That's true. The man did not go around the squirrel. They both were orbiting some point near the center of the tree trunk. Otherwise, one could say that the farther point on the Moon's surface is going around the point that is facing Earth.
One could argue that the moon is orbiting the sun. The fact that it's orbit is a little wobbly because of interferes from the earth is a rounding detail, no?
> An enduring myth about the Moon is that it doesn't rotate. While it's true that the Moon keeps the same face to us, this only happens because the Moon rotates at the same rate as its orbital motion, a special case of tidal locking called synchronous rotation.
My colleagues once spent a good hour trying to explain this fact to me and I still really struggle to accept it. I can see that the moon is rotating on its own axis from the point of view of a space that is external to the system it forms with the earth. But then isn’t everything on earth rotating about its own axis with respect to that external space? It seems arbitrary to isolate the moon from all this other stuff and make a special case of it…
1. Unlike position and velocity, which are relative (there is no given "origin" for them, no way to say where a thing is or how fast it's moving except relative to other things), rotation is absolute. A thing is either rotating or not, regardless of its relation to other things. Objects that rotate "experience (centrifugal) forces as a result" or "require (centripetal) forces to hold them together" depending on how you choose to describe it. This is detectable: hook two weights together with a newton-meter in space - and the newton-meter will read non-zero when the assemblage is rotating, zero when not. The reading tells you how fast it is rotating regardless of any external reference point. (An equivalent device to detect position or velocity is not possible, but it is for acceleration.)
2. Yes, everything "at rest" on earth is in fact rotating at the rate the earth rotates. If you stand on the equator at midday and do not rotate you will be standing on your head at midnight.
>no way to say where a thing is except relative to other things
This is always true. The origin is just a thing that other things are relative to. It's just as possible to define an origin un the real world as it is on a piece of graph paper.
Pick the sun as reference: the moon rotates. Pick the earth as reference: the moon rotates. Stand on the moon and pick any star as reference: the moon rotates.
Yes but from the point of view of the earth the moon does not appear to be rotating around its own axis since it is tidally locked. In that sense it’s confusing to me to distinguish it from everything else on earth but the comment above about centripetal force clarifies this for me I think
I'm probably butchering this, but in my mind it is something like:
1. From the squirrels frame of reference and local coordinate system, the man has remained "in front" of the squirrel. The squirrel is orienting and rotating in sync with the man and therefore has not observed that the man has "gone round" it.
2. From our perspective (and on reflection from the man), the man has circled the squirrel in the global coordinate system of the scene.
As the reader we assume that our perspective is the authoritative one, but I am sure the squirrel disagrees.
I remember this being mentioned by Charles Peirce as an argument for pragmatism (the philosophical kind): It's a nonsensical question unless you can phrase it in terms where the answer has some practical consequence.
I take it that the squirrel didn't circle the man?
Two squirrels running around the same tree, are they circling each other? Or is it that when two bodies are orbiting the same center, then the body with the larger orbit is circling the one with the smaller?
What is the definition of "circling"?
Say instead of just walking, the man was laying down a net/barricade around the tree. As soon as the man completes the circumference, the squirrel must admit that it has been gone around.
Now let us suppose the squirrel is at the same distance as the man.
Has the man have gone around the squirrel and the squirrel around the man?
If it's only radii less than the other, where is the limit?
To get it I think I have to re-frame it like this:
If you hold out an object toward the centre, you clearly go around it when completing an orbit.
If you keep extending that to the origin but then go beyond, so your arm is longer than the radius, then you still go around it, until your arm reaches twice the radius.
https://science.nasa.gov/resource/the-moons-rotation/
2. Yes, everything "at rest" on earth is in fact rotating at the rate the earth rotates. If you stand on the equator at midday and do not rotate you will be standing on your head at midnight.
This is always true. The origin is just a thing that other things are relative to. It's just as possible to define an origin un the real world as it is on a piece of graph paper.
From which reference frame would it not rotate?
I'm probably butchering this, but in my mind it is something like:
1. From the squirrels frame of reference and local coordinate system, the man has remained "in front" of the squirrel. The squirrel is orienting and rotating in sync with the man and therefore has not observed that the man has "gone round" it.
2. From our perspective (and on reflection from the man), the man has circled the squirrel in the global coordinate system of the scene.
As the reader we assume that our perspective is the authoritative one, but I am sure the squirrel disagrees.
https://www.quantamagazine.org/can-math-help-you-escape-a-hu...
Has the man have gone around the squirrel and the squirrel around the man?
If it's only radii less than the other, where is the limit?
To get it I think I have to re-frame it like this:
If you hold out an object toward the centre, you clearly go around it when completing an orbit.
If you keep extending that to the origin but then go beyond, so your arm is longer than the radius, then you still go around it, until your arm reaches twice the radius.
But yeah if your circuit completely fits inside the other person's circuit, then you've been gone around, no matter how slow or fast you both are.