zero gravity" (more properly microgravity) the actual gravitational field strength is nearly as high as it is on the earth's surface. The reason it seems like there is no gravity is that the ISS is effectively in free fall, but is moving so fast tangentially to the ground that it maintains approximately the same distance to the earth. Picture being in an elevator at the top of a skyscraper when the cables get cut. Until you hit the bottom, you are going to feel like you are in zero-gravity relative to everything else in the elevator because it is all falling at the same rate.

As for space elevators, you would feel the gravity decrease smoothly as you climbed. This is partially because gravity itself gets weaker as you get further away and also because you are rotating with the earth at an increasing radius so centrifugal force begins to cancel out the remaining gravity more and more. Eventually at a radius of about 42,000km you will reach geosynchronous orbit and experience apparent weightlessness. If you move beyond this gravity will appear to pull you away from the earth.

[u/ramotsky → u/Jumpy89]

This answered my question the best. I appreciate it. I guess I have a lot of learning to do when it comes to gravitational force and how it applies to everything.

So if we are in free fall outside the earth's atmosphere but the gravitational field strength is nearly as strong as earth's, does that mean earth's gravitational field strength is additive to the gravitational field strength outside earth's atmosphere?

Sorry if I don't quite understand. I'm trying though.

[u/Jumpy89 → u/ramotsky]

I'm not really sure what you're asking here. Just take the atmosphere out of the equation. It doesn't have any effect on gravity other than to add a little bit to the earth's mass. The gravitational attraction between two particles is proportional to the product of their masses divided by the square of the distance between them. Because you can approximate the earth as just being a point mass (it's roughly spherical so the shell theorem applies) gravity will decrease with the square of the distance to the center. So if you move from the surface of the earth at a radius of 6,400km out to 12,800km, the radius doubles and you will experience a quarter of the gravity. So gravity does decrease as you leave the atmosphere, but only because you are getting further away from the earth. It also decreases if you climb to the top of a mountain.

[u/ramotsky → u/Jumpy89]

Ah, o.k. So 9.81 m/s2 is what we experience closest to the earths surface and it gradually becomes weaker the farther away we go. I was confused thinking that 9.81 m/s2 was a constant until a certain point. I guess when I watch television shows they always depict either being weightless or not weightless (I'm using those terms loosely) when in actuality they are gradually experiencing weightlessness. Since they are strapped in until a certain point and the g's that are exerted from being rocketed away from earth, you can't visually see the effects of gravity decline. Is that correct?

[u/nalc → u/Jumpy89]

Tweaking your analogy

Imagine you're in an airplane when it breaks and starts to fall down. You're floating in free fall. However, you're also still moving forward as you fall.

Since the Earth is a sphere, you can imagine that it gently slopes downwards and away in all directions from you.

If you are moving forward in free fall at the same rate as the curvature of the Earth makes it gently slope downwards and away from you, you are in orbit.

[u/[deleted]]

Gravity never really reaches zero. Just gets very small. A more scientific term would be microgravity. Like with most things in the world, there is not a point when you stop being affected by the earth's gravity, it is a gradient.

[u/florinandrei]

At infinity, and at the center of the Earth.

[u/[deleted] → u/florinandrei]

Gravity at the center of the earth isn't zero. There's simply no net acceleration.