Weight of object in outer space away from galaxies

[Entr0py]

Homework Statement

Suppose an object were sent far out in space away from galaxies, stars, or other bodies. How would its weight change?

Homework Equations

w=mg where w and g are vectors

The Attempt at a Solution

Since mass is an intrinsic property and doesn't depend on external sources, then its mass is constant. But its weight would change. Let's say it has a mass m=1 kg. Then its weight on Earth would be 9.8 N. Then since the object is in space away from gravitational influences, wouldn't it be in a state of weightlessness? Because it has nothing to accelerate towards. So would its weight and apparent weight equal 0 N?

 

[CWatters]

Correct.

 

[Entr0py]

Thanks

 

[Entr0py]

Would that mean that the object is freely falling. I would think not because it has nothing causing it to accelerate towards (like a planet)

 

[CentrifugalKing]

Would that mean that the object is freely falling. I would think not because it has nothing causing it to accelerate towards (like a planet)

It's not free falling. If it were to, it would have an acceleration, which you clearly said it didn't.

 

[Entr0py]

It's not free falling. If it were to, it would have an acceleration, which you clearly said it didn't.

So the object is just still in space?

 

[Entr0py]

Not moving relative to everything else?

 

[CentrifugalKing]

So the object is just still in space?

Yes.

Not moving relative to everything else?

No. It is moving as motion is relative. However, it isn't explicitly in free fall. Free fall only occurs when there is gravity or any form of gravitational forces.

 

[phinds]

Technically there is no place in the known universe that is totally free of gravitational influence, since gravity extends to infinity.

For practical purposes an object can be far enough away from large bodies / gas clouds that it is effectively weightless, but it is never exactly weightless unless all gravitational forces cancel each other out and for a body in intergalactic space I would think that unlikely simply because it's a many-body problem of magnitude pretty much beyond human comprehension.

On the other hand, given the Cosmological Principle, perhaps it's reasonably to assume that forces DO cancel out, but I wouldn't bet on it.

 

[jbriggs444]

So the object is just still in space?

The idea that the object is still in space presupposes that "still" has a meaning in this context. It does not. An object sitting in the middle of nowhere is neither still nor moving unless you specify what it is still or moving relative to.

Space is not something that you can move relative to.

It's not free falling. If it were to, it would have an acceleration, which you clearly said it didn't.

Free fall can include the case of zero gravity. In physics, the term "free fall" means that a body is subject to no outside forces other than gravity.

 

[Entr0py]

The idea that the object is still in space presupposes that "still" has a meaning in this context. It does not. An object sitting in the middle of nowhere is neither still nor moving unless you specify what it is still or moving relative to.

Space is not something that you can move relative to.
Would this object be still relative to the very far away objects in space?

Free fall can include the case of zero gravity. In physics, the term "free fall" means that a body is subject to no outside forces other than gravity.

But wouldn't this object have ZERO gravitational attraction to anything in space if it is located far enough away that it isn't gravitationally attracted to anything (so an infinite distance away from everything else).

 

[phinds]

But wouldn't this object have ZERO gravitational attraction to anything in space if it is located far enough away that it isn't gravitationally attracted to anything (so an infinite distance away from everything else).

You cannot be "an infinite distance away from every things else". Please reread post #9

 

[jbriggs444]

Technically there is no place in the known universe that is totally free of gravitational influence, since gravity extends to infinity.

For practical purposes an object can be far enough away from large bodies / gas clouds that it is effectively weightless, but it is never exactly weightless unless all gravitational forces cancel each other out and for a body in intergalactic space I would think that unlikely simply because it's a many-body problem of magnitude pretty much beyond human comprehension.

On the other hand, given the Cosmological Principle, perhaps it's reasonably to assume that forces DO cancel out, but I wouldn't bet on it.

Imagine a pair of planets in deep space. Imagine that they are supported in some manner so as to remain a fixed distance apart. Consider a line drawn from the center of one planet to the center of the other. In a region near this line, the component of the net gravitational influence perpendicular to this line always points toward the line. Exactly on the line, the net gravitational force is entirely along the axis of the line.

Consider the gravitational force along the line. At the one end it points toward the one planet. At the other end it points toward the other planet. It varies smoothly along the length of the line. There must be a point somewhere along the line where gravity is exactly zero.

If you factor in the gravitational influence of the rest of the universe, the position where this happens may change. But there will still be such a point.

 

[phinds]

Imagine a pair of planets in deep space. Imagine that they are supported in some manner so as to remain a fixed distance apart. Consider a line drawn from the center of one planet to the center of the other. In a region near this line, the component of the net gravitational influence perpendicular to this line always points toward the line. Exactly on the line, the net gravitational force is entirely along the axis of the line.

Consider the gravitational force along the line. At the one end it points toward the one planet. At the other end it points toward the other planet. It varies smoothly along the length of the line. There must be a point somewhere along the line where gravity is exactly zero.

If you factor in the gravitational influence of the rest of the universe, the position where this happens may change. But there will still be such a point.

Even given your rather awkward scenario, I don't agree with the statement I bolded.. Suppose, for example, that the rest of the universe nets out to the equivalent of a small third body off to one side somewhere. Then the net gravitational force isn't even ON the line.

It may be, as I said, that the Cosmological Principle does end up requiring that the net forces from everything cancel out but that is unlikely to happen on a line between two specific bodies.

 

[jbriggs444]

Even given your rather awkward scenario, I don't agree with the statement I bolded.. Suppose, for example, that the rest of the universe nets out to the equivalent of a small third body off to one side somewhere. Then the net gravitational force isn't even ON the line

Gravitational force is not a position. It makes no sense to say that it is or is not on the line.

It may be, as I said, that the Cosmological Principle does end up requiring that the net forces from everything cancel out but that is unlikely to happen on a line between two specific bodies.

You have failed to understand the scenario. If the planets are alone in the universe then surely you agree that there will be a point where gravitational force is zero and that this point will be somewhere on the line between the planets, right?

If the gravitational influence of the rest of the universe in the neighborhood of the planets is small, there will still be a path between the two planets where the component of the net force of gravity perpendicular to the axis between the planets is zero. This path may not coincide with the line between the two planets, but it will exist. There will be a point on this path where the gravity is zero.

 

[phinds]

Gravitational force is not a position. It makes no sense to say that it is or is not on the line.

you're right. What I meant was that the zero point of gravitational attraction was not on the line. Very careless of me. Thanks.

You have failed to understand the scenario. If the planets are alone in the universe then surely you agree that there will be a point where gravitational force is zero and that this point will be somewhere on the line between the planets, right?

You didn't say they were alone. Yes, if they are alone then I agree but that is not a real-world scenario, it's like a freshman physics problem finding the zero point between the Earth and the moon, ignoring all other forces.

If the gravitational influence of the rest of the universe in the neighborhood of the planets is small, there will still be a path between the two planets where the component of the net force of gravity perpendicular to the axis between the planets is zero. This path may not coincide with the line between the two planets, but it will exist. There will be a point on this path where the gravity is zero.

I don't understand the bolded part but as I have said, it is possible that the cosmological principle dictates that the forces would all cancel out; I just don't think so. In the idealized case where the rest of the universe is represented by a single body, then it's a 3-body problem and I agree there is a zero point.

 

[jbriggs444]

I don't understand the bolded part but as I have said, it is possible that the cosmological principle dictates that the forces would all cancel out; I just don't think so. In the idealized case where the rest of the universe is represented by a single body, then it's a 3-body problem and I agree there is a zero point.

Not the Cosmological Principle. The intermediate value theorem.

 

[Entr0py]

You cannot be "an infinite distance away from every things else". Please reread post #9

Thanks for clearing up my confusion.

 

[Entr0py]

Not the Cosmological Principle. The intermediate value theorem.

How so? Isn't that a rule from calculus?

 

[phinds]

How so? Isn't that a rule from calculus?

Yeah, don't get that either.

 

[jbriggs444]

How so? Isn't that a rule from calculus?

It is a theorem in real analysis, yes.

 

[Entr0py]

Gracias for the reply.

 

[Entr0py]

Yeah, don't get that either.

I'm confused by what you mean? By the way, is that a Great Pyrenees in your picture?

 

[phinds]

I'm confused by what you mean? By the way, is that a Great Pyrenees in your picture?

I meant that the Great Pyrenees shares your confusion as to why that theorem was brought up in this context.

 

[Entr0py]

Ahh, clever way to answer my question.

 

[jbriggs444]

I meant that the Great Pyrenees shares your confusion as to why that theorem was brought up in this context.

Apply the theorem three times. For convenience place the two planets in directions labelled "east" and "west". We have a region of space where the vertical component of gravity points downward near the top of the region and points upward near the bottom. Accordingly, there is a surface where the vertical component is zero.

Within this surface, the north/south component of gravity is northward in the southern area and southward in the northern area. Accordingly there is a path where the north/south component is zero.

Within this line, the east/west component of gravity is eastward in the eastern area and westward in the western area. Accordingly there is a point where the east/west component is zero.