# Relativistic Velocity Problem

• Woolyabyss
Thank you for clarifying.In summary, the astronomer sees two objects moving away from each other with velocities of 2.5×108 m/s and 1.8×108 m/s respectively. The question asks for the relative speed of the objects as observed by the astronomer, not the speed of one object with respect to the other. This can be determined using the Lorentz transformation equations.

## Homework Statement

An astronomer sees two objects moving along the same line of sight away from each other. The first object moves away from the Earth with a velocity of 2.5×108 m/s, and the second object moves towards the Earth with a velocity of 1.8×108 m/s.
According to this astronomer how fast are the two objects moving away from each other?

## Homework Equations

Lorentz transformation
V'x = (Vx - u)/(1-(u*Vx/c^2))
Vx = (V'x + u)/(1+ (u*V'x/c^2))

## The Attempt at a Solution

I'm not sure how to apply the transformations here.
Should I take the the reference frames used in the equations to be on the objects and attempt to find u?
Normally In a problem like this I would take the Earth to be the first frame of reference

Hint: The question is how fast the astronomer finds that the objects are moving away from each other, not how fast the objects find that they are moving away from each other.

Woolyabyss
Orodruin said:
Hint: The question is how fast the astronomer finds that the objects are moving away from each other, not how fast the objects find that they are moving away from each other.
I don't read it that way.

I think it means that knowing special relativity, what does the astronomer conclude is the relative speed of one of the objects with respect to the other.

Also, Woolyabyss needs to fix his powers of ten notation.

SammyS said:
I don't read it that way.
Woolyabyss said:
According to this astronomer how fast are the two objects moving away from each other?
I don't see how this can be read in any other way. If the relative speed was intended, this would have been the statement:
SammyS said:
what does the astronomer conclude is the relative speed of one of the objects with respect to the other.
not "according to the astronomer". This is a typical question to raise awareness over the difference between separation speed and relative speed.

Orodruin said:
I don't see how this can be read in any other way. If the relative speed was intended, this would have been the statement:

not "according to the astronomer". This is a typical question to raise awareness over the difference between separation speed and relative speed.
Yes, you have convinced me.