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

The number of stars that the Gaia satellite can measure parallax for is roughly 400 times greater than the Hipparcos satellite. Assuming a constant stellar density, this means that Gaia will be able to measure parallax for stars that are 4 times further away than Hipparcos. The volume of space that contains stars at a distance of 150 pc is proportional to (150 pc)^3, which is approximately 3.4 x 10^6 pc^3. Therefore, the volume of space that Gaia will be able to probe is approximately 4 x 3.4 x 10^6 pc^3, which is 13.6 x 10^6 pc^3. Solving for the radius of the spherical volume, we get (4/3)πr^3 = 13.6 x 10^6 pc^3, which gives r ≈ 350 pc. Therefore, the best choice is C) 350 pc.

The Hipparcos Satellite Was Able to Measure Parallax for Stars