The closest exoplanet to earth that is thought to potentially be habitable is Gliese 667Cc, which is only 22 light-years away. This planet is at rest with respect to the Earth. Suppose we fly a spaceship toward Gliese 667Cc at constant speed 0.8c. In the Earth's reference frame the spaceship is launched at position x = 0 and time t = 0. The aliens on Gliese 667Cc are concerned that we may be a threat, so they send a diplomatic vessel to meet our ship before we make it to their planet. Their ship launches from Gliese 667Cc when our ship is 12 light-years away from them (in the rest frame of the planets). (a) If they fly their diplomatic vessel at a speed 0.4c, how fast do they see our ship moving? (b) The aliens forget to decelerate, so instead of docking with our ship when they reach us they continue to fly past at a constant speed. In the rest frame of the Earth, what are the spacetime coordinates (x, y, z, t) of spacetime event A: "our spaceship and the alier- ship pass each other"? =) The reference frame of our spaceship coincides with the rest frame of the earth at laun- (x' = x = 0 at t' = t = 0). What are the spacetime coordinates (x', y', z', t') of event. in the reference frame of our spaceship?

Gliese 667 Cc (also known as GJ 667Cc, HR 6426Cc, or HD 156384Cc)^[3] is an exoplanet orbiting within the habitable zone of the red dwarf star Gliese 667 Cc, which is a member of the Gliese 667 Cc triple star system.