- #1

- 182

- 2

- B
- Thread starter Einstein's Cat
- Start date

- #1

- 182

- 2

- #2

Simon Bridge

Science Advisor

Homework Helper

- 17,857

- 1,655

- #3

Chronos

Science Advisor

Gold Member

- 11,408

- 742

- #4

- 182

- 2

How does proper distance change with time? Is there an equation to describe that? I looked on Wikipedia and found no such thing

- #5

Chronos

Science Advisor

Gold Member

- 11,408

- 742

- #6

- 182

- 2

I see, so proper distance changes with the expansion of the universe and thus with time because theoretical observers along it would appear to have relative velocity to a relative stationary observers? Therefore, meaning that the relatively moving observers would have a different interpretations of cosmological time and thus the proper distance would appear to be longer? Is this correct please?

Last edited by a moderator:

- #7

George Jones

Staff Emeritus

Science Advisor

Gold Member

- 7,414

- 1,054

If ##D## is the (now) proper distance between us and a distant galaxy, thenHow does proper distance change with time?

$$D \left( t \right) = R \left( t \right) \chi,$$

where ##R \left( t \right)## is the scale factor for the universe (a solution to Friedmann's equation), ##\chi## is the constant comoving coordinate difference between us and the galaxy, and ##t## is cosmological time.

Einstein's Cat, are you familiar with calculus? Assuming you are, the rate of change of proper distance is given by

$$\frac{dD}{dt} = \frac{dR}{dt} \chi.$$

If the scale factor is known, then so is its rate of change ##dR/dt## , thus giving the rate change of proper distance, ##dD/dt##.

Multiplying the left side of the above equation by one in the form ##1=R/R##, and using ##D = R \chi## gives the Hubble relation

$$\frac{dD}{dt} = \frac{dR}{dt} \frac{R}{R} \chi = H D,$$

where the Hubble parameter (a function of time) is give by

$$H = R \frac{dR}{dt}. $$

- Last Post

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 897

- Last Post

- Replies
- 38

- Views
- 11K

- Last Post

- Replies
- 2

- Views
- 3K

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 595

- Replies
- 14

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 2K

- Last Post

- Replies
- 13

- Views
- 2K

- Replies
- 1

- Views
- 2K