Question

GAIA is a mission by ESA that is measuring the positions of one billion stars. The precision in the parallax measurements is as small as 24 micro-arcsec (24×10^?6 arcsec).

1.What is the greatest distance that GAIA will be able to measure?

2.The Hipparcos satellite measured parallaxes as small as 10^?3  arcsec. Compared to Hipparcos, by what factor will the volume of space over which we can measure parallax improve with the new GAIA space mission?

Answer 1

1. The maximum distance that can be measured is given by reciprocal of the precision by the measurement so,

Max distance= 1/(24 micro-arcsecs)=4.166*10^4 parsec

2. Max distance by Hipparcos satellite = 1/(10^(-3)arcsec)=10^3 parsec.

Volume of space over which parallax can be measured = volume of the cone formed= (1/3)*(pi*radius of earth's orbit)*(max distance)

this means Volume is proportional to the maximum distance calculated above.

So ratio is 41.66, that means GAIA improves the volume of space by a factor of 41.66 over which parallax is measurable.