Question

Pretend we are on a space mission to Jupiter. Our instruments detect an identical sister space station, Alpha Alberta, moving away from us at80% of the speed of light. Our instruments reveal that, compared to our station. A. clocks and events on Alpha Alberta are (slow) (fast) (the same) B. the length of AA in its direction of motion appears (shorter) (longer) (the same) C. the momentum of AA is (more) (less) (the same) occupants on AA are making measurements of us. They observe that, compared to their station, (SAME QUESTIONS AS ABOVE)

Answer 1

Hi! This is all conceptual, but I'll use an equation later for relativistic momentum.
\[\huge {\text{A. Time Dilation}} \]Look at the term, and we'll get something from it. At great relative speeds, we'll see that time dilates. Like a pupil dilating in bright light, we're talking expansion. What is quick to something at rest with the event... will seem time-consuming to someone at high speeds relative to the event.
\[\huge\text{B. Length Contraction}\]Look at the term, and we'll get something from it (deja vu). At great relative speeds, we'll see that length, in the direction of the relative velocity, will contract. The ends of the object will get closer to one another, like a contracting muscle. A better visualization, though, is resizing an image to SQUISH it.
\[\huge \text{C. The Relativistic Momentum}\]The equation is:\[p_{\text{relativistic}}=\gamma _u m_0u\\m_0\text{ is the rest mass,} \]what the mass of the object is when you are at rest with it.
As you can see, relativistic momentum increases with increasing relative velocity.

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html for relativistic momentum equation.

Answer 2

You can figure it all out from that. Now don't let the last A, B, and C fool you. AA people are nearly at rest with their clocks, events, length, and mass. You'll have to think about what that means!