Plot the space-time diagram of a photon and a spaceship

[pepediaz]

Homework Statement

An inertial observer O ' in a spacecraft, moving with four-speed U = 2 (c, u) seen by a
Earth observer O, passes by Earth and synchronizes his clock with O's clock. This
observer turns to Titan, a moon of Saturn that is (at that time) at a distance
Δx = 1.2 billion km from Earth. The ship throws a pulse of light towards the Earth, with four-moment p' = (E'/c)(1,-1,0,0)

Relevant Equations

I think we don't need any.

Be the red point this spacecraft , the purple line the world line with slope = 2 and the green point a photon thrown towards the Earth from the spacecraft , would this spacetime diagram ok? (distance would be 1.2 billion km, and the time, 1000 times of shown, but scale is badly displayed, even the red point wouldn't be at that position, but I did it like this just for showing it).

 

[mfb]

What is event A?

The photon travels through spacetime, it should be a line not a dot.

The natural zero for this diagram would be the meeting of spacecraft and Earth. That's where the clocks are synchronized.

 

[pepediaz]

event A is the photon, because it has the light cone as world lines because of its speed v=c.
It is plotted as the green point, though it should be a line. That's what I don't grasp, because if photon arrives at the Earth in a certain moment, it should be a point. Nevertheless, I don't know the distance it travels.

 

[mfb]

The photon is not an event. The emission and arrival at Earth are events. They are points that should appear as separate points in the diagram, connected by a line.

Nevertheless, I don't know the distance it travels.

The problem statement tells you, assuming the photon is emitted when the spacecraft reaches Titan (otherwise: why would they tell us about Titan).