Planet 180 degrees from earth in same orbit?

[Dinosaur]

I do not believe in the existence of such a planet. If it existed, could we determine that it was there? My intuition says we could not without a device in a position to actually view it.

There was (is) a series of SciFi novels about such a planet. Its inhabitants knew about us, but we did not know about them.

 

[tamkinrules]

That might be a possibility. If as you say that there is an angle at which there's a blind spot to all, I guess that could be the case. I'm still somewhat confused though, how do you find the angle on a sphere? Also, even if we couldn't see it from earth, what about the moon? People have gone to the moon as well. How do you suppose people wouldn't have seen it from there?

 

[kevinalm]

We might not have seen such a planet, but if it were of significant size (say the size of the Earth) we would almost have certainly known it was there. Its gravitation would create measurable perturbations in the orbits in the solar system.

 

[D H]

That is the L3 libration point, which isn't stable. A planet can't exist there.

 

[Billy T]

That is the L3 libration point, which isn't stable. A planet can't exist there.

Not only that (which of course by itself is enough to rule out the existance of the "180 degree Earth twin"), L3 is made in part by the effect of Earth's gravity reaching 2AU across space, but this gravitational effect is washed out by Venus' gravity, which passes only 0.3AU from L3.

I.e. even if L3 were stable, Venus would quickly drive any planet away from L3.

I suggest this thread be closed or moved to the sesspool.

 

[Fraggle Rocker]

Not only that (which of course by itself is enough to rule out the existance of the "180 degree Earth twin"), L3 is made in part by the effect of Earth's gravity reaching 2AU across space, but this gravitational effect is washed out by Venus' gravity, which passes only 0.3AU from L3. I.e. even if L3 were stable, Venus would quickly drive any planet away from L3. I suggest this thread be closed or moved to the sesspool.

This isn't cesspool material. It isn't even pseudoscience. It's a fairly reasonable question and it has been given a reasonable answer. It raised some interesting scientific points, including yours. That's what this website is all about.

 

[Starthane Xyzth]

Such a "CounterEarth" planet, if it could exist, would be visible from the other planets of the Solar System jsut as easily as Earth is. The Galileo and Cassini probes ought to have spotted it, during their convulted outward journies.

 

[emaad]

intresting

 

[Dinosaur]

The following suggests that I should have been more specific in my description of the question.

That might be a possibility. If as you say that there is an angle at which there's a blind spot to all, I guess that could be the case. I'm still somewhat confused though, how do you find the angle on a sphere? Also, even if we couldn't see it from earth, what about the moon? People have gone to the moon as well. How do you suppose people wouldn't have seen it from there?

If there were no other planets in the solar system, the orbit of the Earth would always be in the same plane. Due to Sol dominating the solar system, this is a close approximation to the actual situation. Imagine a line from the center of the Earth to the center of Sol and extend it beyond Sol. This would define points 180 degrees from Earth. Now imagine an object on this line same distance from Sol as is the Earth. If the velocity of this object matched the orbital velocity of the Earth, this object would have an orbit as stable as the Earths’s, and would be 180 degrees from Earth for at least millions of years.

I do not think this would be some unstable L3 point. An object in such an orbit would not be visible from either the Earth or from Luna. Of course it would sometimes be visible from other planets in the solar system. The following are cogent posts on this subject.

We might not have seen such a planet, but if it were of significant size (say the size of the Earth) we would almost have certainly known it was there. Its gravitation would create measurable perturbations in the orbits in the solar system.

Such a "CounterEarth" planet, if it could exist, would be visible from the other planets of the Solar System jsut as easily as Earth is. The Galileo and Cassini probes ought to have spotted it, during their convulted outward journies.

I think that the perturbations would be measurable and noticed if a long term project were established to check for the existence of such a planet.

I suspect that it might take at least decades of observations to collect enough data to allow an astronomer to be sure that the Counter-Earth planet existed. Unless there were some reason to suspect the existence of such a planet, I doubt that it would be discovered until one of our space probes happened to be in a position to see it and happened to have a telescope pointed in the right direction.

BTW: It would probably take quite a coincidence for some probe like Galileo or Cassini to actually notice it & report the data to NASA.

 

[Billy T]

To Dinosaur:

Your re-worded version is more of a challenge to “shoot down” but still it can be:

If “180 Earth” is small compared to Earth then the prior stability arguments apply. So we will assume it is at least “Mercury size.” If it is to remain 180 degrees from Earth. It also must be in an orbit with Earth’s eccentricity as Earth is moving thru angles faster at perigee than apogee. I.e. it must be near its perigee at same time that Earth is. This is highly unlikely, but possible.

The thing that kills all possibility of it existence is not that it could be seen by a satellite as quite possibly as you note none have looked for it. What removes all doubt is that some satellite trajectories are known to be as calculated without any effect of 180 Earth in the calculations.

APL/ JHU, where I worked, has sent several that would have had different trajectories, if 180 Earth Existed. In the table here: http://en.wikipedia.org/wiki/Lagrangian_point you will STERO A &B and note that each flew thru one of the two stable Lagrangian points, (L4 or L5 but were going too fast to be captured in them. Click on it for more details.)*

APL also has a satellite that will fly very close to the sun and actually sample the solar atmosphere. (It may already have.) Also, as I recall, the APL satellite on its way to Pluto made two or three swing bys of Venus and (possibly one of Mercury?) to get gravitational boost in speed. (It was the fastest at launch ever launched, but needed more speed to reach Pluto in a few more years.) APL also launched a satellite which with some Mercury and/or Venus near misses will be thrown up out of the ecliptic and be the first to look down on the North, I think, Pole of the sun. None of these very precise “near misses” for gravitational boost would have been possible (without including the mass of 180 Earth in the calculations) if 180 Earth existed with any mass large enough to remain at Earth’s L3. All told, I think there have been at least a dozen swing by of the inner planets for gravational boost, none of which would have worked if 180 Earth were real.

Other natural satellites (Mercury and Venus) would precess** at different than their observed rates and surely the line of apsides would change at a different rate.

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*If 180 Earth existed with sufficient mass to remain un seen from Earth, the two stable Lagrange points would be displaced and flying thru where they are not would be different than where they are. For example If 180 Earth had Earth’s mass L4 and L5 would be 90 degrees a head and behind Earth, not +60 & -60 degrees.

**Mercury’s (or is it the line of apsides?) been measured so accurately that even the relativistic effects must be included in the calculations to get agreement with the observations.

PS I tried briefly to find some of the details on inner planet orbit swing bys. Here is an old one:
"... In its roundabout trek to Jupiter, Galileo will first fly to Venus before looping back to the Earth. It will pass within 600 miles of its home planet, and use gravity for a kick that will send it out as far as the asteroid belt between Earth and Mars. This elongated orbit will bring back to Earth a second time, where it will make a startlingly close pass of 185 miles above the surface, a bit less than the distance between New York City to Harrisburg, Pa. As it passes, it will pick up 8,000 miles an hour of additional speed, enough to shoot it outbound toward Jupiter. ..." From: http://www.nytimes.com/1989/10/10/s...with-an-assist-from-venus.html?pagewanted=all

Do you think it would have missed by the 185 miles if the gravity of 180 Earth had been acting on it for months? The APL sun sampler will fly so close to the sun that the solar heating will be about 500 times greater than at launch, as I recall. (I get monthly news letters still from APL but do not save them.)

SUMMARY: We know all the significant masses that orbit the sun. If insignificantly small it would not remain at unstable L3 of Earth.

 

[Janus58]

The following suggests that I should have been more specific in my description of the question.If there were no other planets in the solar system, the orbit of the Earth would always be in the same plane. Due to Sol dominating the solar system, this is a close approximation to the actual situation. Imagine a line from the center of the Earth to the center of Sol and extend it beyond Sol. This would define points 180 degrees from Earth. Now imagine an object on this line same distance from Sol as is the Earth. If the velocity of this object matched the orbital velocity of the Earth, this object would have an orbit as stable as the Earths’s, and would be 180 degrees from Earth for at least millions of years.

It won't last in that position that long. Once it is even slightly perturbed out of its position by another planet it will continue to drift out of position (For one thing, the Earth's gravity which pulled directly towards the Sun when it was 180° opposite now has a slight side component. While small, this pull is constant and compounds over time.)

I ran a quick sim on gravity simulator, and after less than fifty years it had drifted out of position far enough that its line of sight from the Earth was was as far as Mercury's is. IOW, easily visible from Earth.

 

[Dinosaur]

Janus & Billy T: You two seem credible. I accept your views.

It seems strange to me that Earth has had a stable orbit for millions, probably billions, of years & yet a planet 180 degrees away cannot maintain that position relative to Earth for more than 50 years.

Chaos seems to ruin symmetric orbital systems. I wrote a gravity simulator whiich does a not bad job, but I do not have a lot of faith in its precision. All sorts of symmetic systems broke down. For example, I simulated n-bodies (n from 2 to 5) chasing eachother around a common circular orbit, with or without an extra yo-yo like body. The yo-yo initially oscillated along a line perpendicular to the plane in which the n-bodies orbited.

BTW: Some French mathematicians discovered an analytically stable system with 3 objects chasing each other around a figure 8 orbit.

 

[Billy T]

Janus & Billy T: You two seem credible. I accept your views.. ..

Good. Janus58's is much stronger than mine. I only show: "It ain't there." He shows it would be soon gone, even if it were.

 

[Dinosaur]

Janus & Billy T: After thinking a bit, I now believe that I should not have agreed with you folks so readily.

The time for one orbit of the Earth is the basis for the length of a year. The length of the year varies less than a second per century. Orbital perturbations (mainly due to Venus & Mars, our closest planetary neighbors) do not seem to have much effect on our orbit.

If there were a counter Earth (180 degrees from us) with the same orbital parameters, its orbit should be as stable as the Earth’s orbit. It would be subject to essentially the same orbital perturbations as the Earth.

The above indicates that the time for one orbit of counter Earth would also change less than one second per century. I think this suggests that counter Earth would take many thousands of years to move from the 180 degree position to either 179 or 181 degrees. There fore it would not be visible from Earth, Luna, or any Earth satellite for at least 100,000 years. My calculations cut some corners & I think they underestimate the time.

Janus: Do you trust your simulator? Might chaos effects be a problem? A very slight error in initial conditions could cause extreme error in the results of the simulation.

BTW: I still doubt that effects of a Counter Earth on the orbits of Mars & Venus would be noticeable unless there was a project specifically designed to check for the existence of a Counter Earth planet.

 

[Billy T]

Janus & Billy T: After thinking a bit, I now believe that I should not have agreed with you folks so readily.

The time for one orbit of the Earth is the basis for the length of a year. The length of the year varies less than a second per century. Orbital perturbations (mainly due to Venus & Mars, our closest planetary neighbors) do not seem to have much effect on our orbit.

If there were a counter Earth (180 degrees from us) with the same orbital parameters, its orbit should be as stable as the Earth’s orbit. It would be subject to essentially the same orbital perturbations as the Earth....

BTW: I still doubt that effects of a Counter Earth on the orbits of Mars & Venus would be noticeable unless there was a project specifically designed to check for the existence of a Counter Earth planet.

You need to state roughly the mass of your counter Earth has. But since you do not, I will (again) shoot any you choose down, I think:

If it Earth like, I am inclined to agree with you that it would be as stable as Earth, but even it has only (I guess) 10% of Mercury's mass the gravity assist boosts of space craft using Venus or Mercury would not have worked as calculated. Neither would the flights thru L4 and L5 have gone as calculated. So it mass must be more "Queen Mary or QE II like" than Earth like.

If it has such a small mass to not have changed these trajectories, then it is in the unstable L3 of Earth. I do not know how long it takes to throw it into L4 or L5's gravitational potential wells (I assume, that is where it would go.). The Main force acting on a small mass would of course be that of the sun, but Jupitor, Mercury and Venus would have significant forces on it too(and it on them equally); but almost all of the accelerations is a perturbation of that small mass.

It might be an interesting study, which I can not do, to find how long the greatest mass which is small enough to not have had noticble effect on the gravity boost near misses (or L4 & 5 flythru)* could hide behind the sun from direct view from Earth. (And what that mass is.) I bet the allien base camp there from which the UFOs come for closer looks is quite cramped. They probably station keep with a solar sail. :shrug:
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* Unless the gravity boost on Venus or Mercury happened when the boosting planet was nearly on the Earth sun line,** I think the gravity boost will set the lower mass than the L4 or L5 fly thru if it is way too fast to be captured there. (That will not happen even in a slow fly thru, I think, unless it can lose some energy while falling down the potential wells that are there. I.e. interact with some not yet detected rocks in the well. I think that these wells are not really long term stable - Jupitor probably sees to that - so not likely to have any "rocks" in them.) The Jupitor/sun L4 & L5 do have rocks in them that have been observed. (Called the Trojans, one holds the Greek Trojans and the other has the Troy Trojans.)

** Then the calculation error would be like slight error in the mass of the sun used. If not on that line, then there is a force not directed towards the sun acting. Like a micro thruster on the space craft, its effect would be noticed.

The people studing the "Pioneer anomaly" probably have some support for you, but very little, I bet. Also I hesitate to question Janus58, but it does seem possible to me that an Earth mass at Earth's L3 could get into some resonance lock there.

He knows much more than I do about all this, but if counter Earth were to drift away from Earth's L3 then, as he stated, there would be a force on it towards Earth (not the same direction as the towards the sun). It seems to me the component of that force which is not towards the sun is like small rocket thrusting out the back. This, I think mainly raises the orbit so it would slow its angular rate and fall back towards L3. - But again Janus knows much more than me, so I am probably wrong to even suggest there could be some sort of resonance trapping when both have roughly the same mass.

Again, however, even if there could exists a significant mass counter Earth resonately trapped, it ain't there by my arguements about gravity boost & L4/5 fly thru calculations worked.

SUMMARY: The only way there is a significant mass at Earth's L3 is for it to be an allien craft, station keeping but that is consistent with the Pioneer anomaly (and nothing else is) so they must be there. Hope they do not read this - I don't want to be taken there to have my superior brain examined.

 

[PieAreSquared]

Earth's orbit is not exactly concentric , the Earth is in an elliptical orbit

while close;

aphelion ..... 152,097,701 km ,1.0167103335 AU
perihelion ... 147,098,074 km , 0.9832898912 AU

probably enough to rule out any chance of another 180 degree opposed world being undetected... except perhaps in comic books

 

[PieAreSquared]

Such a "CounterEarth" planet, if it could exist, would be visible from the other planets of the Solar System jsut as easily as Earth is. The Galileo and Cassini probes ought to have spotted it, during their convulted outward journies.

and there is always that too

 

[Starthane Xyzth]

Not to mention: if the planetary accretion mechanism of the early Solar System had favoured the simultaneous formation of two planets with the same semimajor axis and orbital period, the chances are that the other planets would also have counterparts on opposite sides of the Sun.

When we see Venus in the morning sky, we would see CounterVenus (Aphrodite?) in the evening the same day. Whenever Jupiter rose, Zeus would set... you get the picture.

 

[Janus58]

Janus & Billy T: After thinking a bit, I now believe that I should not have agreed with you folks so readily.

The time for one orbit of the Earth is the basis for the length of a year. The length of the year varies less than a second per century. Orbital perturbations (mainly due to Venus & Mars, our closest planetary neighbors) do not seem to have much effect on our orbit.

If there were a counter Earth (180 degrees from us) with the same orbital parameters, its orbit should be as stable as the Earth’s orbit. It would be subject to essentially the same orbital perturbations as the Earth.

The above indicates that the time for one orbit of counter Earth would also change less than one second per century. I think this suggests that counter Earth would take many thousands of years to move from the 180 degree position to either 179 or 181 degrees. There fore it would not be visible from Earth, Luna, or any Earth satellite for at least 100,000 years. My calculations cut some corners & I think they underestimate the time.

Janus: Do you trust your simulator? Might chaos effects be a problem? A very slight error in initial conditions could cause extreme error in the results of the simulation.

Yes, I trust the simulator, You can run a entire Solar system sim on it and it remains stable for a looong time.

Your statement about both planets seeing the same perturbations is not exactly true. While over a long time they average out to being the same, they are not the same from moment to moment, and that's where the problem is.

For example, at one particular moment Earth and Jupiter will be on the same side of the Sun and Counter-Earth and Jupiter will be on opposite sides of the Sun. Now imagine that Jupiter's pull on the Earth is such that it slows the Earth slightly in its orbit. As a result, counter-Earth catches up a bit. But now, the gravitational attraction between Earth and Counter-Earth no longer passes through the center of the Sun. This adds a vector component, that tends to pull back (opposite to its orbital motion) on counter-Earth.

Now at first it might seem that this acts as a restoring force that moves Counter-Earth back into position. But this is orbital mechanics and all is not as it seems. Pulling back on an object in orbit causes it fall into a lower faster orbit. So the net effect of this force is to cause counter Earth to catch up with Earth even faster. Not only that, but as it does so, the magnitude of the vector force that contributes to this, grows larger. Th effect snowballs and pulls the planets out of alignment faster and faster.

Now the difference in this perturbing force and the perturbing effect of other Planets is that the pull of the other planets vary in force and direction, fist pulling one way, and then in the other, so that their net forces over time tend to cancel out. But the pull between Earth and Counter-Earth (although small) is constant and pulls in one way.

Now here is another reason I trust the simulator:

According to what I just said, something interesting happens when the planets have drifted to a certain relative position of each other. The angle between Earth, Sun, and Counter-Earth begins to change to where the leading planet begins to pull forward on the trailing planet. This starts to put the trailing planet into a higher, slower orbit. It begins to slow its advance on the leading planet and eventually starts to retreat again.

In time, it will return to its initial 180° position, But will be moving in a slower orbit. it drifts past this point, becomes the trailing planet and the whole process starts over with the roles of the planets reversed.

Now I've run this on the Sim (two planets start 180° apart and one perturbing planet. In this case I used two Earths and Venus). I ran it long enough to watch it go through many of these cycles, just like predicted.

 

[Billy T]

...According to what I just said, something interesting happens when the planets have drifted to a certain relative position of each other. The angle between Earth, Sun, and Counter-Earth begins to change to where the leading planet begins to pull forward on the trailing planet. This starts to put the trailing planet into a higher, slower orbit. It begins to slow its advance on the leading planet and eventually starts to retreat again.

In time, it will return to its initial 180° position, But will be moving in a slower orbit. it drifts past this point, becomes the trailing planet and the whole process starts over with the roles of the planets reversed.

Now I've run this on the Sim (two planets start 180° apart and one perturbing planet. In this case I used two Earths and Venus). I ran it long enough to watch it go through many of these cycles, just like predicted.

Are you here confirming my guess about "resonance trapping" in third from end paragraph of post 15? It was:

"{Janus58} knows much more than I do about all this, but if counter Earth were to drift away from Earth's L3 then, as he stated, there would be a force on it towards Earth (not the same direction as the towards the sun). It seems to me the component of that force which is not towards the sun is like small rocket thrusting out the back. This, I think mainly raises the orbit so it would slow its angular rate and fall back towards L3. - But again Janus knows much more than me, so I am probably wrong to even suggest there could be some sort of resonance trapping when both have roughly the same mass. ..."