Question

How do I solve these? Please show the steps

Thank you

1)A certain star is moving towards the earth at a velocity of 262 km/s. What can we expect to measure for a spectral line, normally found at 815.1 nm?

2)Star B is 41 Mega light years away from us. How fast is Star B receding from Earth in km/s?

3)We measure the velocity of Star A to be 404.5 km/s. How far away is Star A in Mega parsecs?

Answer 1

given

a certian star

velocity towards earth, v = 262,000 m/s

a. lambdao = 815.1 nm

as the light source is moving towards the earth, it will appear to be blue shifted

hence

v/c = (lambdao - lambda)/lambdao = 1 - lambda/lambdao

262,000/3*10^8 = 1 - lambda/815.1

hence

observed lambda = 814.38814 nm

b. given d = 41*10^6 ly

form hubbles law

v = Hod

Ho = 71 km/s Mpc

d = 12.57 Mpc

hence

v = 892.47 km/s

c. Va = 404.5 km/s

distacne from earth = d

hence

v = Ho*d

d = v/Ho = 5.697183 parsecs