The earth moves around the sun in a circle.
This means it is constantly changing direction.
A change in direction is a change in velocity, which means we are accelerating.
In our everyday lives we are always able to feel acceleration, so why can't we feel the earth's supposed orbit?
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answers:
Morningfox say: No, you can't always feel acceleration. You can't feel it if it is too small. Even if it is larger, constant acceleration feels just like weight.
The acceleration from the Earth motion around the sun is about 0.0006 g's. That's equivalent to a 65 kg person gaining or losing 4 grams on a daily cycle. There's no way you could notice that without special instruments.
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Dump the liberals into Jupiter say: The best answer has already been picked, but I want to add additional information.
On planets in the liquid water zone of an ultracool red dwarf, you can indeed feel the centripetal acceleration due to the (rotationally tidally locked) planet's orbit. The tidal differential amounts to a significant fraction of the total gravity that you'd experience, with the maximum weight being on the part of the planet where the sun is directly overhead, and the minimum weight being on the part of the planet where it is forever midnight.
Furthermore, if you were on a part of the planet where the sun was perpetually on the horizon, the direction toward the sun would seem to be a substantial uphill grade, even if the planet were physically a perfect sphere.
Here's an example.
Star's mass = 0.08 suns
Star's luminosity = 0.0004 sols
Planet's orbital radius = 0.02 AU
Planet's orbital period = 3.652569 days