Let's say you built a huge, straight rigid beam out in space, far from the sun (outside the orbit of Pluto). It is very long, say 200,000 miles long, but can be very narrow.
Then you move it to the Earth's orbit, and align it such that it's center point is on the orbit of the earth, and the beam is along the tangent line of the orbit at this point.
At this position, is the beam curved? Does the curved-space that guides the Earth orbit actually curve this beam, such that it would NOT be a tangent, but an arc of the orbit?
Could this curvature be observed if one way far away, say above the plane of the orbit and looking down on it?