I cant reply to your other comment - that is what I assumed you were saying but it does not make sense to me outside the process that naturally occurs - I'm assuming the suns gravity simply cant move objects of such different mass, at the same rate, and thereby the orbit and position changes accordingly?
The speed doesn't have to be much different - 366 days and earth will eventually hit asteroid - 364 days and it will eventually hit the earth.
Ahh, Im still having a hard time figuring out why that would take more energy - I'm going to be researching this all morning tomorrow.
> I'm assuming the suns gravity simply cant move objects of such different mass, at the same rate, and thereby the orbit and position changes accordingly?
Kind of? An object moving in a circular motion at a constant speed must have an acceleration towards the center of the circle of (velocity^2)/(radius). This means that two objects in the same circular orbit moving at different speeds must be experiencing different accelerations towards the center of the circle.
In the simplified case of orbits around the Sun, that acceleration towards the center of the orbit is due to the Sun's gravity. However, gravity accelerates everything at a given distance at the same rate. As a result, you can't have two objects solely influenced by the Sun's gravity that orbit around the Sun with the same orbital shape but moving at different speeds. You'd need something in addition to the Sun's gravity to pull that off.
> The speed doesn't have to be much different - 366 days and earth will eventually hit asteroid - 364 days and it will eventually hit the earth.
Sure. When I said slightly-larger-than-Earth-sized orbit, I really meant it. Kepler's third law of planetary motion states (approximately) that (orbital period)^2 is proportional to (radius)^3. Assuming I did my math correctly, if your orbital period goes from 365 to 366 days your orbital radius gets ~0.18% larger, which is roughly 274000 km increase over the radius of Earth's orbit. That would fit inside the Moon's orbit (~385000 km from the Earth)!
> Ahh, Im still having a hard time figuring out why that would take more energy
At least the way I was thinking, the short answer is that one alteration to an orbit is likely to be cheaper than two, especially if you aren't particularly concerned in what manner the asteroid eventually collides with Earth.
The speed doesn't have to be much different - 366 days and earth will eventually hit asteroid - 364 days and it will eventually hit the earth.
Ahh, Im still having a hard time figuring out why that would take more energy - I'm going to be researching this all morning tomorrow.
Thanks for the help!