Satellite with period equal to that of its planet?

[Humaj]

Would it be possible to have a satellite orbiting Earth slowly enough that it always stays between Earth and the sun? Not necessarily directly between so that its shadow is always on Earth, but such that, with an orbit that would take it "behind" Earth, it would orbit at a speed such that when it gets halfway through its orbit, Earth has gone halfway through its own, and its still on the inside of Earth's orbit? Probably much farther away than geosynchronous satellites?
This wouldn't be the same thing as an L1 point in my understanding of Lagrange points, because the object is solely in orbit around Earth, but might not be possible.
And please be specific as to why it's not possible if it's not, so I know whether to go with a fabricated excuse as to how it could be possible, or go with an actual possible story.

 

[mathman]

I suggest you could calculate the distance and see if it makes sense. My guess (I can be completely wrong) is that it would be as far away as the sun, since planetary orbits depend almost entirely on the distance from the sun.

 

[phyzguy]

Would it be possible to have a satellite orbiting Earth slowly enough that it always stays between Earth and the sun?

This wouldn't be the same thing as an L1 point in my understanding of Lagrange points, because the object is solely in orbit around Earth,

Why do you say this isn't the Lagrange point L1? In order to stay between the Earth and the Sun, it needs to orbit both the Sun and the Earth. Relative to the fixed stars, in one year, it will have made one orbit around the Sun, and it will have made one orbit around the Earth. I think this is what is meant by the Lagrange point L1. So the answer is, yes it is possible.

 

[BobG]

Yes, but your radius would be beyond the L1/L2 Lagrange points.

Nothing wrong with that in theory, but keep in mind the Lagrange points are just orbits around the Sun where orbital perturbations from the Earth would keep a spaceship in a constant location relative to the Earth.

Your radius is so big (over 2 million kilometers) that it doesn't take much for other objects (the Moon, which is only 385,000 kilometers away, and the Sun, 150 million kilometers away) to alter your orbit. Just calculating the orbital period and saying you're good really wouldn't be good enough and I'm not positive you could even find a stable orbit like that around the Earth. Or else it would wind up putting you at the Lagrange point. (I've never actually started from that direction, but it would make sense. Edit: In fact, it has to work out that way regardless of your frame of reference. I've just become so accustomed to visualizing them as orbits around the Sun that it seems almost bizarre to use a geocentric frame of reference.)

So, in practice, it would make more sense to use the Lagrange points, since they accomplish the same thing.

And, no, that distance wouldn't match the Earth's distance from the Sun. Orbital period depends both upon the distance and the mass of the object you're orbiting around. The Earth's mass is much less than the Sun's. However, if you're talking only about how long for planets to orbit the Sun, or only how long for spacecraft to orbit the Earth, the mass of the object that you're orbiting around is usually treated as a constant (hence the possible confusion).