The Earth and the Planet of the Apes are in a reference frame where they are stationary relative to one another, and are measured to be 2 light years apart. The observers on Earth send a TV signal to the Planet of the Apes with a picture of a banana. 0.6 years later, the observers on Earth receive a TV signal from the Planet of the Apes saying "Give us the banana!".
Question 1: What is the minimum speed that the TV signals must travel to fulfill the above conditions? (This was not the original wording but feel free to ignore this question, I don't quite remember it anyway)
Question 2: What is the spacetime interval between the two events, as measured by an observer on Earth?
Question 3: What is the spacetime interval between the two events as measured by an observer on a rocket traveling from Earth to PoA who finds that the two events (Earth and PoA sending their respective TV signals) are simultaneous?
Question 4: According to the observer, what is the distance between the two planets?
Question 5: At what speed is the observer moving relative to Earth and the PoA?
The Attempt at a Solution
Event 1: Earth sends TV signal to PoA
Event 2: PoA sends TV signal to Earth
Most of the people in my class (including me) assumed that one event caused the other, but is that possible if an observer in a reference frame measures them to be simultaneous?
If I take Event 2 to happen at t = -1.4 years and Event 1 to happen at t = 0 years (for the signal from PoA to reach the Earth at t = 0.6 years), the spacetime interval turns out to be a negative number. Answer to Question 4 turns out to be 1.4 x 10^16 meters, and the answer to Question 5 turns out to be 0.63c
Was I on the right track?