How do Trojan Asteroids effect a planets' orbits

[Eric M. Jones]

Question:

What would happen if a planet's trojans were removed or added to? And I don't mean "very little" please. What exactly would happen, for example, if a planet's huge trojan asteroids were pushed out of orbit into the Sun? What would happen if L4 and L5 had asteroids as big as the planet?

 

[mfb]

L4 and L5 exist for small masses only, a large mass there would not see any special point as its own gravity would influence the other object significantly, and ruin the whole concept of Lagrangian points.

If you remove Jupiter's trojans at one side somehow, the orbit would change a tiny bit.

 

[Eric M. Jones]

>MFB

Thanks for the reply, but I don't really love the answer. If the Trojans were removed, HOW would the planet's orbit be affected? And which, the trojans or the greeks would move the orbit where?

My guess is that if the trailing L point were emptied, the orbital R would increase (and lengthen the period), and emptying the other L would decrease the R and shorten the period.

Can you be more specific?

 

[mfb]

HOW would the planet's orbit be affected?

The orbital parameters would shift slightly. If you remove trojans in front of the planet, I would expect the semi-major axis to decrease a bit. If you remove those behind it, I would expect some increase. The eccentricity change depends on the position where you remove them, the plane of the orbit should stay the same (neglecting long-term influences of other planets).

Where is the point? Do you have some specific goal in mind?

 

[Eric M. Jones]

>>Where is the point? Do you have some specific goal in mind?

I am writing a fictional work where an asteroid that grazes the Sun and changes orbit to impact the Earth in about a century. The size of the asteroid precludes moving it or blowing it up. The ultimate solution is to move the Earth very slightly over the decades. Possible? It's a numbers game. Could the Earths orbit be moved just several seconds of orbit in a century. That's why emptying or moving the trojans is of interest. I am also interested in "slingshot" trajectories, which speed up spacecraft or asteroids, but also change planetary orbits. It's a game of numbers.

 

[mfb]

If you can move earth, moving an asteroid is easy as pie. You need roughly the same velocity change for both, but the asteroid is lighter by a factor of at least 10000.

 

[Eric M. Jones]

>>If you can move earth, moving an asteroid is easy as pie. You need roughly the same velocity change for both, but the asteroid is lighter by a factor of at least 10000.

There is no upper limit to an asteroid's size. That is the point of the story. The one in the story is 20% bigger than the Earth. It's called Nemesis. Moving it or deflecting it would be impossible. Moving the Earth just enough in a century or so might just be possible.

BTW: I write a lot for for www.PerihelionSF.com

 

[StrayCatalyst]

If Nemesis is 20% larger than Earth, its mass would be greater still - you wouldn't be able to simply move the Earth a short distance and watch Nemesis streak past, as the close passage of such a mass would significantly change the orbit of the Earth - we'd still all die, but not as quickly or with as loud a noise. The best chance would be to try to alter the path of Nemesis before it reaches the sun - if you could alter its course by even a small amount, the resulting change in path would be much larger. If you could get Nemesis' path to go off the ecliptic, or closer to the sun (melting it, in addition to slinging it in another direction) it could work. You might also bombard Nemesis with anything needed in order to change its albedo - make it darker and the sun's heat will turn a much greater percentage of its mass into comet tail, thus changing its path again due to the different mass.
If a mass 135% or so of the mass of our planet passes close enough to be of interest to anybody except astronomers, the end result would be a new orbit for Earth, with resulting catastrophic effects. The moon is 1.2% of the weight of the Earth, and has serious effects on tide, and possibly on earthquakes. Increase that by two orders of magnitude... and remember that the majority of the Earth's core is at least semi-liquid.
It's possible that some forms of life would survive, but none of them would be much higher on the food chain than bacteria, and the climate of the planet would be severely impacted by the change in orbit. The new orbit of the planet might or might not be within the "Goldilocks zone" that permits life, as water might boil (if we got closer to the sun) or freeze.
If the asteroid could not be moved or deflected, then your story has a foregone conclusion at the end. However, with a century to prepare, Nemesis could be affected in a lot of ways, to make the sun do the hard work to reduce the threat.

 

[Eric M. Jones]

Dear StrayCatalyst

As I said, it is all about the numbers. Nemesis passes the Earth at 50 kps on its way out to the Kuiper belt. Its eccentricity is 0.997, so getting to it is impossible. When it comes back, same deal. White paint or nukes won't affect it enough. The point of the story is that moving the Earth becomes a possible solution (over many decades), and tossing or rearranging the trojans or greeks might be a way to accomplish this.

In the end, The numbers don't have to make perfect sense, but I wanted to get within shooting distance of scientific possibility.

I appreciate your inputs, so how might you solve the problem? Remember the basic twist to the story is that the asteroid cannot be moved. But we Earthlings have 60-70 years to change the Earth's orbital position by just enough.

 

[StrayCatalyst]

The Earth is fairly heavy, and moving it presents some other problems - we aren't sitting still in space, and it's not a coincidence that life developed in our current conditions. Unless you're relying on wavehandium, the only way to move the Earth in any significant way would be to change its mass enough to alter its orbit. Having a century to reduce or increase the mass of the planet by enough to alter its orbit, would be largely impossible - I'm not sure what percentage it would take to change our orbit enough to dodge Nemesis by enough that its gravity wouldn't ruin ours, but let's assume two percent would do the trick.

1.194438 x 10 to the 23rd kilograms. AKA, 119,443,800,000,000,000,000,000 kilos of mass removed from the planet, if I'm doing the math correctly. And you'd have to get it not only off the surface, but out of orbit! A century isn't nearly long enough for that sort of endeavor, you're talking about removing a mass greater than that of the moon, from the surface of the planet, without rendering the planet unlivable.

That being said, if you found a way to move the moon out of orbit, without the tidal stresses destroying the planet, you could perhaps place the moon where it would be struck by Nemesis, in the hopes that the impact would alter the course of Nemesis. If Nemesis is of comparable mass to Earth, then you want to alter its course, not ours - our planet has to stay pretty close to its current orbit if we want to keep living here.

I can't see a practical way to change the orbit of Earth without making it unable to support life, but I'm only an engineer, not an astrophysicist.

 

[mfb]

The mass of Earth's trojans is negligbile compared to earth, moving them will not have any measurable influence on earth.

If you want to move Earth by 10000km (a very low, optimistic number for the required displacement) in 100 years, you have to change its velocity by about 600μm/s (assuming a constant acceleration relative to the current orbit). Possible ways to achieve this:

• Eject 3*10¹⁵kg per year with a velocity of 10km/s.
  With 100% efficiency, this would require 20 000 000 GW of power (where big power plants generate about 1GW of electric power). And even if we find some way to provide this:
  The StarTram design promises to be able to launch up to ~3*10⁸ kg/year (=10kg/s) into a low Earth orbit. Let's say we can improve this to get the required speed. In that case, we need 10 million StarTrams. The estimated costs for a single one (!) are ~20 billion dollars, even with reduced costs due to mass production this is not possible. There are other, similar projects, but all of them are very expensive.
• Let 2*10¹⁵kg per year in asteroids pass close to earth, giving them an average velocity change of 15km/s.
  This requires a close fly-by of an object with a diameter of ~15 km (big enough to kill us all if it hits earth) every year, or 3 with a diameter of 1.5 km every day. No idea how to achieve this, but it looks more promising than the other option.