Calculate Redshift & Luminosity Distance for Hubble's Law

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SUMMARY

The discussion focuses on calculating the redshift and luminosity distance in the context of Hubble's Law, specifically using the equation H0dL = z + (1/2)(1 - q0)z². The constant q0 is defined as -0.77, which is crucial for determining the luminosity distance of a high redshift supernova with z = 0.5. The participants clarify that O(z) refers to the omission of higher powers of z, simplifying calculations to linear terms only. The discussion highlights the importance of understanding these concepts for accurate astrophysical calculations.

PREREQUISITES
  • Understanding of Hubble's Law and its mathematical formulation
  • Familiarity with redshift and luminosity distance concepts
  • Basic knowledge of quadratic equations and their solutions
  • Comprehension of Taylor series expansion and the notation O(z)
NEXT STEPS
  • Study the implications of the Hubble constant (H0) in cosmology
  • Learn about the significance of the deceleration parameter (q0) in cosmic expansion
  • Explore the calculation of luminosity distance for various redshift values
  • Investigate the relationship between redshift, distance, and the expansion of the universe
USEFUL FOR

Astronomy students, astrophysicists, and researchers involved in cosmological studies will benefit from this discussion, particularly those focusing on the calculations related to Hubble's Law and cosmic distances.

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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

 
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helpcometk said:
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, ...
 

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