# Relativistic Velocity Problem

## 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

Orodruin
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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
SammyS
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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.

Orodruin
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I don't read it that way.
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:
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.

SammyS
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