How long do you have to wait outside of the orbit of the Earth for desired location to be right below? My father had a (very theoretical) idea of a transportation system, where shuttle would be shot directly up from the Earth, it would stay still in the space for so long that the destination would be below, and then it would land directly down.
My brother is sure that the transportation time would be exactly the same as the timezones on earth, for example if going from UK to Finland, the time would be somewhat two hours.
I am not so sure about it, since I don't know enough about physics. What I mean is that, yes, it sounds logical and obvious, but I am hesitant to make conclusion without knowing the factors.
So, if this kind of system would be possible, how long would be the transportation times compared to time on earth and what factors should be taken in account?
 A: The idea about time zones is correct except that you must also add the time going up and the time going down.  
However there are a few things which need to be considered.  
When you are on the Earth you are rotating along with the Earth.
If you wish to hover above the place that you left you must use your engines to counter the rotation.
Then there is the problem that to hover you must use your engines to prevent you from falling back into the Earth.
I have also ignored the complication of the Earth's atmosphere trying to drag the transporting pod around with the Earth.
Going from the UK to Finland using your mode of transportation will take about 22 hours because after taking off from the UK you would have to wait that amount of time for Finland to appear underneath you.
Perhaps it is not such a good idea?
A: Consider Concorde.  If they'd re-instate that beautiful aircraft it would comfortably do the 2000km odd from the UK to Finland in about two hours.  That's a relatively inefficient air transport, but very much more efficient than anything we could now build that would enter space.  We might build a better SST now if we tried ( but probably not as beautiful to look at ).
A ballistic missile would "comfortably" do the trip in minutes, although I would suggest passenger comfort would be minimal.  The big issue is making sure you land in the same shape you took off in. :-)
Also think about the Space Shuttle.  It had a very, very long glide path.  To get down from orbit you have to don't wait until the target is underneath, you're moving down a long time before that.  It took about an hour from re-entry start ( de-orbit burn ) to actual landing.  It traveled about 5000 miles in that time.  So that's overkill for going 2000 km.  Clearly going to orbit is wasted effort for a trip an SST ( like Concorde ) could do in two hours.
