Gravity & conservation of energy with two bodies

[mjcguest]

I just want to get my head straight on something with regards to relativity and gravity - I think it's a simple question (or rather has a simple answer!) so there's no trick agenda here.

If I have two bodies orbiting each other in deep space - far enough out for other gravitational forces to be effectively ignored, then will their orbits remain stable for effectivly ever, or will their orbits gradually decay?

For the purpose of the question, assume that they are perfect spheres, the same temperature as the space they travel through and tidally locked respect to each other (they are the only three energy sapping things I can think of that are relevant)

Thanks
Matt

 

[fatra2]

Hi there,

I also suppose that the two objects are in orbit since a while, meaning that they are in an equilibrium state. Then the simple answer is "no". The bodies will keep orbiting forever. There is no such things as a fading gravitational force.

Cheers

 

[Relena]

you don't have to make any assumptions, classically, the gravitational field is conservative, when the moon orbits the Earth it's moving in an equipotential surface, so it doesn't gain or lose energy.
in general relativity, you have to redefine the straight line as the shortest distance in time connecting two points in space, according to this definition the moon is moving in a straight line inertially.

 

[LURCH]

This may seem like a nit-pick, but I think it's somewhat important;

With two bodies orbiting each other, GR predicts that gravity waves will be generated. These gravity waves will serve as a mechanism for energy loss, and the orbits will decay over time. It is an extremely slow process, and the detection of gravity waves has not yet been confirmed with much certainty (at least, it hadn't been the last time I checked).

The fact that the energy loss is so small can lead one to say that the orbits are essentially eternal. But, the fact that there is any energy loss at all is a reminder that nothing lasts forever.

 

[mjcguest]

Ah - If I have this right, then I think something I've read a number of times and never really thought about what it means has finally clicked; That is

- Gravity is not a force in the sense of "one thing doing something to another"- if it were, then it implies a spend of energy, which would have to be compensated for in some way, be it enlarged orbit or whatever...
- Gravity really does "tell space how to bend", so an object in a stable orbit is simply following the law that deals with objects continuing to move constantly in a "straight" line until a force acts upon them.

Lurch - thank you for your point; a nice reminder that nothing is ever quite as simple as it seems!

It's so nice to find a forum where a newb question isn't met with derisory comments and flames. Thanks all!

 

[Cleonis]

I just want to get my head straight on something with regards to relativity and gravity - I think it's a simple question (or rather has a simple answer!) so there's no trick agenda here.

If I have two bodies orbiting each other in deep space - far enough out for other gravitational forces to be effectively ignored, then will their orbits remain stable for effectivly ever, or will their orbits gradually decay?

For the purpose of the question, assume that they are perfect spheres, the same temperature as the space they travel through and tidally locked respect to each other (they are the only three energy sapping things I can think of that are relevant)

Thanks
Matt

If the orbits of the two bodies are non-circular then according to GR the system as a whole will lose orbital energy to emission of gravitational waves. This will tend to circularize the orbits. Once the orbits are circular the system will no longer lose orbital energy.

Source of this information: the following fascinating article by Kevin Brown:
http://www.mathpages.com/home/kmath249/kmath249.htm
'Lead-Lag Frequency Response'
(For a shortcut to the goodies, find the word 'quadrupole' in that article)

Cleonis