Two stars have proper motions of one arcsecond per year. Star A is 20 light-years from Earth, and Star B is 10 light-years away from Earth. Which one has the faster velocity in space?

Star A

Explanation:

μ = proper motion = 1 arcsecond per year

r = 20 light-years = Distance

Transverse velocity

V = 1.45 * μ * r

⇒ V = 1.45 * 1 * 20

⇒ V = 29 km/sec

When r = 10 light-years

V = 1.45 * 1 * 10

⇒ V = 14.5 km/sec

∴ Star A which is 20 light-years from Earth is moving faster compared to Star B which is 10 light-years from Earth.