Also not an astral physician, but I think actually no. Using the moon as an example, I'm pretty sure we technically orbit the moon, while the moon orbits us. It pulls us back and forth as it orbits around us, and that balances out since it comes from all directions. If you trace the Earth's orbit around the sun close enough we should be moving in a slightly wobbly or spiraly shape. I think since gravity pulls equally on all matter, a satellite and a planet with the same speed and direction would have the same orbit, and to mess with that you would have to increase our mass to the point where we were affecting the sun's orbit. But please don't make Earth massive enough to seriously affect the sun's orbit, because no one would ever be able to break the high jump record again.