That's a good point. I haven't done the math but my gut tells me the earth's orbit around the sun is almost circular so the acceleration is probably too small to notice given that it takes A YEAR to complete one orbit.

I just looked up the flight path for the Orion capsule and it's pretty impressive. It took off from earth to meet up with where the moon would be by the time it got there, used the moon's gravity to fling it away in the opposite direction, and it's now on its way to meet up with the moon a second time and use its gravity to fling it back toward earth for a landing.