Mutually orbiting bodies in an isolated universe

[Jens K Munk]

Hi Forum,

I've been pondering about this for a while and I hope someone here can help!

Imagine two bodies orbiting each other in tidal locking (https://en.wikipedia.org/wiki/Tidal_locking) just like Pluto and Charon, or as Earth and a geostationary satellite.

Nothing else exists in this imagined universe.

What determines that these two bodies orbit each other at all? Can they not be considered at rest, but for some reason not attracting each other and colliding? Does there not need to be an external reference, such as a 3rd body, relative to which the two bodies orbit each other? And if so, what is this reference?

I guess there's a flaw to my thinking. Please show it to me!

Thanks in advance,

/Jens

 

[sophiecentaur]

Someone on one of the bodies would come to the conclusion that they are rotating because they do not crash together.
The "some reason" would be figured out by a PF member on one of the bodies.
They wouldn't need to be out in deep space - just in a large uniform cloud of dust.

 

[Khashishi]

If they weren't moving, gravity would pull them together.

If you stipulate that gravity works differently in your imagined universe, then all bets are off.

 

[Jens K Munk]

Thanks for the replies so far.

Let's go deeper.

I know PF members are bright, but not even Newton would be able to deduce the bodies orbiting had he not had an external reference - the Sun.

I also know that gravity will cause the objects to collide - and gravity is the same in my imagined universe - but that doesn't answer the question. In the absence of an external reference, what is there to determine that the bodies are orbiting each other? Where do the dimensions through which they travel during orbit come from?

/Jens

 

[Nugatory]

What determines that these two bodies orbit each other at all? Can they not be considered at rest, but for some reason not attracting each other and colliding?

Although the relative position of the two objects wouldn't change, other more sensitive experiments could still detect the rotation of the each body about its axis, because rotation is not relative. Foucault's pendulum is one example.

Local Cavendish-style experiments on the surface of the body could lead to the discovery of the inverse-square gravitational law. That and the observed rotation leads to the two bodies orbiting around their mutual center of gravity.

 

[PeroK]

And, eventually, they would send a satellite into orbit to settle the matter.

 

[Dale]

In the absence of an external reference, what is there to determine that the bodies are orbiting each other?

Accelerometers, gyroscopes, Foucault pendulums, ring interferometers, etc.

 

[sophiecentaur]

In the absence of an external reference, what is there to determine that the bodies are orbiting each other?

They would know that 'things fall down' so they would need a reason why the other body doesn't fall down. A bit of study of circular motion would give a reason - leading to the idea of an orbit. Isaac would probably have got there. They wouldn't have needed to discover that the law is inverse square to figure out that there must be rotation.

 

[Yolander]

A definitive answer should be available once we understand what gravity is. Speculation before then. The absence any other objects eliminates some external influence but if gravity is determined to be a variable force, collision or separation is possible. Also, if your two object universe has all the other qualities of our universe than, if Paul Dirac and Werner Heisenberg are right, matter ("virtual particles"), could spontaneously appear in the area of your two objects and cause minute changes in their orbits which, given enough time...??

 

[Nugatory]

A definitive answer should be available once we understand what gravity is. Speculation before then.

This exact situation (two bodies isolated in an otherwise empty universe) is most often used in introductory texts to derive the equations of orbital motion, and the results are in excellent agreement with what we observe in our real non-empty universe. Thus, it's not speculation to apply either Newtonian gravity or Einstein's general relativity (they will produce the same answer except under fairly extreme conditions) to this problem. It would be more speculative, and involve more unwarranted assumptions, to assume the existence of some as-yet-undiscovered physics that makes two isolated bodies different from the well-understood problem of two bodies that just happen to be far enough away from everything else that we can neglect external influences. Of course that's possible, but because there's no way of knowing, there's no reason to write off the understanding we have as mere speculation.

(SAFETY WARNING: If someone speaks the M-name or mentions the principle associated with that name... A massive rathole will open in the fabric of the internet, and the entire thread will be sucked into it - even the superpowers of the mentors may be inadequate to save us).

if Paul Dirac and Werner Heisenberg are right, matter ("virtual particles"), could spontaneously appear in the area of your two objects and cause minute changes in their orbits which, given enough time...??

This is a bit of a digression, but Dirac and Heisenberg said no such thing, and the popular notion that virtual particles spontaneously pop into existence in empty space is a myth. A good start would be the Insights articles by @A. Neumaier starting with https://www.physicsforums.com/insights/physics-virtual-particles/

 

[Jens K Munk]

Ah, I see. I am now convinced that rotation is detectable in the absence of an external reference.

Thank you, Physics Forum! :)

/Jens