<p>As ganbustein says, this is not too difficult to imagine.  The simplest case (approximating with circular orbits and only the Sun, Earth and Satellite) would have the satellite orbit orthogonally to the Earth with a 1 year orbit.  The Satellite will pass the Earth orbit plane in two places, call these "down crossing" and "up crossing" points.</p>

<p>To minimize Earth - Satellite iterations, keep them 90 degrees apart.  Have the Satellite over the north solar pole when the Earth is at the "down crossing" point.  Then when the satellite gets to the "down crossing point" the Earth will be furthest from the Satellite plane.  When the earth is at the "up crossing point" the satellite will under the Suns south pole. And so on.</p>

<p>This would not be completely stable when we include Jupiter and the mutual interactions, but I think they should be small, allowing this to work generally.  If someone "does the math" and proves me wrong, I will accept that.</p>

CC BY-SA 3.0
2014-12-19T18:34:34.910Z
I would be interested to know how stable (n x years), but take the rep.
Neomada
CC BY-SA 3.0
2014-12-19T18:49:41.597Z
I think that's  a difficult question.  The worst purtibations  will probably be one that results in precession of the Satellite plane.  That will affect the timing, allowing Earth - Satellite interactions to grow....
Robert Farley
CC BY-SA 3.0
2014-12-19T19:01:50.917Z
This is related to the Kozai mechanism mentioned by David Hammen yesterday in the orignial comments. I have thought about this a little more and realized that all polar orbits will be slowly perturbed. But that has now taken me onto thoughts of 3 body solutions (or not as it may eventually pan out).
Neomada
CC BY-SA 3.0
2014-12-19T19:47:38.023Z
I originally accepted ganbustein's answer (sorry ganbustein) but realised after the comment from Dr Hammen this could not be stable.
Neomada
CC BY-SA 3.0
2014-12-19T20:40:26.507Z
I don't think we can PROVE any 3+ body system is fully stable.  I do not believe there will be a closed form solution.  Stability is, then, a relative term.  If the system is stable for many times longer than the lifetime of the Satellite, who cares?  The Earths orbit is stable for the next few billion years   http://en.wikipedia.org/wiki/Stability_of_the_Solar_System  but who knows how much longer?
Robert Farley
CC BY-SA 3.0
2014-12-19T20:58:54.847Z
I was waiting for an answer that maybe gave a reasonably long stability solution. Your answer was more complete, accepting that the orbit would be perturbed. A 90deg phase solution presents an orbit that could be used, but with a finite lifetime. Is a it crime to postulate a 3-body solution. That would be a holy grail of physics/astronomy :-)
Neomada
CC BY-SA 3.0
2014-12-19T21:02:24.877Z
and finite element analysis, fluid dynamics etc....
Neomada
CC BY-SA 3.0
2014-12-19T18:30:28.870Z
2014-12-19T18:30:28.870Z
Robert Farley
<p>Sure. Imagine an object orbiting the Sun in a plane normal to the plane of Earth's orbit. Let AB the the intersection of these two planes. (Imagine that A and B are points on the celestial sphere. We're not interested for now in distance from the Sun.)</p>

<p>Then the only time the Sun hides the Earth from the object is when the object is at A and the Earth is at B, or vice versa. The Earth will be at A or B every 6 months, so we only need to arrange that the object is not at the other point at either of these times. Put it in a circular orbit whose period is a multiple of 6 months, and time it so that whenever the Earth is at A or B the object is due north (or south) of the Sun.</p>

<p>Every six months, the Earth will be at A or B, and the object will be north of the Sun and can see Earth. At all other times, the Earth is not at A or B, and the object can see Earth no matter where the object is.</p>

CC BY-SA 3.0
2014-12-18T02:49:25.547Z
2014-12-18T02:49:25.547Z
ganbustein
<p>I could imagine a polar orbit that is in a plane which rotates to stay orthogonal to the direction of the Earth.  The rotation would be very slow and match the revolution rate of the Earth.  The satellite path would be similar to how a ball of yarn is wound.</p>

<p>There's nothing too fancy about this (you could do the same switching Earth and the Sun), so I wouldn't expect any abnormal forces that would decay the orbit quicker than any other.  Also, with a little ion engine, it'd be that much easier to maintain.</p>

CC BY-SA 3.0
2014-12-18T02:50:55.603Z
An orbit that has to rotate is not what I would consider "stable".
ganbustein
CC BY-SA 3.0
2014-12-18T03:00:19.980Z
@ganbustein Planets' orbits [change](https://en.wikipedia.org/wiki/Apsidal_precession), yet they're still considered stable.
HDE 226868
CC BY-SA 3.0
2014-12-17T23:42:30.447Z
2014-12-17T23:42:30.447Z
Jonny D
<p>Is there a stable polar solar orbit such that the Earth is always in view and not eclipsed by the Sun?</p>

CC BY-SA 3.0
2014-12-18T02:59:10.377Z
Are you referring to the poles of Earth or the Sun?
HDE 226868
CC BY-SA 3.0
2014-12-18T03:05:26.853Z
There's a basic problem with long-term stability of a polar orbit. That problem is the [Kozai mechanism](http://en.wikipedia.org/wiki/Kozai_mechanism).
David Hammen
CC BY-SA 3.0
2014-12-18T22:53:57.097Z
@HDE 226868 polar solar orbit refers to the sun's poles
Neomada
CC BY-SA 3.0
2014-12-18T23:44:19.660Z
@David Hammen Does your comment wrt the Kozai mechanism infer that there is no stable orbit due to the perturbation effects of the earth/other planets?
Neomada
CC BY-SA 3.0
2014-12-20T10:16:22.007Z
@Neomada: Noordung's edit makes your question more appealing to snobs like me who are more likely to read a question that is properly formatted than one which isn't. You should be thanking him, not insinuating that his motives were cynical.
dotancohen
CC BY-SA 3.0
2014-12-20T11:05:09.387Z
@Noordung thanks for the capitalization that I had missed.
Neomada
<orbit><solar-system>
Stable polar solar orbit with the Earth continuously observable
Neomada
# Stable polar solar orbit with the Earth continuously observable

(Asked by: username_0 on 2014-12-17)

Is there a stable polar solar orbit such that the Earth is always in view and not eclipsed by the Sun?

**Tags:** orbit, solar-system

> **Comments:**
> **username_1**: Are you referring to the poles of Earth or the Sun?  
> **username_2**: There's a basic problem with long-term stability of a polar orbit. That problem is the [Kozai mechanism](http://en.wikipedia.org/wiki/Kozai_mechanism).  
> **username_0**: @username_1 polar solar orbit refers to the sun's poles  
> **username_0**: @username_2 Does your comment wrt the Kozai mechanism infer that there is no stable orbit due to the perturbation effects of the earth/other planets?  
> **username_3**: @username_0: Noordung's edit makes your question more appealing to snobs like me who are more likely to read a question that is properly formatted than one which isn't. You should be thanking him, not insinuating that his motives were cynical.  
> **username_0**: @Noordung thanks for the capitalization that I had missed.  

---

## 3 answers

### Answer by username_4 on 2014-12-19. Score: 2 | Accepted answer

As username_5 says, this is not too difficult to imagine. The simplest case (approximating with circular orbits and only the Sun, Earth and Satellite) would have the satellite orbit orthogonally to the Earth with a 1 year orbit. The Satellite will pass the Earth orbit plane in two places, call these "down crossing" and "up crossing" points.

To minimize Earth - Satellite iterations, keep them 90 degrees apart. Have the Satellite over the north solar pole when the Earth is at the "down crossing" point. Then when the satellite gets to the "down crossing point" the Earth will be furthest from the Satellite plane. When the earth is at the "up crossing point" the satellite will under the Suns south pole. And so on.

This would not be completely stable when we include Jupiter and the mutual interactions, but I think they should be small, allowing this to work generally. If someone "does the math" and proves me wrong, I will accept that.

> **Comments:**
> **username_0**: I would be interested to know how stable (n x years), but take the rep.  
> **username_4**: I think that's  a difficult question.  The worst purtibations  will probably be one that results in precession of the Satellite plane.  That will affect the timing, allowing Earth - Satellite interactions to grow....  
> **username_0**: This is related to the Kozai mechanism mentioned by username_2 yesterday in the orignial comments. I have thought about this a little more and realized that all polar orbits will be slowly perturbed. But that has now taken me onto thoughts of 3 body solutions (or not as it may eventually pan out).  
> **username_0**: I originally accepted username_5's answer (sorry username_5) but realised after the comment from Dr Hammen this could not be stable.  
> **username_4**: I don't think we can PROVE any 3+ body system is fully stable.  I do not believe there will be a closed form solution.  Stability is, then, a relative term.  If the system is stable for many times longer than the lifetime of the Satellite, who cares?  The Earths orbit is stable for the next few billion years   http://en.wikipedia.org/wiki/Stability_of_the_Solar_System  but who knows how much longer?  
> **username_0**: I was waiting for an answer that maybe gave a reasonably long stability solution. Your answer was more complete, accepting that the orbit would be perturbed. A 90deg phase solution presents an orbit that could be used, but with a finite lifetime. Is a it crime to postulate a 3-body solution. That would be a holy grail of physics/astronomy :-)  
> **username_0**: and finite element analysis, fluid dynamics etc....  

---

### Answer by username_5 on 2014-12-18. Score: 0

Sure. Imagine an object orbiting the Sun in a plane normal to the plane of Earth's orbit. Let AB the the intersection of these two planes. (Imagine that A and B are points on the celestial sphere. We're not interested for now in distance from the Sun.)

Then the only time the Sun hides the Earth from the object is when the object is at A and the Earth is at B, or vice versa. The Earth will be at A or B every 6 months, so we only need to arrange that the object is not at the other point at either of these times. Put it in a circular orbit whose period is a multiple of 6 months, and time it so that whenever the Earth is at A or B the object is due north (or south) of the Sun.

Every six months, the Earth will be at A or B, and the object will be north of the Sun and can see Earth. At all other times, the Earth is not at A or B, and the object can see Earth no matter where the object is.


---

### Answer by username_6 on 2014-12-17. Score: 0

I could imagine a polar orbit that is in a plane which rotates to stay orthogonal to the direction of the Earth. The rotation would be very slow and match the revolution rate of the Earth. The satellite path would be similar to how a ball of yarn is wound.

There's nothing too fancy about this (you could do the same switching Earth and the Sun), so I wouldn't expect any abnormal forces that would decay the orbit quicker than any other. Also, with a little ion engine, it'd be that much easier to maintain.

> **Comments:**
> **username_5**: An orbit that has to rotate is not what I would consider "stable".  
> **username_1**: @username_5 Planets' orbits [change](https://en.wikipedia.org/wiki/Apsidal_precession), yet they're still considered stable.  

---

