SCIENCE! - Orbits and relativity

[Joose]

Seeing as the discussion about Dyson Spheres was quite popular, I thought I would throw a confusion bomb into the forum in the shape of a physics problem that's been bugging me for ages. Its all about the concept of objects orbiting each other and the concept of velocity in Relativity. I have a reasonable understanding of both, but when you put the two together there's something that doesn't quite mesh for me. Obviously I'm not suggesting I've found a fundamental flaw in the Theory of Relativity or anything like that. Somewhere along the line I'm either lacking a vital bit of information or my logic has gone wonky, but I'm buggered if I know where. Lets see if you lot do any better.

Orbits work by getting an object (call it A) moving around another object (call it B) at the right velocity. If you have the velocity of object A parallel to the surface of object B, and get it so that it wants to move away from object B the exact same amount that gravity wants to pull it towards object B, it will just keep spinning around at the same height. As long as there are no other factors involved (nothing hits it, no atmosphere to slow it down etc) and you get the speed exactly right then it will keep doing this for ever. All pretty simple stuff.

One of the fundamental bits of relativity is that everything is only moving from the point of view of something else. In other words, there is no such thing as an object having a definitive speed. For example, if I am sat in a car going down the motorway, I am moving at 0mph compared to the car, 70mph compared to the road, if you take into account the spin of the earth I am going about 100mph, if you take into account the orbit of the earth around the sun I'm going at about 67000mph, and so on. All of the above are (roughly) accurate descriptions of how fast I am going, all at the same time, just taken in different frames of reference.

Now, this is the bit that makes my brain go "nope" and fuck off without me:

Imagine a universe that is empty of everything other than a single planet. Put a geostationary satellite in orbit around the planet. Although the satellite is orbiting the planet it is staying over the exact same point of the planet at all times. So, from the frame of reference of the planet, the satellite isn't moving. So why the fuck is it still in orbit, and not crashing into the planet? If its not moving, there is no velocity to counteract the effects of gravity! But that suggests that if all the other stuff in the universe were to suddenly disappear, all of the Earths geostationary satellites would fall down, which definitely doesn't sound right to me.

Anyone got an explanation that works?

[friznit]

Change "speed" for "acceleration" in your explanation for it to make sense. Speed is relative, but acceleration remains constant. The rate at which the satellite's velocity is changing is constant, so in this case the satellite is falling away from the planet at the same rate that it is being pulled towards the planet by gravity - i.e. relative to each other they are sitting still. The relative speed in a straight line (velocity) of either body is not a factor.

[Dog Pants]

Momentum? The planet is presumably spinning, and even though there isn't a point of reference it still has energy in the form of its momentum. Unless it isn't spinning and there is zero momentum, in which case you're right, the satellites will fall out of the sky (or rotate in orbit if they retain their own momentum).

Note that I'm no astrophysicist either, but my own meanderings have led me to read a bit into energy types and transfer recently.

[Joose]

Change "speed" for "acceleration" in your explanation for it to make sense. Speed is relative, but acceleration remains constant. The rate at which the satellite's velocity is changing is constant, so in this case the satellite is falling away from the planet at the same rate that it is being pulled towards the planet by gravity - i.e. relative to each other they are sitting still. The relative speed in a straight line (velocity) of either body is not a factor.

But if the satellite is geostationary, it has no velocity relative to the planet, so how can there be any acceleration? If its not moving around the planet, were does the acceleration to counter gravity come from?

Besides which, I don't think you are correct about acceleration remaining constant. If I am accelerating away from you, it would be equally valid to say you are accelerating away from me.

Momentum? The planet is presumably spinning, and even though there isn't a point of reference it still has energy in the form of its momentum. Unless it isn't spinning and there is zero momentum, in which case you're right, the satellites will fall out of the sky (or rotate in orbit if they retain their own momentum).

But you only get momentum from movement, so even with spinning you get into the frame of reference problem. For example, taken as part of the solar system the Earth is spinning. But from my personal frame of reference it isnt.

[FatherJack]

Geostationary orbits are like running on a treadmill at just the right speed*, too fast and you fly into space, too slow and you crash into the planet, in that they're the same any any orbit - the geostationary bit comes from careful positioning at a certain precise height above the equator such that the satellite's orbit cycle exactly matches the planet's spin (the satellite doesn't care that the planet is spinning, it's still moving). However without a sun to orbit, the planet wouldn't be spinning, so you could only have a normal orbit, not a geostationary one.

*as Friz says, actually acceleration, as gravity is also measured in units of acceleration, which is what you'e fighting against.

[Joose]

Geostationary orbits are like running on a treadmill at just the right speed*, too fast and you fly into space, too slow and you crash into the planet, in that they're the same any any orbit - the geostationary bit comes from careful positioning at a certain precise height above the equator such that the satellite's orbit cycle exactly matches the planet's spin (the satellite doesn't care that the planet is spinning, it's still moving).

But thats what I mean: From the frame of reference of the solar system, the planet is spinning and the satellite is spinning around it at the same speed. From the frame of reference of the planet, the satellite isn't moving at all. No acceleration, no velocity, nothing.

Ok, I think maybe im overcomplicating things by making it a planet and a satellite, actually. So scrap that, here is a different example of what im struggling with:

Take two objects that are exactly identical. If you get things right you can get them to orbit each other. This is completely independent of whether they are spinning or not, and completely indipendant of whether they are orbiting suns or whatever. Real world example that is close to this: Binary star systems. If they are moving around each other in this way they are both stationary from thier own frame of reference. There is no movement, so how can there be any acceleration to fight against gravity?

Shorter version: If you only take the two objects into account, how can you tell the difference between two objects spinning around each other and two objects *not* spinning around each other? If there is no measurable difference, how come one pair will eventually bump together and the other pair wont (or at least one pair would bump together quicker than the other)?

[Dog Pants]

I'm still going with the energy thing on this. Regardless of whether they are moving relative to anything, they will still maintain kinetic energy until it is reduced by some means (e.g. friction). Just because there's nothing else around doesn't mean that energy ceases to exist. So the gravitational energy of the two objects is countered by the kinetic energy of their movement. If they have no kinetic energy then they aren't moving and the gravitational energy will pull the objects together (which will eventually turn into all manner of other energy types as they collide).

[friznit]

You're not thinking in 3 dimensions (well, 4 if you include Time but that's irrelevant here). Because you have neutralised 2 dimensional relative velocity (zero vector) in this case the objects are still moving away from each other. They may be static in two dimensions (geostationary) but they are constantly falling away from each other, but they are also constantly falling towards each other at the same rate, so they just sit still. In your satellite example, it's falling towards the earth because of gravity (a constant horse), but its constant acceleration is pushing it away from the planet at the same rate, so it's velocity remains zero. Pants is correct insofar as E=MC(2) - energy assumes both objects have mass, but essentially it's the same argument.

[Dog Pants]

(Moved to general, unless we're talking about Universe Sandbox. Which probably isn't a game either.)

[Joose]

I'm still going with the energy thing on this. Regardless of whether they are moving relative to anything, they will still maintain kinetic energy until it is reduced by some means (e.g. friction). Just because there's nothing else around doesn't mean that energy ceases to exist. So the gravitational energy of the two objects is countered by the kinetic energy of their movement. If they have no kinetic energy then they aren't moving and the gravitational energy will pull the objects together (which will eventually turn into all manner of other energy types as they collide).

Nope. Short version: Kinetic energy is based on motion, motion is relative, therefore kinetic energy is also relative. That doesn't mean that the kinetic energy goes away of course, just that from the frame of reference of the two objects orbiting each other they are going at the same velocity as each other, therefore there is no kinetic energy in the first place.

[Joose]

.They may be static in two dimensions (geostationary) but they are constantly falling away from each other, but they are also constantly falling towards each other at the same rate, so they just sit still.

Um...I may be misunderstanding your point here, but how is sitting still not static?

[Joose]

Holy shit! I was googling to try and find some more informations, and I stumbled across the following in a reddit thread:

planets are not actually being pulled by a "horse" around the sun, but that they are actually moving in a straight line via inertia. It's only that space has been warped so severely that the straight line curves in a circle around the sun.

Which is something I knew, but hadn't thought about the implications of in this instance. If things moving in orbit around each other are actually moving in a straight line through curved spacetime, then in the frame of reference of the orbiting object and the object being orbited they do have a velocity....no, wait. No they don't. Even taking the curvature of spacetime into account they are not getting closer or further away from each other, nor are they moving around each other relative to each other, so there still isn't any velocity. God damn it.

I was excited for a second.

[FatherJack]

Scientists often demonstrate gravity wells or space-time curvature with a rubber sheet where they put a heavy ball in the middle and roll a marble "moon" around the dip it makes - which kind of shows how two objects can't just sit within the effect of this curvature without moving towards each other.

Wasn't there something in Red Dwarf about this when they played golf on a moon?

[Dog Pants]

two objects can't just sit within the effect of this curvature without moving towards each other.

Maybe this is the thing, you're approaching it from the wrong direction, Joose. The fact that they aren't moving towards each other is indicative of the fact that they are moving, even though it isn't relative to anything. Otherwise they'd move towards each other. They can't possibly be stationary while they exist together, so the fact that they appear so merely indicates that there are horses in balance, movement being one of them.

[ProfHawking]

two objects can't just sit within the effect of this curvature without moving towards each other.

Maybe this is the thing, you're approaching it from the wrong direction, Joose. The fact that they aren't moving towards each other is indicative of the fact that they are moving, even though it isn't relative to anything. Otherwise they'd move towards each other. They can't possibly be stationary while they exist together, so the fact that they appear so merely indicates that there are horses in balance, movement being one of them.

I like this answer
They need to be moving relative to each other (even if they don't look like they are) in order for them to remain in that position without falling together. The fact they look stationary is just due to the lack of points to visualise them against, and is inconsequential.

[friznit]

.They may be static in two dimensions (geostationary) but they are constantly falling away from each other, but they are also constantly falling towards each other at the same rate, so they just sit still.

Um...I may be misunderstanding your point here, but how is sitting still not static?

Relatively sitting still, not actually sitting still.

[Joose]

Ah, but you are all making the mistake there of slipping back to the concept of absolute velocities. *All* velocity (and by extension, acceleration) is relative to something else. If they something doesn't look like it is moving because there is nothing to see it moving against, then according to relativity it *isnt* moving. So relativily sitting still *is* sitting still.

Think about it this way: you say that it is moving even if it doesn't look like it is. Ok, so how would you go about measuring how fast it is going?

[Thompy]

I don't think it's helping you get your head around it by imagining this universe where nothing else exists other than these two bodies orbiting each other. There's always some external point of reference where by you'd see the objects moving, even if there isn't a floating something to sit on and watch.

So relativily sitting still *is* sitting still.

And I think you've answered yourself. Yes, relative to each other, but they're not all that exists. Even if you did make everything else in the universe disappear there's still that imaginary point in space you could observe from. If there was no space around the orbiting bodies then the universe just wouldn't exist anyway.

[Dog Pants]

By calculating how much centrifugal inertia they'd need to negate their combined gravity. Which they must have, or else they would collide.