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

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  • $\begingroup$ Are you referring to the poles of Earth or the Sun? $\endgroup$ – HDE 226868 Dec 18 '14 at 2:59
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    $\begingroup$ There's a basic problem with long-term stability of a polar orbit. That problem is the Kozai mechanism. $\endgroup$ – David Hammen Dec 18 '14 at 3:05
  • $\begingroup$ @HDE 226868 polar solar orbit refers to the sun's poles $\endgroup$ – Neomada Dec 18 '14 at 22:53
  • $\begingroup$ @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? $\endgroup$ – Neomada Dec 18 '14 at 23:44
  • $\begingroup$ @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. $\endgroup$ – dotancohen Dec 20 '14 at 10:16
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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.

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.

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  • $\begingroup$ I would be interested to know how stable (n x years), but take the rep. $\endgroup$ – Neomada Dec 19 '14 at 18:34
  • $\begingroup$ 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.... $\endgroup$ – Robert Farley Dec 19 '14 at 18:49
  • $\begingroup$ 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). $\endgroup$ – Neomada Dec 19 '14 at 19:01
  • $\begingroup$ I originally accepted ganbustein's answer (sorry ganbustein) but realised after the comment from Dr Hammen this could not be stable. $\endgroup$ – Neomada Dec 19 '14 at 19:47
  • $\begingroup$ 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 en.wikipedia.org/wiki/Stability_of_the_Solar_System but who knows how much longer? $\endgroup$ – Robert Farley Dec 19 '14 at 20:40
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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.

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  • $\begingroup$ An orbit that has to rotate is not what I would consider "stable". $\endgroup$ – ganbustein Dec 18 '14 at 2:50
  • $\begingroup$ @ganbustein Planets' orbits change, yet they're still considered stable. $\endgroup$ – HDE 226868 Dec 18 '14 at 3:00
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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.

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