The Hipparcos satellite was able to measure parallax for stars out to about 150 pc. This distance includes roughly 2.5 million stars. The new Gaia satellite should be able to measure the parallax of roughly a billion stars. Assuming the density of stars is approximately constant, what distance would this correspond to? (Hint: The volume of a sphere is proportional to the cube of the radius.)
A) 35 pc
B) 167 pc
C) 350 pc
D) 20 kpc

Question

Quizplus · Accepted Answer

Given that the volume of a sphere (and thus the space in which stars are measured) is proportional to the cube of the radius (distance), we can set up a proportion based on the increase in the number of stars observed. If 2.5 million stars are within 150 pc, and Gaia observes roughly a billion (400 times more stars), the distance to which Gaia can measure would be the cube root of 400 times 150 pc, which is 7.937 times 150 pc, approximately equal to 350 pc.

The Hipparcos Satellite Was Able to Measure Parallax for Stars