Calculate Redshift & Luminosity Distance for Hubble's Law

[helpcometk]

Homework Statement

Hubble's law may be written as
H0dL = z +(1/2)(1 - q₀)z²
Working to O(z) only, what is the redshift of a galaxy at a luminosity distance of 100 Mpc
from Earth?
What is the role of the constant q0? Given that observations show that q0 = -0.77,
calculate the luminosity distance (in Mpc) of a high redshift supernova with z = 0.5.

Homework Equations

the first question is what O(z) might mean and second if i make the substitution ,q0 which is given later i get a quadratic equation with imaginary solutions.The second part is just a metter of calculations i suppose ,but it seems that for the first question I am missing something.

The Attempt at a Solution

 

[George Jones]

the first question is what O(z) might mean

O(z) means leave out any powers of z that are higher than z, i.e., omit z^2, z^3, ...

O(z)^2 means leave out any powers of z that are higher than z^2, i.e., omit z^3, z^4, ...