# speed of light question

The starships Q-Bert and Pac-Man move away from Earth in opposite directions, on missions to save the world from snakes and ghosts. Their velocity relative to Earth is .7 lightspeed. What is their velocity relative to each other? I know according to relativity it must be less than 1, so how do they calculate this? If Q-Bert sent a message to Pac-Man on a laser, how would the message be affected? Would it get there? What would the constellations look like from a starship travelling close to lightspeed?

distance and time change at those speeds.
Basically lets say the good ship qbert is exactly 1 lightyear (distance) from the happy boat pacman. the message will take exactly 1 year for the message to be recieved. Light will always approach and leave you at the sOL

rather than atempt to explain all of general relativity, I’m just going to point you to

http://math.ucr.edu/home/baez/physics/relativity.html

which has a copy of the Usenet Relativity FAQ. It’s what I used to make sure I was remembering the equations right (and it took me 3 seconds to find with google.

[sup][sub][subliminal]This is a hint.[/subliminal][/sub][/sup]

Anyhow, the point is that simply adding velocities together doesn’t work with speeds near c. Instead, you must sum the velocities (call them u and v) as follows to determine their total velocity w with regard to a point directly between them:

``````
u + v
w = ---------
uv
1 + ---
c^2

``````

which, in this specific case gves a total velocity of approximately 0.94 times c.

I’ve got a couple of problems with what you said. The ships are moving. If you say the distance is one light-year, you must say as measured by what frame of reference. If I one light year away from a stationary source and going away from it, by the time the light reaches me, the distance travelled by the light will be greater than a light year, so the time will be longer than one year.

As to how a message would be affected, it would be red-shifted, but the speed of a light-signal would be SoL.