Imagine you're in a car, cruising along the motorway (freeway in the US, I think?) at 85 mph. Although you're thumping along, you don't feel any motion. Now imagine you have to brake suddenly (some twat in a Passat cuts you up), you'll be thrown forward in your seat by the deceleration, and then as you get up to speed again when the idiot in the Passat gets out of your way you'll be pressed back in your seat.
Now, imagine doing the same thing but being blind-folded. Suppose for a second the car's so good you can't hear any wind or road noise, or fell any vibrations or bumping through the suspension. There's now no way you can tell the difference between travelling at 85mph, 40mph and being stationary. However as soon as your speed changes you can feel the acceleration acting on your body.
Einstein's theories extend this principle. There is no experiment you can perform that can distinguish between being stationary, and travelling at speed but you can tell the difference between constant speed and changing speed.
The same applies for your planets, although the forces produced will be tiny - they are still (theoretically) measurable.
You'd also be able to tell you're in orbit because it's the only way two gravitationally attracted bodies could be arranged such that the could appear not be approaching one another.