If the Earth orbited the Sun at twice its current distance, what impact would this have on the accuracy of our ground-based astrometry?
If the Earth was at double the distance from the Sun we would be able to determine the distances of stars double the maximum we can measure in our current orbit.
An accurate way of measuring the distance of nearby stars is using parallax. This works by measuring the position of a star and then measuring it again 6 months later when the Earth is at the opposite side of its orbit.
The parallax angle is the angle between the star and the Earth and the star and the Sun. This is half the angular difference measured at opposite sides of the earth's orbit. The distance in parsecs (3.26 light years) is the inverse of the parallax angle measured in arc seconds.
The distance is given by:
Ground based telescopes can measure parallax to about 0.01". Which means that distances can be measured for stars up to 100 parsecs (326 light years) away.
If the Earth's orbit was 2AU. We would be able to measure the positions of stars up to 200 parsecs using parallax.