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> This means that if large triangles could be ‘drawn’ in space, their internal angles would add up to less than 180 degrees. I wonder if this could somehow be

by jurjenh 13y ago

> This means that if large triangles could be ‘drawn’ in space, their internal angles would add up to less than 180 degrees. I wonder if this could somehow be done with the voyager 1 and 2, although I imagine this would involve setting the two voyagers up to look for each other - something that may well be many orders of magnitude outside what is possible, though they still seem to be able to contact us. Also it may not be a large enough distance, but I'd guess its the largest available to us that we could actually test.

bdg 13y ago
It's not the drawing of them in space that's the issue. Remember, you're in space right now in addition to being on the earth. The issue is in making the measurement. The 180 degree problem is really complex.
- rwmj 13y ago
  I'm not saying it's easy to send three probes to the edge of the solar system, but how come measuring the angles is hard? (Granted you cannot do it with the Voyager probes). Also does anyone know what total interior angles you'd have to measure, ie. would be it ~179° or ~179.99999999°?
andrewcooke 13y ago
i imagine the problem is finding an area of space that's smooth enough to make the measurement accurately. the distribution of mass within would need to be very uniform and "average" (mass curves space; what you're trying to find here is the average curvature). so it would need to be a very large area (since matter in the universe is clumped into galaxies and the like - you want a region so large that those clumps are averaged out). since the voyagers are only separated by a scale similar to the size of the solar system, and we're talking of sizes much larger than the separation of galaxies (or superclusters), the answer is no (unfortunately) (and of course, at those scales, you have the practical problem of light having a finite speed, so your experiment would take a long time!). in fact, that's why this comes from cmb (cosmic microwave background) measurements. because those give you, in effect, measurements across the largest chunk of universe observable. having said all that, measuring changes in curvature is an easier problem. and that's what gravitational wave detectors try to do. and i am pretty sure there have been proposals to do that with satellites (measuring (changes in) distances to each other with lasers).

by jurjenh 13y ago

bdg 13y ago

It's not the drawing of them in space that's the issue. Remember, you're in space right now in addition to being on the earth. The issue is in making the measurement. The 180 degree problem is really complex.

rwmj 13y ago
I'm not saying it's easy to send three probes to the edge of the solar system, but how come measuring the angles is hard? (Granted you cannot do it with the Voyager probes). Also does anyone know what total interior angles you'd have to measure, ie. would be it ~179° or ~179.99999999°?

andrewcooke 13y ago

i imagine the problem is finding an area of space that's smooth enough to make the measurement accurately. the distribution of mass within would need to be very uniform and "average" (mass curves space; what you're trying to find here is the average curvature). so it would need to be a very large area (since matter in the universe is clumped into galaxies and the like - you want a region so large that those clumps are averaged out). since the voyagers are only separated by a scale similar to the size of the solar system, and we're talking of sizes much larger than the separation of galaxies (or superclusters), the answer is no (unfortunately) (and of course, at those scales, you have the practical problem of light having a finite speed, so your experiment would take a long time!). in fact, that's why this comes from cmb (cosmic microwave background) measurements. because those give you, in effect, measurements across the largest chunk of universe observable. having said all that, measuring changes in curvature is an easier problem. and that's what gravitational wave detectors try to do. and i am pretty sure there have been proposals to do that with satellites (measuring (changes in) distances to each other with lasers).