The feasibility of a satellite orbiting at a fixed time I was speaking with some friends of mine, one of whom was an aerospace engineer. He posited the infeasibility of a hypothetical "Margaritaville Satellite" that orbited earth in such a way that wherever it was above, it was six-o'clock (the idea being, the Margaritaville Satellite is in Happy Hour 24/7), matching Earth's rotation exactly.
However, there was disagreement on whether or not the satellite could actually be put in such an orbit, as if it were rotating at the exact speed of earth, it would effectively just be "falling" straight towards Earth.
Is it possible to sync a satellite's orbiting with the time of day of the earth without some sort of propulsion to keep it aloft?
 A: There is definitely satellites that achieve this. The type of orbit is called "Sun synchronous". It's impossible to always be 6:00 PM, but it can always be either 6:00 PM or 6:00 AM. The trick is that it's a slight retrograde polar orbit, that allows for this feat to be achieved. 
It's very common for earth observing (And for that matter, Mars, Moon, Venus, and Mercury observing) satellites to follow this type of orbit, due to the illumination remaining consistent for all photos.
A: Agreed with Ted Bunn's answer, that it is possible to keep a satellite over a fixed time point on earth by using the Lagrange points.  One of those L-points is on the opposite side of the sun, which doesn't help much.  There are two problems with the other four.  One is that there are exactly four solutions, corresponding to exactly 4 local times on Earth: high noon; midnight; ROUGHLY 7am; and ROUGHLY 5pm.  The other problem is that all such L-points are far, FAR outside of LEO or geosynchronous orbit.
Another possibility, which would take very little station-keeping fuel, would be to send the satellite into exactly the same orbit around the Sun as Earth.  Thus, it would appear to an Earth-bound observer as if the satellite was always above the dividing point of day and night (6:00am or 6:00pm, depending on whether the satellite was leading or lagging earth in the shared orbit around the Sun).  
The satellite would have to be  much, much farther away than geosynchronous orbit in order to be able to fight the constant pull of Earth.  It might be possible to place it far enough out, and close enough inside lunar orbit, to gain enough periodic lunar pull to aid in stationkeeping.
So, six solutions have surfaced, for stationkeeping over a fixed local Earth time with little or no stationkeeping fuel burn: ~7:00 am; 6:00 am; noon; ~5:00 pm; 6:00 pm; and midnight. Happily, one of those solutions coincides with "Margaritaville time."
A: There's another possibility, aside from the sun-synchronous orbit mentioned by @Pearsonartphoto. If you want your satellite to maintain a constant position relative to both Earth and Sun, you can put it at one of the Earth-Sun Lagrange points. It's always noon at L1 and always midnight at L2. L4 is always directly above a point on Earth corresponding to some time in the morning, and L5 is always directly above a point corresponding to some time in the afternoon, although in the latter cases the points are so far away that it's a bit funny to identify those terrestrial times of day with times on board the satellite.
