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2.8: S08. The Distance-Redshift Relation - SOLUTIONS

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Exercise 8.1.1

Answer

c1aedaa2H=d0dr=d

H=˙aa and ˙a= constant, so we have H=H0a. Now,

d=cH01aedaa=cH0[ln(1)ln(ae)]

Exercise 8.2.1

Answer

cH0[ln(ae)]=dd=cH0ln(1ae)d=cH0ln(1+z)dcH0z

Now multiply both sides by (1+z),

d×(1+z)=cH0z(1+z)dlum=cH0z(1+z)

Since z<<1 we can simplify our result to cz=H0dlum.


This page titled 2.8: S08. The Distance-Redshift Relation - SOLUTIONS is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Lloyd Knox.

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