# Orbiting eternally

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1. May 13, 2015

### Stephanus

Dear PF Forum,

I have a question to ask,

Can two celestial bodies orbiting each other eternally without external influence? Does this process need energy?

Thanks for any answer

Steven

2. May 13, 2015

### phinds

You've got the question a bit backwards: if two bodies are in a stable orbit it would require energy to get them to change

3. May 13, 2015

### Stephanus

Thanks Phinds for the answer, I remember you answer me about the shape of the universe with balloonanalogy. It's the best explanation I've ever got.
Suppose the universe is open or flat, and the orbit doesn't change, what I want to know is, that it can orbit for trillion of years till the end of time? (if there is such thing as end of time in open/flat universe)

Steven.

4. May 13, 2015

### phinds

That's a reasonable question and I don't know for sure but since it would take energy to change the stable orbit, I see no reason why it wouldn't just go on forever. Basically, if it goes on for 1 second with no change (and I mean NO change, not just no measurable change) then it should go on forever absent the application of any new force.

I'm not an expert in celestial mechanics and it's possible that there is some reason that orbits decay with time. I know that satellite orbits decay with time but I think that's because they are not in a simple 2-body relationship with the Earth.

5. May 13, 2015

### Stephanus

Yeah, Phinds. The earth, mars altough it's far away, sun, earth ocean tides, etc can cause satellite orbits decay.

Thanks for the answer though

6. May 13, 2015

### CWatters

In addition to the above..

If the bodies are very massive and orbit close together they should emit gravitational waves and this lost energy can cause them to move closer together until they collide.

Wijipedia...

http://en.wikipedia.org/wiki/Gravitational_wave#Wave_amplitudes_from_the_Earth.E2.80.93Sun_system

..calculates that for ...

Two Neutron stars... "the gravitational radiation from them would be 1.38×10^28 watts, which is about 100 times more than the Sun's electromagnetic radiation".

For the earth sun system..."only 200 joules per second [200W] is lost through gravitational radiation, leading to a decay in the orbit by about 1×10^−15 meters per day or roughly the diameter of a proton. At this rate, it would take the Earth approximately 1×10^13 times more than the current age of the Universe to spiral onto the Sun".

So it's significant for Neutron stars but not most planets.