Two Questions, related to Physics - sort of

[eX.A.K.R.]

OK, I have two questions, one of which has been burning in my mind for quite some time now, which I hope someone here will answer...

1. Suppose a very bright object (let's say it's a spaceship bright enough to be observed light years away with the naked eye) appears one light year from Earth. It then travels at the speed of light towards us, in a straight line.
A) When are we able to observe this spaceship from Earth?
B) How fast will it appear to be traveling from it's starting point to us?
C) What if the speed of the spaceship is reduced to half a light year?

2. Let's say there is an elevator that is so tall it will take several seconds to go from the top to the bottom (and vice versa), even at faster than free-fall speeds. Say some people get on it at the top. The elevator then speeds down to the bottom; at one point it reaches a speed that is faster than the speed of a person free-falling to Earth. Will the people in the elevator experience weightlessness at that point??

 

[Zhen Lin]

The first question is answered by the theory of special relativity. First things first though, nothing that has mass can travel at the speed of light. If, however, we assume we are talking about a particle of light, i.e. a photon, then we will be able to see it at the very moment it arrives on Earth, in other words, one year after it departs. If we instead assume that we are talking about a object with mass travelling at some appreciable fraction of the speed of light, it will be seen to us to be approaching at that speed (assuming we ourselves are not moving). Light from the object will travel to us, as expected, at the speed of light, and so the object will be visible to us no sooner than the light from it reaches us, i.e. one year. The thing is, travelling at high speeds towards the observers results in a phenomenon known as blueshifting, which is the light analogue of the Doppler effect. As the fast-moving object approaches the observer, the observer perceives the frequency of light being emitted by the object to be ever-increasing, i.e. becoming more and more blue.

The second question is not well-conceived. The concept in question is not speed but acceleration. If acceleration is equal to 9.81ms^-2 in the downwards direction, then yes, the occupants of the elevator will indeed experience free-fall.