Age of the Universe: Solve for t_0

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Homework Help Overview

The problem involves demonstrating a relationship for the age of a flat universe, specifically showing that \( t_{0} = \frac{2}{3} (H_{0})^{-1} \). The context is rooted in cosmology and the application of Hubble's law.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the implications of a flat universe and the constancy of the Hubble constant. There are attempts to relate the problem to time intervals and kinematic equations, with some questioning the relevance of these equations to the cosmological context.

Discussion Status

The discussion is ongoing, with participants seeking guidance on how to approach the problem. Some have offered insights regarding the relationship between the Hubble constant and time, while others are exploring different equations and their applicability.

Contextual Notes

There appears to be some confusion regarding the definitions and implications of a flat universe, as well as the appropriate equations to use in this context. Participants are also expressing uncertainty about how to proceed with their attempts.

NeedPhysHelp8
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Hi all,
Hoping you can help with this problem!

Homework Statement


For a flat universe, show that [tex]t_{0}=2/3 (H_{0})^{-1}[/tex] ? Seems like a simple problem I just don't really know where to start.

Homework Equations


Hubble's law [tex]v= H_{0}r[/tex]
and then [tex]t= 1/H_{0}[/tex]

The Attempt at a Solution


I just need guidance where to start. Flat universe means that expansion is constant in any direction right? What do I do?
 
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flat universe means the Hubble constant is constant.

Then 1/hubble constant has units time.
Think of the equations for something that doubles/halves with a constant time interval
 
How about the kinematic equation: x(t)= vt + 1/2at^2
Not sure if this is right and what to do with it? maybe take a derivatives of both sides?
 
I still can't figure out the answer, can someone give me a hint please
 

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