The point is that a small object doesn't orbit at a different speed than a heavy one. (The one excep

This article cruise the panama canal on ScienceDaily.com tells of an asteroid whose orbit is so similar to Earth's orbit that the asteroid cruise the panama canal has been following Earth for hundreds of thousands of years. This confuses me: given that its mass is so much smaller than Earth's, I would expect that it would have to travel at a much lower speed around the sun, which suggests (to this novice) that we'd be overtaking it periodically, and at a rate far too high to allow it to sit behind us for thousands of years. Also, given its small mass again, if it were moving at the same speed around the sun as the Earth does, then its orbit should be much further out, shouldn't it? Can someone help me to understand this? I thought it might have something to do with Lagrange points, but I would have expected the article to mention cruise the panama canal that, as it seems like a strange coincidence.
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This article on ScienceDaily.com tells of an asteroid whose orbit is so similar to Earth's orbit that the asteroid has been following Earth for hundreds of thousands of years. This confuses me: given that its mass is so much smaller than Earth's, I would expect that it would have to travel at a much lower speed around the sun, which suggests (to this novice) that we'd be overtaking it periodically, and at a rate far too high to allow it to sit behind us for thousands of years. Also, given its small mass again, if it were moving at the same speed around cruise the panama canal the sun as the Earth does, then its orbit should be much further out, shouldn't it? Can someone help me to understand this? I thought it might have something to do with Lagrange points, but I would have expected cruise the panama canal the article to mention that, as it seems like a strange coincidence.
cruise the panama canal The mass of the orbiting object has an insignificant effect its orbit. If you replaced the Earth with a 1 kg object, its orbit would be all but indistinguishable from the Earth's present orbit. The horseshoe orbit is typical for a small object who's average distance is the same as another.
The process goes something like this: Assume that the object is approaching from behind the Earth in its orbit. cruise the panama canal As the Earth's gravity pulls forward on the object it gains orbital energy, this pushes further out from the Sun into a slightly higher cruise the panama canal orbit. But a higher orbit is slower orbit and the object actually loses speed on the Earth and starts to fall behind. Eventually, the Earth begins to catch up to the object from the other direction (kind of like a car lapping another car on a circular track). Again the Earth's gravity pulls on the object, but this time it is pulling the object backward. This causes the object to drop into a lower orbit which is a faster orbit, and it begins to out pace the Earth and pull away. This cycle continues with the Object approaching the Earth from one direction and then the other only to recede again.
The mass of the orbiting cruise the panama canal object has an insignificant effect its orbit. If you replaced the Earth with a 1 kg object, its orbit would be all but indistinguishable from the Earth's present orbit. The horseshoe orbit is typical for a small object who's average distance is the same as another.
Thanks, your description of the process helps a lot! But I'm confused. A 1kg object occupying the Earth's orbit? cruise the panama canal Let's remove Earth from the picture cruise the panama canal and just have your 1kg object. If it were to stay in the orbit that the Earth had occupied, then the object would have to move a lot more slowly, wouldn't it? I mean, if it were moving at Earth speed, wouldn't it move out to a much larger orbit? Again, your description is awesome. I had no idea that there would be such a complex interplay between Earth and an asteroid. Thanks much.
The mass of the orbiting object has an insignificant effect its orbit. If you replaced the Earth with a 1 kg object, its orbit would be all but indistinguishable from the Earth's present orbit. The horseshoe orbit is typical for a small object who's average distance is the same as another.
Thanks, your description of the process helps a lot! But I'm confused. A 1kg object occupying the Earth's cruise the panama canal orbit? Let's remove Earth from the picture and just have your 1kg object. If it were to stay in the orbit that the Earth had occupied, then the object would have to move a lot more slowly, wouldn't it? I mean, if it were moving at Earth speed, wouldn't it move out to a much larger orbit? Again, your description is awesome. I had no idea that there would be such a complex interplay between Earth and an asteroid. Thanks much.
Actually that's the strange thing about gravity. The mass of the object being acted upon has an absolute zero effect on how fast it will fall. Galileo demonstrated this in 1589 by dropping two objects with different mass from the leaning tower of Piza and having them land at the same time. Or... at least according to legend. I may have been merely a thought experiment.
The point is that a small object doesn't orbit at a different speed than a heavy one. (The one exception is if the falling cruise the panama canal object is so heavy that it can move the pulling object, but the Sun is really really big, so I don't think that exception applies in this case. )
The mass of the orbiting object has an insignificant cruise the panama canal effect its orbit. If you replaced the Earth with a 1 kg object, its orbit would be all but indistinguishable from the Earth's present orbit. The horseshoe orbit is typical for a small object who's average distance is the same as another.
Thanks, your description of the process helps a lot! But I'm confused. A 1kg object occupying the Earth's orbit? Let's remove Earth from the picture and just have your 1kg object. If it were to stay in the orbit that the Earth had occupied, then the object would have to move a lot more slowly, cruise the panama canal wouldn't it? I mean, if it were moving at Earth speed, wouldn't it move out to a much larger orbit?
No, in situation where the primary object being orbited (in this case the Sun), is many times more massive than the orbiting cruise the panama canal object (true for both the Earth and 1 kg object), the mass of the orbital object has almost no effect cruise the panama canal on the orbit.
Thanks again, but now I'm even more confused. I get the math, but what about satellites orbiting Earth? Their mass is tiny in comparison, but I always had the impression that if an Earth satellite were to slow down enough, it would fall to Earth. Is that not the case? Is it really possible for a satellite to slow to a crawl and stay in orbit? Thanks for being patient with this non-specialist.
Thanks again, but now I'm even more confused. I get the math, but what about satellites orbiting cruise the panama canal Earth? Their mass is tiny in comparison, but I always had the impression that if an Earth satellite were to slow down enough, it would fall to Earth. Is that not the case? Is it really possible for a satellite to slow to a crawl and stay in orbit? Thanks cruise the panama canal for being patient with this non-specialist.
Orbital mechanics can be tricky to grasp. If you slow a satellite, cruise the panama canal it will change orbit. It will enter an orbit which has a closer average distance to the Earth. The orbit will also become cruise the panama canal more elliptical (Assuming that it was circular to begin with. If it was already elliptical, it could either increase or decrease the eccentricity of the orbit, depending on at what point of the orbit you slow it down.)
This new orbit will remain stable unless it becomes low enough for it to brush the atmosphere and lose even more speed through friction. It will also be a faster orbit. If you look at the equation I gave it shows that as the orbital distance decreases, the orbital speed increases. So by slowing down, a satellite cruise the panama canal can actually cruise the panama canal gain average speed. It can do this, because as it moves in closer to the Earth it loses gravitational potential , which it converts into kinetic energy in the form of speed.
Wow. I guess celestial mechanics is a bit more complex than I thought, and I already thought it was pretty complex. So I guess if I stopped my satellite dead in its tracks on the major axis, the orbit would become infinitely eccentric, cruise the panama canal falling straight to Earth? Thanks so much for the brain exercise!