RE: No perfect circles in space...
July 21, 2018 at 12:30 pm
(This post was last modified: July 21, 2018 at 12:43 pm by Anomalocaris.)
(July 21, 2018 at 11:54 am)BrianSoddingBoru4 Wrote: Well, you can increase the circumference of any circle, but how do you do that while keeping the radius the same?
Boru
As an example, take a flat surface, make a dimple on it. Trace an enclosed line, exactly equidistant from some other point on the surface as measured along the surface, and passing through the dimple. This line forms a perfect circle from the perspective of the surface.
But notice if you project this circle onto another truly flat surface, it won’t be circular anymore because where it passes though the dimple, it has to pinch in towards the center to accommodate for the fact the line of radius has longer to go to follow the dimple down to the circumference of the circle. At the same time, the segment of the circle crossing the dimple is also longer than its project onto the surface, because that section of the circle has longer to go follow the dimple down and then back up. So I just made a circle whose circumference is longer than its radius times twice pi.
Now to show I can arbitarily increase the circumference of this circle further from the perspective of the surface, all I have to do is to keep the same radius, against as measured by tracing along the surface, but add more dimples where the circumference goes. I can also change the geometry of the dimple from a simple dimple to dimples with convoluted surfaces, or dimples that balloon outwards near their tips.
(July 21, 2018 at 12:16 pm)Jehanne Wrote:(July 21, 2018 at 10:04 am)Anomalocaris Wrote: Yes. A circle inscribed on a non-flat surface?
Ha, ha; on a flat surface? Or, for the above example, in our planet's orbit about the Sun? Can you visualize that??
Who said a planet’s orbit about the sun has to lie on a flat plane? Gravitational purterbation from other bodies can make some pretty non-planar orbits. Lots of asteroids have radically non-planar orbits Due to purterbations of the planets. There is at least one earth crossing asteroid that is locked into a strange orbit bobbing up and down many times per revolution by the the gravity of the earth right now.
The sun itself bobs up and down by hundreds of light years as it orbits Milky Way.
