Zip and Zap go to Zarkon. A question of relativity.?

They are both correct. The ship must be aimed at the location Zarkon will be in 60,000 years (as measured in the frame of the Earth), which is exactly the same location it will be in after 6 years (in the frame of the spacecraft).

Everyone remembers time dilation and length contraction, but no one ever remembers poor old Relativity of Simultaneity. Different observers disagree on which events are simultaneous.

Before they leave, they observe Zarkon to be in a particular position "now," in other words, its position at a time simultaneous with their looking through the telescope. Call this position "A."

Now consider the moment when they start their journey. They are still on Earth, but in a reference frame going towards Zarkon at nearly c. They immediately notice that position A is not Zarkon's current position (even accounting for effects of length contraction): it was Zarkon's position 59,994 years ago! This is because observers in different reference frames do not agree on which events are simultaneous. Zarkon-at-A is simultaneous with Earth-here-and-now in the frame of reference of the Earth, but Zarkon-at-A is 59,994 years in the past in the reference frame of the moving spaceship being launched at Earth.

Similarly, when Zip and Zap measure the current location of Zarkon (in their frame), the astronomer back on Earth disagrees; according to him, Zip and Zap have chosen the location in which Zarkon will be located 59,994 years from now.

Six years later, everyone agrees that they made it to Zarkon and the year is 60,000, as measured both at Earth and Zarkon.

Some side points: Einstein did NOT, repeat: NOT consider mass to be another direction similar to time and space. He did, initially, interpret the equations to mean that mass increases as the speed of light is attained, but we no longer interpret them that way. It is merely a redefinition of momentum to be (gamma)*mv rather than mv, with m ALWAYS representing the rest mass. "Mass" in physics ALWAYS refers to rest mass, and the concept of relativistic mass is no longer used, and for good reason (i.e. it is wrong).

I think Pf. ZZ has made the issue too complicated.

The nice thing about relativity is that, if you know what you are doing, you can do the calculation in the frame in which it is simplest. In this case, it is the frame of the center of the galaxy: In this frame, the stars are circling around, and the Studmuffin is racing.

This is the frame that Zap is using to calculate a 60,000-year journey, and therefore steering a 60,000-year course. And he is absolutely right. He is also absolutely right in understanding that his & Zip's experience of this will only be 6 years (actually, I get 6.572671 years - better pack a little more beer).

Zip is wrong, because, although he is ALLOWED to do the calculation in his frame, he then has to remember to describe the motion of the stars in his own frame - and it's a mess. They will NOT be undergoing uniform circular motion but instead their orbit about the hub will be squashed flat and they will be doing some weird squashed ellipse. It will be ugly ugly ugly. If he finally succeeds in disentangling the trajectories and the shapes of the orbits, he will get exactly the same answers as Zap does.

The lesson of relativity is: Do the calculation in the easiest frame you can, and then translate the result. This is what Zap has done. He's RIGHT.

The doctor is correct when he points out that Zarkon is actually in a position 60,000 years future to its appearant position from earth before Zip and Zap start. But, reading jerrywickey's account, I am going to assume Zip and Zap are smart enough to figure out where Zarkon is simultaneous to Earth.

And therefore jerrywickey is more correct. Zip and Zap still have a problem. Before they start their trip, as they are deciding which way to go they share the Earth's reference at relative rest. Lets say they choose to point the ship at the position Zarkon will be in 60,000 years.

Once they begin their journey, only six years will pass for them. But they observe Zarkon approaching them. This distance between them is shrunk by 10,000 to 1 but Zarkon is not traveling around the galaxy in that direction.

It is traveling in a direction at right angles to that. And since from the Studmuffin's frame of reference, Zarkon is traveling at them at nearly the speed of light covering the 6 light years distance between them, the rate at which it passes through time will slow by 10,000 times. That means that Zarkon will not travel the distance it would have in 60,000 years. It will only cover 6 years worth of distance.

For Zarkon to travel the 60,000 years worth of distance, motion must not be relative. All motion must be absolute. But this can't be. If motion is truly relative then Zarkon must be moving slower for Zip and Zap than it is for observers at rest on earth.

This isn't an answer. I know. But I don't think the doctor answered it either.