How close is too close?

[TransformerRobot]

Me again, with another problem in my story concept.

 

I've been considering the fact that if planets were too close to each other's orbit that it would drastically affect what happens on them.

 

I don't know exactly how close that would be though.

 

What would happen if two planets were only 500,000 km apart? Would it depend on the physical traits of each planet?

[Sensei]

Orbit would be unstable. One or both planets would be ejected from star system, sooner or later.

 

Distance is not the only parameter. It's important what is their mass. They can be also have different angular momentum, and different ecliptic.

There is couple star system simulators on the net.

See this one for example

https://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html

Pick up preset Slingshot. Planet is ejected from such system.

Edited December 14, 2014 by Sensei

[MigL]

Robert L Foreward ( physicist/author ) wrote a story following Dragon's Egg which had two planets in close enough proximity that a waterfall 'fell' from one planet to the other. I don't recall the name of it, you'll need to look it up.

[TransformerRobot]

Orbit would be unstable. One or both planets would be ejected from star system, sooner or later.

 

Distance is not the only parameter. It's important what is their mass. They can be also have different angular momentum, and different ecliptic.

There is couple star system simulators on the net.

See this one for example

https://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html

Pick up preset Slingshot. Planet is ejected from such system.

 

Okay, what about 2 million k apart?

[Sensei]

 

Okay, what about 2 million k apart?

 

2 mln k of what?

Meters?

Kilometers?

Astronomic Unit?

C?

[TransformerRobot]

Kilometres.

[Sensei]

2 million kilometers is very short distance in cosmic scale. It's just 5x distance to the Moon.

Earth to Sun is ~150 million kilometers.

Earth to the closest planet ~38 million kilometers in the most optimal situation.

 

[swansont]

One measure of too close would be the Roche limit

http://en.wikipedia.org/wiki/Roche_limit

[TransformerRobot]

Okay, then what factors would there need to be of hypothetical planets that were 10 million kilometres apart?

[mothythewso]

Wouldn't density play a role? I would think 2 dense iron cores could orbit closer than 2 gas giants of equal mass. But then, biology major

[swansont]

Wouldn't density play a role? I would think 2 dense iron cores could orbit closer than 2 gas giants of equal mass. But then, biology major

 

Surfaces would be closer, but the centers would have the same separation.

[TransformerRobot]

 

Surfaces would be closer, but the centers would have the same separation.

 

Then what about two planets having the same density and iron cores but are 20 million kilometres apart?

[swansont]

Then what about two planets having the same density and iron cores but are 20 million kilometres apart?

What about them?

[mothythewso]

Think the Roche limit applies when 2 bodies are significantly different in mass, for instance the Earth-Moon system. If the Moon's orbit should decay to inside the Roche limit, the Earth's gravitational pull would rip it apart, perhaps forming rings.

Swansont, I'm having trouble grasping the concept of 2 orbiting, equally massive bodies having a separation of their centers of mass independent of their density, or "surfaces would be closer". If the densities of 2 objects of equal mass were sufficiently different, couldn't the smaller body have an orbit inside the surface of the larger body? Or am I phrasing this wrong?

[swansont]

Think the Roche limit applies when 2 bodies are significantly different in mass, for instance the Earth-Moon system. If the Moon's orbit should decay to inside the Roche limit, the Earth's gravitational pull would rip it apart, perhaps forming rings.

Swansont, I'm having trouble grasping the concept of 2 orbiting, equally massive bodies having a separation of their centers of mass independent of their density, or "surfaces would be closer". If the densities of 2 objects of equal mass were sufficiently different, couldn't the smaller body have an orbit inside the surface of the larger body? Or am I phrasing this wrong?

 

The force of attraction is GmM/r²

 

r is the distance from the center of each object. The size of the object does not enter into the equation. The two object will orbit the center of mass of the system.

 

Density only comes into play if you measure the distance from the surface. Yes, it's possible that one object would orbit within the the other object. The distance between their surfaces can be zero . If it becomes negative, the mass of the diffuse system is effectively reduced, because the force of attraction only depends on the mass inside of the sphere at your distance from the center (Gauss's law, aka the shell theorem) The mass outside makes no contribution.

[TransformerRobot]

 

The force of attraction is GmM/r²

 

r is the distance from the center of each object. The size of the object does not enter into the equation. The two object will orbit the center of mass of the system.

 

Density only comes into play if you measure the distance from the surface. Yes, it's possible that one object would orbit within the the other object. The distance between their surfaces can be zero . If it becomes negative, the mass of the diffuse system is effectively reduced, because the force of attraction only depends on the mass inside of the sphere at your distance from the center (Gauss's law, aka the shell theorem) The mass outside makes no contribution.

 

Then what would be the safest distance to have two planets of the same mass, of close to the same size, only 20 million kilometres apart? Yes, I understand that we're going by the cosmic scale, but surely, 20 million kilometres can't be too small a distance by which to separate to similar planets or other celestial bodies.

Edited January 19, 2015 by TransformerRobot

[swansont]

 

Then what would be the safest distance to have two planets of the same mass, of close to the same size, only 20 million kilometres apart? Yes, I understand that we're going by the cosmic scale, but surely, 20 million kilometres can't be too small a distance by which to separate to similar planets or other celestial bodies.

 

You still haven't really clarified by what you mean by safe. As others have said, you risk the orbits being unstable if planets get close to each other. It really needs to be simulated to know what happens — the solution can't be done analytically.

[TransformerRobot]

What I mean is would they be able to be separated by only 20 million kilometres without any disastrous effects on each other?

Edited January 19, 2015 by TransformerRobot

[elfmotat]

What I mean is would they be able to be separated by only 20 million kilometres without any disastrous effects on each other?

 

And as everyone else has been trying to explain, it depends. It depends on the mass of the planets, the planets' compositions, whatever debris might be between them, the relative planes of their orbits, the eccentricity of their orbits, etc., etc. Asking, "is 20 mil km safe(?)" is a nonsensical question. There are too many unspecified variables here to make a blanket statement of "yes" or "no."

[mothythewso]

Going to have to look for my old copy of Sears and Zemansky and figure this out for myself. Though I really didn't get much out of it when I was an undergrad. Probably explains why I never made it to grad