Order of Kilopi
I know none have been observed yet, but is it impossible that there are a few objects at the Earth/Sun L4/L5 points?
They are consistently 1.5x10^8 km away, so are difficult to see, if they are there.
How difficult would it be to get there, and what would be the cheapest route?
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It seems Mars has a handful of trojan asteroids; why can't we have some?
Order of Kilopi
1) Mars is closer to the asteroid belt Which is the source of possible trojans).It seems Mars has a handful of trojan asteroids; why can't we have some?
2) Jupiter tends to fling asteroids around.
3) An asteroid perturbed by Jupiter would be more likely to be moving slowly enough to be captured by the Mars trojan gravity well than by the Earth's.
The above is a SSWAG*, so take it with an appropriate quantity of NaCl. :wink:
*SSWAG = Semi-Scientific Wild A** Guess
Established Member
Wouldn't just about every object -- i.e. planet -- of significant mass have a set of Trojans? They may not be terribly stable, but given the amount of junk that floats around I'd say it's a safe bet that Earth has a set of objects at those points. But I would also bet that they don't necessarily stay there for long timescales, that is, billions of years.
Honored Member
I thought that earth's Trojans come from New Jersey.
Order of Kilopi
I mostly agree with you. If Mars and even Dione can have them, it would seem that Earth and maybe Venus should have them too. One possible reason why we might not have any is because the perturbations of Jupiter that cause some asteroids to acquire high eccentricities and become Mars-, Earth-, and even Venus-crossers are most likely to produce Mars-crossing asteroids than Earth-crossing asteroids. (They do have to cross Mars' orbit before they can cross the Earth's!) The probabilities for capture near a Lagrange point may also be unfavorable for Earth and Venus.Originally Posted by Emspak
What I wonder about is whether Saturn and Uranus have any. Trojans have been discovered for Neptune, and I think Saturn at least should have them too. Uranus would be less likely since it is far from both sources (asteroid belt and Edgeworth-Kuiper belt). I thought of searching for Saturnian Trojans many years ago, but I don't have the telescopic equipment for it.
If the Earth has Trojans, one reason why we haven't seen them yet is that our searches for NEO's are not optimal for finding objects near the Lagrange points. A Trojan in a tadpole orbit would normally be found within a few degrees of 60 degrees east and 60 degrees west elongation from the Sun. It would move slowly with respect to its Lagrange point, so exposures of search areas about the points on successive nights would show these objects standing almost still while the star fields stream past them.
How bright would these objects be? This is a "back of the envelope" calculation. The asteroid 1 Ceres gets as bright as magnitude 6 at opposition. Rounding the Sun-Ceres and Earth-Ceres distances to 3 and 2 AU respectively, we see that if Ceres were placed at one of Earth's Lagrange points it would receive 9 times the light and we would be half as far, so that it would be 36 times = 4 magnitudes brighter, that is magnitude +2. Now take the diameter of Ceres to be 1000 km. For every division of the diameter by 10 we have 1/100th the area and this means 5 magnitudes fainter. Thus a 100 km asteroid would shine at magnitude +7, a 10 km asteroid at +12, a 1 km asteroid at +17, and a 100 meter asteroid at +22. I think we can rule out 10 km asteroids at the Earth's Lagrangian points, but not yet 1 km asteroids.
The above computation is for an asteroid in a tadpole orbit. Horseshoe orbits would be difficult because they could be anywhere in a 240 degree arc, much of it too close to the Sun, and only their slow changes in elongation from the Sun would give them away.
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