# How the Earth observer would see (time-ticks wise) a traveller rushing away or towards Earth at near-light speed?

There is an observer on the Earth.

1) There is a traveller moving away from the Earth at a speed approaching the speed of light.

2) There is a traveller moving towards the Earth at a speed approaching the speed of light.

In both cases there would be (exactly same) time difference of clocks - one tick of the traveller's clock would be very-very many ticks of the observer clock on earth.

I don't understand the following: what would the observer from earth see? Just that the traveller is moving away or towards at a great speed?

In case a traveller approaches a blackhole it is said that the earth observer would never see the traveller disappear behind the horizon (because one tick of travellers clock would be infinite time of observer's clock). Is this right?

But we have the same time dilution (caused by difference in relative speed, not gravity) in our first example, so it seems that the traveller shall "freeze" and seem not to move for the earth observer in both cases (1) and (2), even when the traveller is rushing towards Earth with tremendous speed!

I cannot find error in my reasoning.

So what the Earth observer (and the traveller) would see and why? I mean time difference (how many ticks of traveller per one tick of observer), not physical seeing (so that not to complicate things with doppler effect).