# Messages at near-light speed

I’ve been reading up a bit on time dilation and near-light-speed travel for a personal project, and I’m having trouble wrapping my head around some of the numbers involved. Any help would be appreciated!

Alice and Bob are located on interstellar objects exactly one light-year apart. Alice is going to visit Bob, and right before she leaves, she sends a message to Bob that she’s on her way. As soon as Bob receives the message, he sends one back.

With her spaceship, Alice travels at 0.98c. The messages are sent at 0.9999c.
a) If Alice leaves home on January 1st, 3019, when does Bob receive her message?
b) From Alice’s point of view, when does she receive Bob’s return message? How long does she have from when the message arrives until she lands at Bob’s place, in her subjective time?

For the first one, my understanding is that Alice’s message would arrive shortly after January 1st 3020, and she herself would land about a week later, around the 8th. After that, however, the variables start getting a bit jumbled in my head, so I figured I’d ask here. Thanks in advance!