Circular orbits on a warped spandex fabric

In Einstein’s theory of general relativity (GR), gravity is described as the warping of space and time due to the
presence of matter and energy. In GR gravity is understood not as a force of one massive object acting on another,
but rather as the manifestation of an object residing in the warped spacetime of another. In Newtonian gravitation
planetary orbits arise as the result of a planet encountering the attractive force of the Sun. In GR, orbits arise
from geodesics of free bodies moving in curved spacetime, in which their “straight line” paths are curved due to the
non-Euclidean geometry involved.

spandex eh….

the 70’s called…

ChrispenEvan said:

Circular orbits on a warped spandex fabric

In Einstein’s theory of general relativity (GR), gravity is described as the warping of space and time due to the
presence of matter and energy. In GR gravity is understood not as a force of one massive object acting on another,
but rather as the manifestation of an object residing in the warped spacetime of another. In Newtonian gravitation
planetary orbits arise as the result of a planet encountering the attractive force of the Sun. In GR, orbits arise
from geodesics of free bodies moving in curved spacetime, in which their “straight line” paths are curved due to the
non-Euclidean geometry involved.

So what was the conclusion of their investigations?

The Rev Dodgson said:

ChrispenEvan said:

Circular orbits on a warped spandex fabric

In Einstein’s theory of general relativity (GR), gravity is described as the warping of space and time due to the
presence of matter and energy. In GR gravity is understood not as a force of one massive object acting on another,
but rather as the manifestation of an object residing in the warped spacetime of another. In Newtonian gravitation
planetary orbits arise as the result of a planet encountering the attractive force of the Sun. In GR, orbits arise
from geodesics of free bodies moving in curved spacetime, in which their “straight line” paths are curved due to the
non-Euclidean geometry involved.

So what was the conclusion of their investigations?

rubber sheets while good for initial demos fall down with closer inspection.

ChrispenEvan said:

The Rev Dodgson said:

ChrispenEvan said:

Circular orbits on a warped spandex fabric

In Einstein’s theory of general relativity (GR), gravity is described as the warping of space and time due to the
presence of matter and energy. In GR gravity is understood not as a force of one massive object acting on another,
but rather as the manifestation of an object residing in the warped spacetime of another. In Newtonian gravitation
planetary orbits arise as the result of a planet encountering the attractive force of the Sun. In GR, orbits arise
from geodesics of free bodies moving in curved spacetime, in which their “straight line” paths are curved due to the
non-Euclidean geometry involved.

So what was the conclusion of their investigations?

rubber sheets while good for initial demos fall down with closer inspection.

as we all know. they explain why.

ChrispenEvan said:

ChrispenEvan said:

The Rev Dodgson said:

So what was the conclusion of their investigations?

rubber sheets while good for initial demos fall down with closer inspection.

as we all know. they explain why.

Where does dark matter fit into this?

Tamb said:

ChrispenEvan said:

ChrispenEvan said:

rubber sheets while good for initial demos fall down with closer inspection.

as we all know. they explain why.

Where does dark matter fit into this?

nowhere.

some people don’t think rubber be frictioned but it do.

ChrispenEvan said:

Tamb said:

ChrispenEvan said:

as we all know. they explain why.

Where does dark matter fit into this?

nowhere.

But it is ~85% of the universe. Surely it has an effect.

Tamb said:

ChrispenEvan said:

Tamb said:

Where does dark matter fit into this?

nowhere.

But it is ~85% of the universe. Surely it has an effect.

27% this analogy is about a planet obitting a star. DM on those scales has little to no effect. also this is about why the rubber sheet analogy is an inaccurate representation of how gravity works.

ChrispenEvan said:

Tamb said:

ChrispenEvan said:

nowhere.

But it is ~85% of the universe. Surely it has an effect.

27% this analogy is about a planet obitting a star. DM on those scales has little to no effect. also this is about why the rubber sheet analogy is an inaccurate representation of how gravity works.

OK
But DM is ~85% of matter & ~25% of energy.

Tamb said:

ChrispenEvan said:

Tamb said:

But it is ~85% of the universe. Surely it has an effect.

27% this analogy is about a planet obitting a star. DM on those scales has little to no effect. also this is about why the rubber sheet analogy is an inaccurate representation of how gravity works.

OK
But DM is ~85% of matter & ~25% of energy.

I think you are thinking of Dark Energy, which is a completely different thing, if it is a thing at all.

ChrispenEvan said:

The Rev Dodgson said:

ChrispenEvan said:

Circular orbits on a warped spandex fabric

In Einstein’s theory of general relativity (GR), gravity is described as the warping of space and time due to the
presence of matter and energy. In GR gravity is understood not as a force of one massive object acting on another,
but rather as the manifestation of an object residing in the warped spacetime of another. In Newtonian gravitation
planetary orbits arise as the result of a planet encountering the attractive force of the Sun. In GR, orbits arise
from geodesics of free bodies moving in curved spacetime, in which their “straight line” paths are curved due to the
non-Euclidean geometry involved.

So what was the conclusion of their investigations?

rubber sheets while good for initial demos fall down with closer inspection.

Yep.

Here’s a good fun question, to see if you understand the warping of space in GR. A ball thrown up under the influence only of gravity follows a parabolic arc. But in GR the warping of space ensures that under a constant gravitational force, the curvature of the geodesic is constant. A ball thrown up travels along a geodesic, a circular arc not a parabolic arc.

How can you resolve the discrepacy?

Every time i ask myself this question i have to look up the answer. It always seems obvious in retrospect, but i can never remember it.

mollwollfumble said:

ChrispenEvan said:

The Rev Dodgson said:

So what was the conclusion of their investigations?

rubber sheets while good for initial demos fall down with closer inspection.

Yep.

Here’s a good fun question, to see if you understand the warping of space in GR. A ball thrown up under the influence only of gravity follows a parabolic arc. But in GR the warping of space ensures that under a constant gravitational force, the curvature of the geodesic is constant. A ball thrown up travels along a geodesic, a circular arc not a parabolic arc.

How can you resolve the discrepacy?

Every time i ask myself this question i have to look up the answer. It always seems obvious in retrospect, but i can never remember it.

:)

I hope you tell us the answer.

The Rev Dodgson said:

Tamb said:

ChrispenEvan said:

27% this analogy is about a planet obitting a star. DM on those scales has little to no effect. also this is about why the rubber sheet analogy is an inaccurate representation of how gravity works.

OK
But DM is ~85% of matter & ~25% of energy.

I think you are thinking of Dark Energy, which is a completely different thing, if it is a thing at all.

https://www.space.com/20502-dark-matter-universe-mystery-infographic.html

The Rev Dodgson said:

Tamb said:

ChrispenEvan said:

27% this analogy is about a planet obitting a star. DM on those scales has little to no effect. also this is about why the rubber sheet analogy is an inaccurate representation of how gravity works.

OK
But DM is ~85% of matter & ~25% of energy.

I think you are thinking of Dark Energy, which is a completely different thing, if it is a thing at all.

No, what Tamb wrote is correct

Dark matter is a form of matter thought to account for approximately 85% of the matter in the universe and about a quarter of its total energy density. Most dark matter is thought to be non-baryonic in nature, possibly being composed of some as-yet undiscovered subatomic particles.

wiki.

mollwollfumble said:

ChrispenEvan said:

The Rev Dodgson said:

So what was the conclusion of their investigations?

rubber sheets while good for initial demos fall down with closer inspection.

Yep.

Here’s a good fun question, to see if you understand the warping of space in GR. A ball thrown up under the influence only of gravity follows a parabolic arc. But in GR the warping of space ensures that under a constant gravitational force, the curvature of the geodesic is constant. A ball thrown up travels along a geodesic, a circular arc not a parabolic arc.

How can you resolve the discrepacy?

Every time i ask myself this question i have to look up the answer. It always seems obvious in retrospect, but i can never remember it.

Your initial premise is wrong. A ball thrown up under the influence of gravity alone does not follow a parabolic arc.

ChrispenEvan said:

The Rev Dodgson said:

Tamb said:

OK
But DM is ~85% of matter & ~25% of energy.

I think you are thinking of Dark Energy, which is a completely different thing, if it is a thing at all.

No, what Tamb wrote is correct

Dark matter is a form of matter thought to account for approximately 85% of the matter in the universe and about a quarter of its total energy density. Most dark matter is thought to be non-baryonic in nature, possibly being composed of some as-yet undiscovered subatomic particles.

wiki.

OK, so if we are looking at the motion of visible matter in space, it would be the 85% figure that was relevant, wouldn’t it?

btm said:

mollwollfumble said:

ChrispenEvan said:

rubber sheets while good for initial demos fall down with closer inspection.

Yep.

Here’s a good fun question, to see if you understand the warping of space in GR. A ball thrown up under the influence only of gravity follows a parabolic arc. But in GR the warping of space ensures that under a constant gravitational force, the curvature of the geodesic is constant. A ball thrown up travels along a geodesic, a circular arc not a parabolic arc.

How can you resolve the discrepacy?

Every time i ask myself this question i have to look up the answer. It always seems obvious in retrospect, but i can never remember it.

Your initial premise is wrong. A ball thrown up under the influence of gravity alone does not follow a parabolic arc.

Well it’s much closer to a parabolic arc than a circular arc.

The Rev Dodgson said:

ChrispenEvan said:

The Rev Dodgson said:

I think you are thinking of Dark Energy, which is a completely different thing, if it is a thing at all.

No, what Tamb wrote is correct

Dark matter is a form of matter thought to account for approximately 85% of the matter in the universe and about a quarter of its total energy density. Most dark matter is thought to be non-baryonic in nature, possibly being composed of some as-yet undiscovered subatomic particles.

wiki.

OK, so if we are looking at the motion of visible matter in space, it would be the 85% figure that was relevant, wouldn’t it?

yes.

it would be interesting to model the effect of DM on the path of an object on earth. I mean if DM is real and is causing galactic rotation curves to be weird, then I wonder how much of an affect it does have on an object at human scales..

Dropbear said:

it would be interesting to model the effect of DM on the path of an object on earth. I mean if DM is real and is causing galactic rotation curves to be weird, then I wonder how much of an affect it does have on an object at human scales..

about || this much.

*not to scale.

Dropbear said:

it would be interesting to model the effect of DM on the path of an object on earth. I mean if DM is real and is causing galactic rotation curves to be weird, then I wonder how much of an affect it does have on an object at human scales..

Following the rubber sheet analogy. because it is pretty evenly distributed on a local scale it doesn’t change the curvature of the sheet, so it doesn’t have a measurable effect.

The Rev Dodgson said:

because it is pretty evenly distributed on a local scale

that’s quite definitive given that we have no idea what it is

Dropbear said:

The Rev Dodgson said:

because it is pretty evenly distributed on a local scale

that’s quite definitive given that we have no idea what it is

Yeah, I was thinking that too.

Dropbear said:

The Rev Dodgson said:

because it is pretty evenly distributed on a local scale

that’s quite definitive given that we have no idea what it is

it is something that interacts gravitationally.

ChrispenEvan said:

Dropbear said:

The Rev Dodgson said:

because it is pretty evenly distributed on a local scale

that’s quite definitive given that we have no idea what it is

it is something that interacts gravitationally.

yes but I am gently taking issue with the definitive statement that it’s evenly distributed..

Dropbear said:

ChrispenEvan said:

Dropbear said:

that’s quite definitive given that we have no idea what it is

it is something that interacts gravitationally.

yes but I am gently taking issue with the definitive statement that it’s evenly distributed..

Well since “it” interacts gravitationally, if it was not uniform locally the non-uniformity would be detectable in the motion of planets.

Wouldn’t it?

The Rev Dodgson said:

Dropbear said:

ChrispenEvan said:

it is something that interacts gravitationally.

yes but I am gently taking issue with the definitive statement that it’s evenly distributed..

Well since “it” interacts gravitationally, if it was not uniform locally the non-uniformity would be detectable in the motion of planets.

Wouldn’t it?

it depends if the strength of the interaction was so weak (on a local scale) that any difference in the maths would be lost in rounding errors..
if we had a big clump of DM somewhere and it had a very weak interaction then it might take a LONG time for any interaction to be noticeable.

The Rev Dodgson said:

btm said:

mollwollfumble said:

Yep.

Here’s a good fun question, to see if you understand the warping of space in GR. A ball thrown up under the influence only of gravity follows a parabolic arc. But in GR the warping of space ensures that under a constant gravitational force, the curvature of the geodesic is constant. A ball thrown up travels along a geodesic, a circular arc not a parabolic arc.

How can you resolve the discrepacy?

Every time i ask myself this question i have to look up the answer. It always seems obvious in retrospect, but i can never remember it.

Your initial premise is wrong. A ball thrown up under the influence of gravity alone does not follow a parabolic arc.

Well it’s much closer to a parabolic arc than a circular arc.

That’s an interesting hypothesis, Rev. Perhaps you could explain your reasoning.

btm said:

mollwollfumble said:

Yep.

Here’s a good fun question, to see if you understand the warping of space in GR. A ball thrown up under the influence only of gravity follows a parabolic arc. But in GR the warping of space ensures that under a constant gravitational force, the curvature of the geodesic is constant. A ball thrown up travels along a geodesic, a circular arc not a parabolic arc.

How can you resolve the discrepacy?

Every time i ask myself this question i have to look up the answer. It always seems obvious in retrospect, but i can never remember it.

Your initial premise is wrong. A ball thrown up under the influence of gravity alone does not follow a parabolic arc.

Incidentally, I’d argue that a ball in a GR geodesic follows an elliptical arc, rather than strictly circular (cf. comets.) So mollwollfumble’s second premise is —- well, too restrictive, since a circle is an ellipse with e=0 —- though it’s not exactly wrong.

btm said:

btm said:

mollwollfumble said:

Yep.

Here’s a good fun question, to see if you understand the warping of space in GR. A ball thrown up under the influence only of gravity follows a parabolic arc. But in GR the warping of space ensures that under a constant gravitational force, the curvature of the geodesic is constant. A ball thrown up travels along a geodesic, a circular arc not a parabolic arc.

How can you resolve the discrepacy?

Every time i ask myself this question i have to look up the answer. It always seems obvious in retrospect, but i can never remember it.

Your initial premise is wrong. A ball thrown up under the influence of gravity alone does not follow a parabolic arc.

Incidentally, I’d argue that a ball in a GR geodesic follows an elliptical arc, rather than strictly circular (cf. comets.) So mollwollfumble’s second premise is —- well, too restrictive, since a circle is an ellipse with e=0 —- though it’s not exactly wrong.

No, btm. Not surprising, because the resolution of the dilemma is that it’s space-time that GR bends, not space itself. Time becomes a spacelike variable by multiplying it by i*c where i is the square root of minus one. The spacelike component of time becomes very long. A second in time is a light second in space, 300,000 km. So throwing a ball up and catching it means that the ball travels more than 300,000 km in space-time, not just a few metres. Because the time component is so much larger than the space component, it’s the time component that is by far the most influenced by the curvature of space-time. It’s this gravitational warping of the time component that generates the circular geodesic.

btm said:

The Rev Dodgson said:

btm said:

Your initial premise is wrong. A ball thrown up under the influence of gravity alone does not follow a parabolic arc.

Well it’s much closer to a parabolic arc than a circular arc.

That’s an interesting hypothesis, Rev. Perhaps you could explain your reasoning.

It’s not really a hypothesis.

It follows directly from the maths assuming constant horizontal velocity and constant vertical acceleration; i.e. ignoring friction effects and treating gravitational acceleration as constant:

Horizontal displacement, x, is proportional to time.
Vertical velocity, y’, is proportional to time.
Vertical displacement , y, is proportional to time^2.

So y = kx^2

The Rev Dodgson said:

btm said:

The Rev Dodgson said:

Well it’s much closer to a parabolic arc than a circular arc.

That’s an interesting hypothesis, Rev. Perhaps you could explain your reasoning.

It’s not really a hypothesis.

It follows directly from the maths assuming constant horizontal velocity and constant vertical acceleration; i.e. ignoring friction effects and treating gravitational acceleration as constant:

Horizontal displacement, x, is proportional to time.
Vertical velocity, y’, is proportional to time.
Vertical displacement , y, is proportional to time^2.

So y = kx^2

I think your initial assumptions are incomplete, Rev. Here’s a hypothetical for you:
Suppose I went to the “far” end (the end furthest from the orbited body) of a highly eccentric (e=1 – 10^-100, say) comet and threw the ball at the same speed and in the same direction as the comet at that point. Would the ball follow a parabolic path? If so, why doesn’t the comet follow the same path? If not, why would it follow a different path under identical gravitational circumstances on the surface of a planet?

btm said:

The Rev Dodgson said:

btm said:

That’s an interesting hypothesis, Rev. Perhaps you could explain your reasoning.

It’s not really a hypothesis.

It follows directly from the maths assuming constant horizontal velocity and constant vertical acceleration; i.e. ignoring friction effects and treating gravitational acceleration as constant:

Horizontal displacement, x, is proportional to time.
Vertical velocity, y’, is proportional to time.
Vertical displacement , y, is proportional to time^2.

So y = kx^2

I think your initial assumptions are incomplete, Rev. Here’s a hypothetical for you:
Suppose I went to the “far” end (the end furthest from the orbited body) of a highly eccentric (e=1 – 10^-100, say) comet and threw the ball at the same speed and in the same direction as the comet at that point. Would the ball follow a parabolic path? If so, why doesn’t the comet follow the same path? If not, why would it follow a different path under identical gravitational circumstances on the surface of a planet?

No, my assumptions were absolutely complete for the event I was describing. The event you are describing is something completely different, principally in that the acceleration is not near constant.

The Rev Dodgson said:

btm said:

The Rev Dodgson said:

It’s not really a hypothesis.

It follows directly from the maths assuming constant horizontal velocity and constant vertical acceleration; i.e. ignoring friction effects and treating gravitational acceleration as constant:

Horizontal displacement, x, is proportional to time.
Vertical velocity, y’, is proportional to time.
Vertical displacement , y, is proportional to time^2.

So y = kx^2

I think your initial assumptions are incomplete, Rev. Here’s a hypothetical for you:
Suppose I went to the “far” end (the end furthest from the orbited body) of a highly eccentric (e=1 – 10^-100, say) comet and threw the ball at the same speed and in the same direction as the comet at that point. Would the ball follow a parabolic path? If so, why doesn’t the comet follow the same path? If not, why would it follow a different path under identical gravitational circumstances on the surface of a planet?

No, my assumptions were absolutely complete for the event I was describing. The event you are describing is something completely different, principally in that the acceleration is not near constant.

No, over the distances involved the two events are identical. That’s why I specified the far end of the comet’s orbit.

btm said:

The Rev Dodgson said:

btm said:

I think your initial assumptions are incomplete, Rev. Here’s a hypothetical for you:
Suppose I went to the “far” end (the end furthest from the orbited body) of a highly eccentric (e=1 – 10^-100, say) comet and threw the ball at the same speed and in the same direction as the comet at that point. Would the ball follow a parabolic path? If so, why doesn’t the comet follow the same path? If not, why would it follow a different path under identical gravitational circumstances on the surface of a planet?

No, my assumptions were absolutely complete for the event I was describing. The event you are describing is something completely different, principally in that the acceleration is not near constant.

No, over the distances involved the two events are identical. That’s why I specified the far end of the comet’s orbit.

If the change in acceleration is negligible and the acceleration is zero in the direction of travel, then the path will be parabolic. Since the acceleration perpendicular to the direction of travel is very small the parabolic path will also be very close to elliptical which will be very close to circular.