Yes, this is a good way to view this.
I am not sure how to explain the elliptical orbit condition other than to say the orbit is just how two object's gravity wells interact depending on their position, speed and direction with respect to each other.
Alexander has given us some formulas to think about. That may prove useful to you.
Hmmm, here is a thought. Have you ever been to the mall and seen one of those coin vortex things? They take coins usually for some charity. Anyway, this thing is shaped much like the gravity well of a black hole with a 2 inch or so hole in the center and a funnel shape extending up and out till it hits the edge. The transistion from the "black hole" to the edge goes smoothly from a vertical two inch diameter pipe to a 36 inch or so wide mouth.
You feed this thing a coin in a special aiming device along the edge which launches the coin in a long lasting spiral round and round. You would think this would just spiral smoothly in ever shrinking circles as the coin looses energy to friction, but imperfections in the surface tend to mess with the coins momentum. This results in the coin suddenly falling faster towards the hole, but it gains lots of speed and zooms back out; This is where it approaches an elliptical orbit with the "black hole" being one focii and some other point being the other focii.
If you want to get your coin going in a non circular orbit, try launching it by hand so it starts out with a really screwed up direction. Bring lots of coins.
I know folks, this representation does not really explain all that much, but with other's inputs, it may help.