Dual Planet Orbit, what would be the outcome?

[Crossroads Inc.]

So what if we had a planetary system where you have an Earth sized planet and a moon. However in this case the "moon" is about the size of Mercury. Could you have a stable orbit? How far away would the moon have to be to ensure stability?

Also another odd idea.. Could oyu have a Yearly cycle that needed more then one year to repeat? Exp: Our moon is on a 9 year lunar cycle. As in, in order for the moon to 'exactly' repeat going from what is called a "Minimum" extreme" to a "maximum" extreme takes 9 years.
Could a planet do something similar? For instance go around the sun and create normal seasons, Summer Autumn Winter Spring... But in order to 'perfectly' repeat, needed two years? Like The solstices would happen once every two years?

[Serafina]

It's "dual", not duel.

Anyway, i am no expert on orbital mechanics, so i will only add that much:
To have a stable orbit for a moon, there must not be any tides. So your planet must have no oceans on it (or comparable things).
Why? Well, the tides are basically giving energy from the earth to the moon, slowing the earths rotation and increasing the orbit of the moon. Over millions of years, that has accumulated substantially.

[Ethereal235]

In the Earth-Moon system, technically both orbit around a common center of gravity between both; the Earth has a perceptible wobble. With a massive enough 'moon,' the common center of gravity could lie outside of the Earth's radius. Consider, for instance, Pluto and Charon. At the opposite extreme with incredibly massive bodies, you have binary star systems, which are actually fairly common.

As for the distance apart, I don't think (could be wrong) that it's just their distance that matters, but also their speed; the same two objects could maintain a stable orbit at varying distances so long as they moved at the proper speeds. Uniform circular motion doesn't generally apply to real orbits, but it's close enough for a basic example. The relationship of acceleration, velocity, and distance generally takes the form a=v^2/r, so since a is gravitational attraction in this case, a= m1*m2*G/r^2, so a little bit of algebra gives us v=(m1*m2*G/r)^1/2. You could establish a stable circular rotation for any two bodies around a common center of gravity at varying distances, so long as they moved fast enough.

I don't know about the other question.

[Ariphaos]

Replacing the Moon with something the size of Mercury can certainly happen. Our day would be somewhat longer, and the tides that much more fierce, though without knowing the initial conditions of the Earth-Moon system exactly it would be hard to pick out specifics.

For the second question, are you asking if our axial precession could be so extreme that it gets completed in two years? That sort of thing might happen for a double planet in a distant enough orbit, but at the Earth-Sun distance it would seem the planet would instead melt and end up with a less extreme precession.

[Crossroads Inc.]

To have a stable orbit for a moon, there must not be any tides. So your planet must have no oceans on it (or comparable things).
Why? Well, the tides are basically giving energy from the earth to the moon, slowing the earths rotation and increasing the orbit of the moon. Over millions of years, that has accumulated substantially.

Are we having a different definition of 'stable' ?

I am mostly talking about the two bodies orbiting over an over an over, without fear of them ever smashing into each other. Given that the Earth has tides, does that mean its not 'stable' by your definition? On the world in question here I would imagine quite immense tides around the oceans.

A guess what I am after isn't a 'perfect' orbit IE circular, but simply a 'safe' orbit.

On the second part... I'm not sure what I mean, it was one of those more "What If" moments. It largely sprang from the concept of our year repeating, once a year. I just wondered if you could have an orbit that needed two, (or more) trips to repeat. So oyu would have a complete trip around the sun, but the various celestial markers would be spaced around two years. I don't know if thats even possible. It really started because for a Fictional story, I was contemplating a society that thought it 'shared' a year with its twin planet, Because One full rotation around the sun had one set of Markers, solstice, etc. but the next trip would be different. So it was like two different Yearly systems going back and forth.

Just random musings.

[Simon_Jester]

Are we having a different definition of 'stable' ?

I am mostly talking about the two bodies orbiting over an over an over, without fear of them ever smashing into each other.

Of course that could happen, quite easily.

On the second part... I'm not sure what I mean, it was one of those more "What If" moments. It largely sprang from the concept of our year repeating, once a year. I just wondered if you could have an orbit that needed two, (or more) trips to repeat. So oyu would have a complete trip around the sun, but the various celestial markers would be spaced around two years. I don't know if thats even possible. It really started because for a Fictional story, I was contemplating a society that thought it 'shared' a year with its twin planet, Because One full rotation around the sun had one set of Markers, solstice, etc. but the next trip would be different. So it was like two different Yearly systems going back and forth.

For this to happen, you'd need a planet with axial precession fast enough that the planet's axis of rotation makes at least one complete circuit in a year.

Intuitively, I doubt that this is possible for natural methods of planet formation; it would require intervention by some godlike* force.

*Where 'godlike' is defined roughly as "Has access to more power than I can reasonably imagine humanity ever having, and being able to use it in ways that I cannot reasonably imagine being physically possible."

[Serafina]

Are we having a different definition of 'stable' ?

Apparently, yes.
"Stable" means that it is more-or-less constant. Say, the orbital distance is between 300.000 and 400.000 km and stays that way. Which is not the case with Luna, since it's moving away from the earth at a speed of a couple of inches each year.

But i see now what you meant, i just wanted to clarify this.

[dragon]

Hum we did this problem in my orbital mechanics class but that was a long time ago, I doubt I have the papers still. What we figured out yes it possible but you require a greater distance between the two inorder to stabalize the pair. If you want to add tidal effects than an even greater distance is required. Also on top of the distance several other things are needed but I honesty can't rember.