Orbit of Moons & Shapes of Planets due to Warped spacetime

[venton]

First post, I am just a layman, so go easy.
The way I understand it, the moon is following a straight line through space. However, the mass of the Earth is so great that it warps the fabric of spacetime and it appears that the moon is going around the earth. Same with any moon or planet, they follow a path along a sphere shape because spacetime has been warped into that shape. But truly they are all flying along in a straight line. The way I understand it gravity doesn't really exist, it is just a manifestation of warped spacetime.

Well if spacetime is warped to that degree, surely the apparent shape of a planet will be warped as well? And so it seems, all planets and stars appear to be spheres, in the same way that their moon skim along a sphere shape just above them.

So in the same way that the moon is flying along a straight line, am I traveling along a straight line when I walk along the surface of the earth? But because of the huge mass of the planet I appear to walk in a sphere.

So what does this mean? Are planets actually flat, but their mass warps them into spheres of space time?

I dunno, what do you think.

 

[Jonathan Scott]

First post, I am just a layman, so go easy.
The way I understand it, the moon is following a straight line through space. However, the mass of the Earth is so great that it warps the fabric of spacetime and it appears that the moon is going around the earth. Same with any moon or planet, they follow a path along a sphere shape because spacetime has been warped into that shape. But truly they are all flying along in a straight line. The way I understand it gravity doesn't really exist, it is just a manifestation of warped spacetime.

Well if spacetime is warped to that degree, surely the apparent shape of a planet will be warped as well? And so it seems, all planets and stars appear to be spheres, in the same way that their moon skim along a sphere shape just above them.

So in the same way that the moon is flying along a straight line, am I traveling along a straight line when I walk along the surface of the earth? But because of the huge mass of the planet I appear to walk in a sphere.

So what does this mean? Are planets actually flat, but their mass warps them into spheres of space time?

I dunno, what do you think.

Welcome to PF!

Gravity is due to warping of spacetime, not just space. The curvature of space is almost invisible (the radius of curvature is R=c²/g for acceleration g), and only affects things which are moving. The curvature with respect to time is the same, but if you measure space and time in equivalent units then the "speed" through time is c, so given the same radius of curvature the effective acceleration is v²/R = c²/(c²/g) = g, as expected.

 

[venton]

Thanks. So is it true that the moon is following a straight path (as far as it is aware) , but is following an orbit around the Earth due to warping of spacetime caused by the mass of the earth? If so, it occurs to me that the mass of the Earth is warping its own shape into a sphere?

 

[Jonathan Scott]

Thanks. So is it true that the moon is following a straight path (as far as it is aware) , but is following an orbit around the Earth due to warping of spacetime caused by the mass of the earth? If so, it occurs to me that the mass of the Earth is warping its own shape into a sphere?

The moon is effectively following a straight path (a "geodesic") in space-time which is curved by the mass of the earth. If you plot the path in space and time within a flat coordinate system using equivalent space and time units, it looks like a very elongated helix in the direction of the time axis, where the very slight curvature of the line forming the helix matches the curvature with respect to time.

The near-spherical shapes of the Earth and moon are nothing to do directly with the curvature of space-time but are rather the shape that has the lowest potential energy, in that any part which was sticking up would tend to fall into a nearby hollow.

The curvature of space is so tiny that it is difficult to find direct evidence for it. The most famous evidence was from Eddington's 1919 expedition to Principe which photographed stars near to the sun during a total eclipse. He confirmed that those closest to the sun were slightly displaced from their normal positions, and that the amount of the displacement was consistent with the predictions of General Relativity using the curvature of space (equal to twice the displacement expected from gravitational acceleration of light without curvature of space).

 

[venton]

Thanks, I don't yet understand all your points as my maths is too elementary.

In my minds eye I can imagine an onion with the surface of the Earth being the middle skin of the onion, and the moons going around it on an outer onion skin.
From the moon, which is following a straight line in space time, we can imagine moving through the onion skins one at a time towards the the earth. At what point do we say (when walking along an onion skin) that we are no longer following a straight line but are walking around a sphere - eg the Earth's surface?
As the Earth is the cause of the curvature of space time, I don't see the difference between us walking on the surface, or the moon going around the Earth on an outer 'skin'.
Perhaps the answer is beyond my comprehension as my maths is not good enough.

 

[Jonathan Scott]

Thanks, I don't yet understand all your points as my maths is too elementary.

In my minds eye I can imagine an onion with the surface of the Earth being the middle skin of the onion, and the moons going around it on an outer onion skin.
From the moon, which is following a straight line in space time, we can imagine moving through the onion skins one at a time towards the the earth. At what point do we say (when walking along an onion skin) that we are no longer following a straight line but are walking around a sphere - eg the Earth's surface?
As the Earth is the cause of the curvature of space time, I don't see the difference between us walking on the surface, or the moon going around the Earth on an outer 'skin'.
Perhaps the answer is beyond my comprehension as my maths is not good enough.

You're still thinking in terms of curvature of space, but the effect gravity has on space is tiny. If gravity worked like that, then slow-moving objects would follow the same orbits as fast-moving ones, and objects at rest wouldn't fall at all, but that isn't the case.

Objects in free fall aren't restricted to near-circular orbits. They can be in strongly elliptical orbits, or even falling straight down (accelerating) or rising straight up (decelerating). If you choose the plane of the orbit and plot the position in space against time using equivalent units and a time axis perpendicular to that plane, then the line which that describes will curve slightly toward the location of the earth, and the curvature of that line in space units is g/c² where g is the local acceleration (or equivalently, the radius of curvature is the reciprocal of that, c²/g, which near the Earth comes to about a light year!).

Within the solar system, the orbits of many of the major bodies are fairly circular, but that is mainly because over a sufficiently long time, slight disturbances to orbits from other bodies and other tidal effects tend to damp down strongly elliptical orbits towards more circular ones.

 

[venton]

But I think space is warped a lot by the mass of the Earth... at least by the radius of the moons orbit which is quite a lot.

I did some googling and found this which explains my understanding:-
http://www.suite101.com/content/gravity-and-general-relativity-a44580"

"An object traveling through space, according to General Relativity, could be traveling in a perfectly straight line, and if it happened to pass by a large object, it would appear to “curve” toward that object. While prior to Einstein it would have been said that the object had been caught up in the larger object's gravitational field, General Relativity boldly states that this is not so. The object itself continues to travel in a perfectly straight line, but it is space itself which curves. The path the object is following – a straight line through curved space – is known in mathematics as a geodesic. Another example of such a path would be over the surface of a globe – where a “straight” line between two points is still forced to curve as it follows the surface.

The moon, to use this example again, is continually orbiting the Earth, and from the perspective of Earth appears to “curve” as it does so. In reality, the moon is moving in a straight line through space which in itself is curved."

 

[D H]

Within the solar system, the orbits of many of the major bodies are fairly circular, but that is mainly because over a sufficiently long time, slight disturbances to orbits from other bodies and other tidal effects tend to damp down strongly elliptical orbits towards more circular ones.

Not true. The planets' orbits are nearly circular now because the planets' orbits were nearly circular when the planets first formed. The tendency toward circularization purportedly came from the dust and other stuff that comprised the protoplanetary disk from which the planets formed. That appears to apply to our solar system, but not to all. Astronomers were initially quite vexed when all those exoplanets with highly elliptical orbits were found. The orbits of those exoplanets did not fit astronomers' understanding of planetary formation and remains somewhat of an open question.

In the case of our solar system, Jupiter is the 800 pound gorilla that throws its weight around. Jupiter's effect on the Earth to make Earth's eccentricity and inclination vary periodically over time. Jupiter's effect on other bodies is not so benign. The so-called missing planet between Mars and Jupiter is missing because perturbations from Jupiter prevented a planet from ever forming there. Jupiter has tossed most of the stuff from the asteroid belt out of the solar system. Jupiter appears to be in the process of tossing Mercury from the solar system as well. Jovian perturbations of Mercury's orbit includes secular terms as well as periodic terms.

 

[Jonathan Scott]

Not true. The planets' orbits are nearly circular now because the planets' orbits were nearly circular when the planets first formed. The tendency toward circularization purportedly came from the dust and other stuff that comprised the protoplanetary disk from which the planets formed. That appears to apply to our solar system, but not to all. Astronomers were initially quite vexed when all those exoplanets with highly elliptical orbits were found. The orbits of those exoplanets did not fit astronomers' understanding of planetary formation and remains somewhat of an open question.

In the case of our solar system, Jupiter is the 800 pound gorilla that throws its weight around. Jupiter's effect on the Earth to make Earth's eccentricity and inclination vary periodically over time. Jupiter's effect on other bodies is not so benign. The so-called missing planet between Mars and Jupiter is missing because perturbations from Jupiter prevented a planet from ever forming there. Jupiter has tossed most of the stuff from the asteroid belt out of the solar system. Jupiter appears to be in the process of tossing Mercury from the solar system as well. Jovian perturbations of Mercury's orbit includes secular terms as well as periodic terms.

OK; that sounds right and I stand corrected. Perhaps what I heard long ago was not up to date, or perhaps I mixed up tidal effects with perturbations. However, the point I'm making is that orbits are not necessarily circular, even though a lot of the main ones in the solar system are approximately so.

 

[Jonathan Scott]

But I think space is warped a lot by the mass of the Earth... at least by the radius of the moons orbit which is quite a lot.

I did some googling and found this which explains my understanding:-
http://www.suite101.com/content/gravity-and-general-relativity-a44580"

"An object traveling through space, according to General Relativity, could be traveling in a perfectly straight line, and if it happened to pass by a large object, it would appear to “curve” toward that object. While prior to Einstein it would have been said that the object had been caught up in the larger object's gravitational field, General Relativity boldly states that this is not so. The object itself continues to travel in a perfectly straight line, but it is space itself which curves. The path the object is following – a straight line through curved space – is known in mathematics as a geodesic. Another example of such a path would be over the surface of a globe – where a “straight” line between two points is still forced to curve as it follows the surface.

The moon, to use this example again, is continually orbiting the Earth, and from the perspective of Earth appears to “curve” as it does so. In reality, the moon is moving in a straight line through space which in itself is curved."

This is a misleading over-simplification. As I've already said a few times, the curvature of space-time which gives rise to the usual gravitational acceleration is with respect to time. That is, if you consider an object like the moon (and the space around it), and plot the position of that object with respect to time, the path of the object as plotted against time curves towards the line describing the path of the earth. This curvature determines the acceleration of the object, but the path of the object depends on its velocity and is not necessarily circular.

If you lifted an object from the Earth to the same distance as the moon and let it go without giving it any horizontal velocity, it would simply fall in a straight line towards the earth, but with roughly the same acceleration as the moon. If you plotted the distance of the object from the Earth against time, you would again get a curved line, but the path in space would be straight.

Although there is also curvature with respect to displacement in space (that is, curvature in the usual geometric sense), the curvature of space due to the Earth's gravity is too small to detect directly. This curvature only has a significant effect on very fast-moving objects. Specifically, for a horizontally moving object with speed v, the acceleration due to a gravitational field g is effectively g (1+v²/c²), where the term involving v is caused by the curvature of space. This means that something traveling at or near c (such as a light beam) is effectively accelerated twice as much as a static object.

 

[D H]

The object itself continues to travel in a perfectly straight line, but it is space itself which curves. The path the object is following – a straight line through curved space – is known in mathematics as a geodesic. Another example of such a path would be over the surface of a globe – where a “straight” line between two points is still forced to curve as it follows the surface.

The moon, to use this example again, is continually orbiting the Earth, and from the perspective of Earth appears to “curve” as it does so. In reality, the moon is moving in a straight line through space which in itself is curved."

I think it might be best to stop talking about "straight lines" and use the term "geodesic" instead. You should at a minimum realize that your naturally Euclidean mindset is adding meanings to the term "straight line" that simply are not correct in curved space-time. Consider two points that are distinct from one another. In Euclidean geometry we can talk about *the* straight line that connects these two points. There is only one straight line that connects two distinct points in Euclidean geometry. The concept of *the* straight line that connects a pair of distinct points no longer exists in the non-Euclidean geometry that describes curved space-time. In some cases an infinite number "straight lines", or geodesics, connect two distinct points in curved space-time. In other cases, no such connection is possible: "You can't get theyah from heyah."

It is also best to stop talking about curved space. It is four dimensional space-time that is curved here.