# Red-shift question from another thread.

• Jufro
In summary, the conversation is about a question regarding the acceleration of a source based on its redshift. The individual is working through the equation and taking the derivative, but has encountered an issue with the sign of the result. They are asking for clarification and guidance on how to proceed.

## Homework Statement

This is not a HW questions but from another thread.

The statement I made was that if z increases for a source, then it is accelerating away. Or, it could that if z is constant then the sources moves with constant velocity away from an observer.

I just need to know where my logic is breaking down and what direction I can try to find the right answer.

## Homework Equations

I took the equation:
1+z = $\sqrt{\frac{1+v/c}{1-v/c}}$

## The Attempt at a Solution

So taking d/dt on both sides I end up with:

dz/dt = 1/2 $\frac{1+v/c}{1-v/c}-1/2$*$\frac{(1/c dv/dt)*(1-v/c)-(1/c dv/dt)*(1+v/c)}{(1-v/c)2}$

Re-writting this:

dz/dt= $\frac{-v* dv/dt}{c2*(z+1)*(1-v/c)2}$

Since the first term is negative (from the minus sign) and v is positive, then a positive dz/dt would require that dv/dt is negative or that the sources acceleration is radially inward when I had suspected outward.

This may be a result of me using the flat-spacetime (Minkowski metric) but I am not sure. Can anyone point me in the right direction.

Please and thank you.

Jufro said:

## Homework Statement

This is not a HW questions but from another thread.

The statement I made was that if z increases for a source, then it is accelerating away. Or, it could that if z is constant then the sources moves with constant velocity away from an observer.

I just need to know where my logic is breaking down and what direction I can try to find the right answer.

## Homework Equations

I took the equation:
$$1+z = \sqrt{\frac{1+v/c}{1-v/c}}$$

## The Attempt at a Solution

So taking d/dt on both sides I end up with:
$$\frac{dz}{dt} = \frac{1}{2} \left(\frac{1+v/c}{1-v/c}\right)^{-1/2} \frac{(1/c\ dv/dt)(1-v/c)-(1/c\ dv/dt)(1+v/c)}{(1-v/c)^2}.$$ Re-writing this:
$$\frac{dz}{dt}= \frac{-v\ dv/dt}{c^2(z+1)(1-v/c)^2}.$$ Since the first term is negative (from the minus sign) and v is positive, then a positive dz/dt would require that dv/dt is negative or that the sources acceleration is radially inward when I had suspected outward.

This may be a result of me using the flat-spacetime (Minkowski metric) but I am not sure. Can anyone point me in the right direction.

Please and thank you.
You dropped a sign when you applied the quotient rule. The numerator should end up as a sum, not a difference.

Ah, I used the wrong derivative in the second half of my quotient rule. Thanks for that.

## What causes red-shift?

Red-shift is caused by the Doppler effect, which is the perceived change in frequency of a wave due to the relative motion between the source of the wave and the observer. In the case of red-shift, the source of the wave (usually a galaxy) is moving away from the observer, causing the wavelength of the light to stretch and appear more red.

## How is red-shift measured?

Red-shift is measured using spectroscopy, which involves splitting the light from an object into its component wavelengths. By analyzing the wavelengths of light emitted by a galaxy, scientists can determine how much the light has been stretched due to red-shift and calculate the object's velocity and distance from Earth.

## What is the significance of red-shift in astronomy?

Red-shift is a fundamental concept in astronomy and is used to measure the distance and speed of objects in the universe. It also provides evidence for the expansion of the universe and the Big Bang theory.

## Can red-shift be used to determine the age of the universe?

Yes, red-shift can be used to estimate the age of the universe. By measuring the red-shift of objects at different distances, scientists can calculate the rate at which the universe is expanding and estimate the age of the universe to be around 13.8 billion years.

## Are there different types of red-shift?

Yes, there are two types of red-shift: cosmological red-shift and gravitational red-shift. Cosmological red-shift is caused by the expansion of the universe, while gravitational red-shift is caused by the gravitational pull of massive objects, such as black holes.