How is Hubble's equations H(t) = 2/3 t^-1 derived?

  • Thread starter damasgate
  • Start date
In summary, Hubble's equations, specifically the Hubble constant (H), are used to calculate the expansion rate of the universe. They are derived from the theory of general relativity and observations made by astronomer Edwin Hubble in the 1920s. The value of the Hubble constant is still debated, but current estimates range from 67 to 73 km/s per megaparsec. Hubble's equations are crucial to the Big Bang theory, as they help determine the age and expansion of the universe since its initial moment. They can also be used to make predictions about the future of the universe, such as whether it will continue to expand or eventually collapse.
  • #1
damasgate
10
0
I know that H(t) = 1/a(t) x da/dt

I know that a(t) is proportional to t^2/3

and da/dt is proportional to a^-1/2

now H(t) should equal H(t) = a(t)^-1 x a(t)^-1/2
= a(t)^-3/2
= (t^2/3)^-3/2
= t^-1

However where is the constant 2/3 coming from? I can't find it anywhere in my calculations!
 
Space news on Phys.org
  • #2
When you differentiate t2/3, you'll get 2/3 t-1/3, but you dropped the "2/3" when you said "da/dt is proportional to a^-1/2". I think that's what you're asking.
BTW at present, a is more like t1.
 

FAQ: How is Hubble's equations H(t) = 2/3 t^-1 derived?

1. What is the significance of Hubble's equations?

Hubble's equations, specifically the Hubble constant (H), are used to calculate the expansion rate of the universe. This helps scientists understand the age, size, and evolution of the universe.

2. How is Hubble's equations derived?

Hubble's equations are derived from the theory of general relativity and the observations of the expansion of the universe made by astronomer Edwin Hubble in the 1920s. It is a mathematical expression that relates the distance and relative velocity of objects in the universe to the expansion of space.

3. What is the value of the Hubble constant?

The value of the Hubble constant is still a topic of debate among scientists, with current estimates ranging from 67 to 73 km/s per megaparsec. This means that for every megaparsec (3.26 million light years) of distance, the universe is expanding by 67 to 73 kilometers per second.

4. How does Hubble's equations relate to the Big Bang theory?

Hubble's equations are a key component of the Big Bang theory. By using these equations, scientists are able to determine the age of the universe and how it has been expanding since the initial moment of the Big Bang.

5. Can Hubble's equations be used to make predictions about the future of the universe?

Yes, Hubble's equations can be used to make predictions about the future of the universe. By studying the expansion rate of the universe, scientists can determine if the universe will continue to expand forever or if it will eventually collapse in a "Big Crunch" scenario.

Similar threads

Replies
3
Views
1K
Replies
3
Views
2K
Replies
18
Views
2K
Replies
11
Views
1K
Replies
27
Views
4K
Replies
12
Views
2K
Back
Top