The semimajor axis of Pluto's orbit is almost 40 au. From its orbit around Earth, the Hipparcos satellite measured stellar parallaxes to an accuracy of about 0.01 arcsecond. Suppose astronomers use this technique to measure parallax from Pluto's orbit (over the course of half a Pluto "year"). What is the maximum distance they could measure?
A) 4 pc
B) 100 pc
C) 4000 pc
D) 8000 pc

Question

Quizplus · Accepted Answer

The maximum distance that can be measured using parallax from Pluto's orbit, given its semimajor axis of almost 40 au and an accuracy of about 0.01 arcsecond, can be calculated using the parallax formula. The parallax angle in arcseconds is inversely proportional to the distance in parsecs. Given that 1 parsec (pc) corresponds to a parallax of 1 arcsecond, and the accuracy is 0.01 arcsecond, the maximum distance measurable is 1/0.01 = 100 parsecs for an Earth-based orbit. However, since Pluto's orbit is about 40 times larger than Earth's, this increases the baseline and thus the distance that can be measured by the same factor, leading to 100 * 40 = 4000 parsecs.

The Semimajor Axis of Pluto's Orbit Is Almost 40 Au