I think I read about this somewhere: that there are asteroids, unknown number, in the earth’s orbit, following it as it revolves around the sun. Is this true?
They’re called Trojan asteroids, and several planets have them. They can orbit either 1/3 ahead or 1/3 behind the planet whose orbit they share.
There are many in the Earth-Sun Lagrangian points. There are also companion asteroids in horseshoe orbits.
That’s actually 1/6 (60 degrees) of the orbit ahead or behind the Earth. The first wasn’t discovered until 2010 and is about 300 meters in diameter so they are pretty small. There are also some very minor ones, I believe, in the L4 and L5 Lagrangian points in the Moon’s orbit around the Earth.
Are any of these interesting for potential mining operations?
Is there anything in orbit at L3?
L1, L2, and L3 are impossible to stay put at or near without continual orbital adjustments, so almost certainly not. Objects such as asteroids can remain near L4 and L5 indefinitely, though.
Whoops! You’re right; it’s 1/6 ahead or behind, not 1/3.
There are some man-made satellites which were deliberately put at the unstable Lagrange points for various reasons, though. The instability is actually a benefit there, since it means there isn’t much naturally-occurring crud to interfere with your satellite.
The number is relatively small, though. A planet “clears its orbit”. That’s true by definition of a planet these days, but any sufficiently large body will clear its orbit of most everything else other than its own moons and bodies that orbit in concert with it.
The latter includes horseshoe orbits as well as L4 and L5 orbits. I wouldn’t be surprised to learn that there are other options.
Of cource, there are also very eccentric near-earth orbits (like comets), but those don’t “follow the Earth” as mentioned in the OP.
“Horseshoe orbits”? 
Please explain.
dougie_monty, here is a nice description of a horseshoe orbit, shown both in an inertial frame and relative to the Earth (where the orbit is bean/horseshoe shaped) 3753 Cruithne - Wikipedia
These are extreme cases of co-orbits. A co-orbit happens when two objects are in similar orbits. One will always be in a somewhat smaller orbit. It will orbit somewhat faster than the other and eventually catch up to it. When that happens, gravitational interactions cause the two to swap orbits, so that the inner one is now in the outer orbit and vice versa.
Now how much their orbits change at this swapping depends on the relative masses of the two bodies. If the two are the same mass, they swap orbits exactly. But if one outmasses the other, the lower mass one changes orbital size more than the other. The bigger the difference in mass, the bigger the difference in how much they change.
Janus and Epimetheus, two satellites of Saturn, co-orbit. Janus masses about three times Epimetheus, so Epimetheus changes it’s orbit about three times as much as Janus. In the case of these co-orbiting asteroids, the asteroids are outmassed by the Earth by many orders of magnitude. Thus the Earth hardly changes orbit at all (at a guess, the change is probably measured in microns) while the asteroid makes a major change (thousands of kilometers). From the perspective of the Earth, the orbit of the asteroid resembles a horseshoe, hence the name.
But there’s no chance of a collision, is there? :eek:
Not from co-orbiting asteroids. The gravitational interactions with Earth that cause the orbit swap happen far enough away that they actually don’t come very close to Earth at all. Their orbits are stable in the short term, although eventually they’ll probably be perturbed out of their co-orbits. At that point you may start worrying.