If the Earth orbited the Sun at twice its current distance, what impact would this have on the accuracy of our ground-based astrometry?

Question

Nolan Aldridge · Accepted Answer

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.

Using parallax, which measures a star's position once and then again six months later when the Earth is at the other side of its orbit, one can accurately determine how far away stars are from us. The distance in parsecs (3.26 light years) is the inverse of the parallax angle measured in arc seconds. The parallax angle is the angle between the star and the Earth and the star and the Sun. It is half the angular difference measured at opposite sides of the earth's orbit. The following provides the distance: #d=r/theta#. Where #r=1# is the mean distance from the Earth to the Sun in Astronomical Units(AU). And #theta# is the parallax angle in arc seconds. Parallax can be measured with ground-based telescopes to within approximately 0.01", meaning that stars up to 100 parsecs (326 light years) away can have their distances measured. By using parallax, we could determine the positions of stars up to 200 parsecs if the Earth's orbit was 2 astronomical units.

Joseph Allen · Answer

undefined The accuracy of ground-based astrometry would probably decline if Earth orbited the Sun twice as far as it does now. This is because a farther orbit would produce a smaller parallax angle, which would make it more difficult to measure the positions of celestial objects precisely against the background stars.